tag:blogger.com,1999:blog-7342829067258066692018-11-15T04:34:07.382-05:00Teaching TidbitsMathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.comBlogger34125tag:blogger.com,1999:blog-734282906725806669.post-91190401707969612582018-05-15T16:03:00.000-04:002018-05-15T16:03:30.286-04:00Farewell from the Teaching Tidbits Blog<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-BK3BW5g1TVU/Wvsg2qgFLII/AAAAAAAALJI/gK3N2nlxEncoge3-0SJup_iuQt2IEkooQCLcBGAs/s1600/GettyImages-879741666.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1068" data-original-width="1600" height="266" src="https://1.bp.blogspot.com/-BK3BW5g1TVU/Wvsg2qgFLII/AAAAAAAALJI/gK3N2nlxEncoge3-0SJup_iuQt2IEkooQCLcBGAs/s400/GettyImages-879741666.jpg" width="400" /></a></div><br /><br />Thank you for visiting the Teaching Tidbits blog, hosted by the <a href="http://www.maa.org/" target="_blank">Mathematical Association of America</a>, written for mathematics instructors by mathematics instructors. Since 2016, we have been posting regularly during the academic year to help you keep up with the latest educational research and pedagogical practices as the <a href="https://www.maa.org/programs-and-communities/curriculum%20resources/instructional-practices-guide" target="_blank">MAA IP Guide</a> was being developed. <br /><br />With 121,470 total pageviews, and 34 total blog posts, we have helped you find and implement the latest advancements in evidence-based pedagogy for your math courses. We all want to engage our math students and invigorate our math classes, and we recognize the challenges of finding the time to research, plan, and execute new ideas. The short and practical posts can serve as a evidence-based resource for new faculty workshops and ongoing professional development. You might even try using one as food for thought to spark discussion about pedagogy in department meetings. Keep this site bookmarked and connect others to the collective wisdom of the Teaching Tidbits blog. <br /><br />We hope you will let us know how the Teaching Tidbits blog is helpful to you as you improve your teaching and your students' learning. <br /><br />Thank you for your support! Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-25521249318036422102018-05-08T09:22:00.000-04:002018-05-08T09:22:25.368-04:00Teaching Tidbits Blog 5 Most Popular PostsAs the summer approaches, the MAA Teaching Tidbits blog is coming to a close after two successful years of helping to increase student engagement in math courses and helping to build confidence and skills in math faculty. <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/--VBdseTryZ8/WvCe6eZj0QI/AAAAAAAALI0/N4winqTDMXMqwCADqTLxpsROyi4oBCHKgCLcBGAs/s1600/Goodjobstockphoto.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1129" data-original-width="1600" height="281" src="https://1.bp.blogspot.com/--VBdseTryZ8/WvCe6eZj0QI/AAAAAAAALI0/N4winqTDMXMqwCADqTLxpsROyi4oBCHKgCLcBGAs/s400/Goodjobstockphoto.jpg" width="400" /></a></div><br />The blog was designed to be a source for evidence-based teaching practices while the MAA Instructional Practices Guide was in development. Now that the <a href="https://www.maa.org/programs-and-communities/curriculum%20resources/instructional-practices-guide" target="_blank">MAA Instructional Practices Guide</a> is <a href="https://www.maa.org/programs-and-communities/curriculum%20resources/instructional-practices-guide" target="_blank">available</a>, we encourage our readers to refer to our blog posts for an in-depth treatment of course design, classroom practices, and assessment. Thank you to our readers for their support. We hope you found Teaching Tidbits a useful resource to help improve your math classroom. <br /><br />Of our 34 posts over the last two years, these are the 5 most popular posts:<br /><br /><ul><li><a href="http://maateachingtidbits.blogspot.com/2017/11/the-role-of-failure-and-struggle-in.html" target="_blank">The Role of Failure and Struggle in the Mathematics Classroom</a> by Dana Ernst </li><li><a href="http://maateachingtidbits.blogspot.com/2016/09/5-ways-to-respond-when-students-offer.html" target="_blank">5 Ways to Respond When Students Offer Incorrect Answer</a> by Rachel Levy </li><li><a href="http://maateachingtidbits.blogspot.com/2016/10/how-to-deal-with-math-anxiety-in.html" target="_blank">How to Deal with Math Anxiety in Students</a> by Jessica Deshler </li><li><a href="http://maateachingtidbits.blogspot.com/2017/10/how-transparency-improves-learning.html" target="_blank">How Transparency Improves Learning</a> by Darryl Yong </li><li><a href="http://maateachingtidbits.blogspot.com/2017/03/5-reflective-exam-questions-that-will.html" target="_blank">5 Reflective Exam Questions That Will Make you Excited about Grading</a> by Francis Su</li></ul><br />We hope you will continue to share the tips on this blog with colleagues and let us know how it has been useful to you. Thank you for your support of the blog! Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-45198676622198643212018-05-01T10:00:00.000-04:002018-05-02T11:49:59.111-04:005 Reasons Math Modeling Should have a Place in your Undergraduate Curriculumby Rachel Levy, Harvey Mudd College<br /><div class="separator" style="clear: both; text-align: center;"></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-eP20peGjFy0/Wund3YmuSTI/AAAAAAAALIk/kBzV1vc9wfI-Av1eE_zqZKY3uF-Vs85EgCLcBGAs/s1600/GettyImages-600000414.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1067" data-original-width="1600" height="266" src="https://1.bp.blogspot.com/-eP20peGjFy0/Wund3YmuSTI/AAAAAAAALIk/kBzV1vc9wfI-Av1eE_zqZKY3uF-Vs85EgCLcBGAs/s400/GettyImages-600000414.jpg" width="400" /></a></div><br /><div style="text-align: left;">I believe students should see mathematical modeling in school because this way of engaging mathematics can be both inclusive and personally empowering. </div><div style="text-align: left;"><br /></div><div style="text-align: left;">Mathematical modeling describes processes used to understand, describe, and predict real-world situations by employing whatever quantitative and computational approaches are useful. Many aspects of applied mathematics, statistics, operations research, algorithms and, data science can fall under this umbrella. <br /><br />When I say mathematical modeling should have a place in your curriculum, I don’t only mean exposing students to ubiquitous well-known models such as the mass-spring system or predator-prey. I mean the creative process of modeling, like the work students would do in a mathematical modeling competition such as the <a href="https://m3challenge.siam.org/" target="_blank">M3 Challenge</a> or <a href="https://www.comap.com/undergraduate/contests/mcm/" target="_blank">MCM/ICM</a> or in the workplace. I believe this can start as early as kindergarten, though of course here we focus on undergraduate education.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">Mathematical modeling is a topic of increased visibility in the education system. First, it appears in the US Common Core Standards for Mathematical Practice (<a href="http://www.corestandards.org/Math/Practice/#CCSS.Math.Practice.MP4" target="_blank">CCSSM-MP4</a>) for students in K-12. Second, job opportunities in business, industry, and government for those trained in the mathematical sciences are increasing while numbers of tenure-track opportunities are flat or decreasing. As someone on a job panel put it: I don’t care what flavor of mathematics you studied in school and bring to the job, once you work for my company, you are an applied mathematician.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">Here are 5 characteristics of mathematical modeling that can make it inclusive and personally empowering:</div><div style="text-align: left;"><br /></div><div style="text-align: left;">1.<b> Mathematical modeling involves genuine choices.</b> Students can be involved in choosing the situation, the topic, the mathematical and computational tools and, the metric for the success of their model. When students make choices, they can feel a different connection to and ownership of mathematics – mathematical tools and ideas are theirs to choose and use. In this way doing mathematics is more like the creative act of a research mathematician, a writer or an artist – the goal of the work is to create something new and of intellectual value.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">2<b>. Students learn how objective functions and assumptions/constraints matter.</b> The general public and the media express some skepticism about mathematical modeling because it seems like maybe you can make the data tell any story you want. <br /><br />Mathematical modeling helps people learn that by clearly communicating your objective function (goal) and assumptions/constraints you can more honestly and clearly convey why the model makes the prediction that it does. Students also learn that aspects of social justice and equity can be brought into play through these aspects of the model. For example, maybe your business goal is to help the people while staying financially viable, rather than just making the most money. </div><div style="text-align: left;"><br /></div><div style="text-align: left;">3. <b>Mathematical modeling can draw on interdisciplinary ideas and ways of knowing. </b>Because modeling problems are situated in the real world, they almost always have interdisciplinary aspects. Maybe the important information is about how a business is run, or how a machine works, or how humans behave. What are the preferences of the end user? What will make a solution useful and usable? How can visualization help communicate the methods and solutions?</div><div style="text-align: left;"><br /></div><div style="text-align: left;">4. <b>Real world problems help students see that mathematics is everywhere. </b>People sometimes think of mathematical modeling as only applied mathematics, but once the problem is extracted and refined to its mathematical form, students can see the structure and beauty of that mathematics. Mathematical modeling can give students ways to practice using familiar tools as well as reach for new mathematical and computational ideas.<br /><br />Reflective aspects of the modeling assignment can help teachers see how student perspectives on mathematics are changing. After modeling, students often report seeing things in a new way (such as noticing an elevator bouncing as it reaches the bottom of a building) and wondering how to describe this mathematically. Students can also envision career pathways that will call on these skills.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">5. <b>Mathematical</b> <b>Modeling is a team sport that focuses on process as much as product</b>. It may be possible to work on a model alone, but almost always models benefit from multiple perspectives and ways of thinking. Well-structured modeling problems encourage teams to start with a simple common solution and then provide opportunities for teammates to add some complexity and test to see if it improves the model. Teamwork has many challenges, and teams need to be monitored so that students are respectful of all voices. <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-DAqzWF4Um8w/Wum_jmom7yI/AAAAAAAALIE/dpXQ_MGwvroGTg5gXM81-cZ1XS6t8l0ZQCLcBGAs/s1600/GettyImages-472404164.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1067" data-original-width="1600" height="266" src="https://1.bp.blogspot.com/-DAqzWF4Um8w/Wum_jmom7yI/AAAAAAAALIE/dpXQ_MGwvroGTg5gXM81-cZ1XS6t8l0ZQCLcBGAs/s400/GettyImages-472404164.jpg" width="400" /></a></div><br />A rich modeling problem will have multiple solution methodologies and solutions (which depend on the selected objective and constraints). Students can experience mathematics as more than a course with feedback that judges when their answers are right and when they are wrong. This eliminates the phenomenon when every “X” mark on a problem can be like a small cut in a student’s confidence and erode their sense of belonging as a mathematics-doer. Instead, students can discuss how various aspects of solutions make them useful and what ways of communicating solutions are most effective. Students can iterate and improve their answers. Instructors can find ideas of value in every solution.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">Here are three ways to make mathematical modeling available to your students:</div><ul><div style="text-align: left;"></div><li><div style="text-align: left;"> Build a final project into a course (could be Calc, Prob/Stats, Lin Al, DEs…) and make sure the project involves some choice. You can still point to a particular tool (such as single value decomposition or compartment modeling) if you need the project to hit a learning objective while leaving the context open to the students.</div><div style="text-align: left;"></div></li><div style="text-align: left;"></div></ul><ul><div style="text-align: left;"></div><li><div style="text-align: left;">Propose a mathematical modeling course for your department. It doesn’t have to be a full number of units – students can take it as an elective. It could be a once a week seminar and it could be pass-fail. Or it could be a full unit, graded course.</div><div style="text-align: left;"></div></li><div style="text-align: left;"></div></ul><ul><div style="text-align: left;"></div><li><div style="text-align: left;">Advise a modeling competition (MCM/ICM) team. Provide time and space for students to do some practice problems and read winning papers. Discuss mathematical and computational approaches. This could be a student club activity or a departmental endeavor.</div><div style="text-align: left;"></div></li><div style="text-align: left;"></div></ul><div style="text-align: left;">To learn more about the teaching and learning of mathematical modeling, see these free downloadable reports:</div><div style="text-align: left;"><br /></div><div style="text-align: left;"><b><a href="http://www.siam.org/reports/gaimme.php" target="_blank">Guidelines for Assessment and Instruction in Mathematical Modeling Education (the GAIMME report)</a></b></div><div style="text-align: left;"><br /></div><div style="text-align: left;"><b><a href="https://www.blogger.com/goog_1414360848"><span id="goog_1414360849"></span>Math Modeling: Getting Started, Getting Solutions<span id="goog_1414360850"></span></a></b></div><div style="text-align: left;"><b><br /></b></div><div style="text-align: left;"><b><a href="https://m3challenge.siam.org/resources/modeling-handbook?_ga=2.4504944.2130197486.1519057583-1282280730.1443189831" target="_blank">Math Modeling: Computing and Communicating</a></b></div><div style="text-align: left;"><br /></div><br />Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-4172039344035814832018-04-18T17:15:00.000-04:002018-04-19T12:13:14.428-04:00The Exercise with No Wrong Answer: Notice and Wonder <div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: "arial";">Guest post by <a href="https://denison.edu/people/may-mei" target="_blank"><span style="color: #0b5394;">May Mei</span></a>, Denison University.</span><br /><span style="font-family: "arial";"><br /></span></div><h2 dir="ltr" style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"></h2><div dir="ltr" style="-webkit-text-stroke-width: 0px; background-color: transparent; color: black; font-family: Times New Roman; font-size: 16px; font-variant: normal; letter-spacing: normal; line-height: 1.38; margin: 0px; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;"><span style="background-color: white; color: #222222; display: inline; float: none; font-family: "arial"; font-size: 13.2px; font-style: normal; font-weight: 400; letter-spacing: normal; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;">How often have your students said nothing rather than risk saying something wrong? And how often in our own writing are we so paralyzed by the fear of imperfection that we end up writing nothing at all? </span></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: "arial";"><b><i><br /></i></b></span></div><div class="separator" dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><a href="https://1.bp.blogspot.com/-wSc2j0UADJs/Wti7kolTOVI/AAAAAAAALFo/kdSrH1PItms9rUZAN1PSBRGvYEnycfu7gCLcBGAs/s1600/GettyImages-653087398%2B%25281%2529.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1068" data-original-width="1600" height="263" src="https://1.bp.blogspot.com/-wSc2j0UADJs/Wti7kolTOVI/AAAAAAAALFo/kdSrH1PItms9rUZAN1PSBRGvYEnycfu7gCLcBGAs/s400/GettyImages-653087398%2B%25281%2529.jpg" width="400" /></a><span style="font-family: "arial";"><br /></span></div><span style="font-family: "arial";"><br />Enter <a href="https://www.nctm.org/mathforum/" target="_blank"><span style="color: #0b5394;">Notice and Wonder</span></a>, the exercise that has no wrong answers. After all, everything you can observe about a problem is a valid thing to notice and every question you can ask about a problem is a valid thing to wonder. <br /><br />Notice and Wonder is a way for instructors to create a safe place of exploration by allowing students to brainstorm before attempting to solve a problem. It’s a simple process-students are presented with a problem and before attempting to solve it, they are asked what they notice about it. When all students have contributed, or nothing new is being noticed, students can then answer what they wonder. <br /><br />This provides opportunities to discuss what is still unknown and puts all students on equal ground-everyone can wonder about something. Because there are no wrong answers for either of these questions, all students can participate in the activity. <br /><br />This <a href="https://www.nctm.org/mathforum/" target="_blank"><span style="color: #0b5394;">handout</span></a> describes Notice and Wonder as an in-class activity, but I like to use it to review for an exam. <br /><br />If my students have an upcoming exam, I will use the class period before as review, and sometime before that review period I ask each of my students to email me one thing they noticed and one thing they’re still wondering about. Just before class on the review day, I put all the students’ Notices and Wonders into one document and distribute it to the class. As I'm making this document I'm able to recognize themes and repeated observations or questions and can focus on those during the in-class review. <br /><br />The purpose of the exercise is to help me see what my students need, but also for the students to take inventory of what content the course has covered and to self-assess their understanding. <br /><br />Note that a brief discussion about what makes a fruitful Wonder may be needed. Let’s consider an upper level course, such as an introductory course on proof techniques. To help students develop ‘good’ Wonders, I provide them with the following examples and ask about the different levels of self-reflection that they display. <br /><br />"I wonder in Chapter 6, Exercise 5 in which it asks us to prove 3 is irrational, which definitions to use. Just like the proof we did for2, here I would say suppose 3 is rational so therefore3can be written as a/b where a and b are in Z. But once I squared both sides and did some algebra it does not come out to show a2 is even. Since we haven't done irrational numbers any other way I am confused as to what to do."<br /><br />3 reasons to consider incorporating this exercise into your math courses:<br /></span><br /><ul><span style="font-family: "arial";"></span><li><span style="font-family: "arial";">Notice and Wonder ingrains good habits of mind. This exercise provides a way for students to engage with material after the initial in-class exposure. The Notice component encourages students to draw connections that may not have been apparent in the first read-through while the Wonder component asks students to evaluate their comprehension of the material.</span></li><li><span style="font-family: "arial";">Notice and Wonder minimizes instructional prep time. I spend about 20 minutes compiling responses. For a class of 25 students, this generates much more material than I can cover in a 50 minute class. The responses provide students with something to work on after class, when they may feel compelled to study. The student-generated ideas provide guidance about how and what to study for students who are unsure of how to proceed and need to develop useful study habits.</span></li><li><span style="font-family: "arial";">Notice and Wonder allows students to gain insight into the thought processes of their peers. How many times have you heard a student say something to the effect of "everyone gets it but me"? Students gain the benefit of seeing that other people have questions, and maybe the same ones as them. Students can also see questions that they may not have thought to ask, and can’t yet answer. </span></li></ul><ul><span style="font-family: "arial";"></span></ul><span style="font-family: "arial";"></span><br /><div><span style="font-family: "arial";">I'm always impressed with the wonderful gamut of things students notice and wonder. Thus the practice makes not only supports student learning, it also makes my own teaching more effective and enjoyable.</span></div><span style="font-family: "arial";"></span><br /><b></b><i></i><u></u><sub></sub><sup></sup><strike></strike><b></b>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-44382987534592231982018-04-03T18:42:00.000-04:002018-04-19T12:12:35.150-04:00Design Practices to Maximize Students Learning <span style="font-family: "cambria"; font-size: 12pt; text-align: justify; vertical-align: baseline; white-space: pre-wrap;">By </span><a href="https://ced.ncsu.edu/people/kakeene/" style="text-align: justify;"><span style="color: #1155cc; font-family: "cambria"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">Karen Keene</span></a><span style="font-family: "cambria"; font-size: 12pt; text-align: justify; vertical-align: baseline; white-space: pre-wrap;">, </span><a href="https://www.ncsu.edu/" style="text-align: justify;"><span style="color: #1155cc; font-family: "cambria"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">North Carolina State University</span></a><span style="font-family: "cambria"; font-size: 12pt; text-align: justify; vertical-align: baseline; white-space: pre-wrap;">, </span><a href="http://www.math.montana.edu/burroughs/" style="text-align: justify;"><span style="color: #1155cc; font-family: "cambria"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">Beth Burroughs</span></a><span style="font-family: "cambria"; font-size: 12pt; text-align: justify; vertical-align: baseline; white-space: pre-wrap;">, </span><a href="http://www.montana.edu/" style="text-align: justify;"><span style="color: #1155cc; font-family: "cambria"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">Montana State University</span></a><span style="font-family: "cambria"; font-size: 12pt; text-align: justify; vertical-align: baseline; white-space: pre-wrap;">, and </span><a href="http://www.unco.edu/nhs/mathematical-sciences/faculty/soto-johnson.aspx" style="text-align: justify;"><span style="color: #1155cc; font-family: "cambria"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">Hortensia Soto</span></a><span style="font-family: "cambria"; font-size: 12pt; text-align: justify; vertical-align: baseline; white-space: pre-wrap;">, </span><a href="http://www.unco.edu/" style="text-align: justify;"><span style="color: #1155cc; font-family: "cambria"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">University of Northern Colorado</span></a><span id="docs-internal-guid-afe24975-8b7a-07ab-89c5-bc050d91bb7c"></span><br /><span id="docs-internal-guid-afe24975-8b7a-07ab-89c5-bc050d91bb7c"></span><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 5pt; text-align: justify;"><span id="docs-internal-guid-afe24975-8b7a-07ab-89c5-bc050d91bb7c"><span style="font-family: "cambria"; font-size: 12pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">This semester Teaching Tidbits continues its posts highlighting the new Instructional Practices Guide (</span><a href="https://www.maa.org/programs-and-communities/curriculum%20resources/instructional-practices-guide" style="text-decoration-line: none;"><span style="color: #1155cc; font-family: "cambria"; font-size: 12pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">IP Guide</span></a><span style="font-family: "cambria"; font-size: 12pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">) from the Mathematical Association of America (</span><a href="https://www.maa.org/" style="text-decoration-line: none;"><span style="color: #1155cc; font-family: "cambria"; font-size: 12pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">MAA</span></a><span style="font-family: "cambria"; font-size: 12pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">). This evidence-based guide is a complement to the </span><a href="https://www.maa.org/sites/default/files/pdf/CUPM/pdf/CUPMguide_print.pdf" style="text-decoration-line: none;"><span style="color: #1155cc; font-family: "cambria"; font-size: 12pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">Curriculum Guide</span></a><span style="font-family: "cambria"; font-size: 12pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;"> published in 2015. The guide provides significant resources for faculty focused on teaching mathematics in evidence-based ways. There are three focus chapters in the guide, Assessment Practices, Design Practices and, Classroom Practices, along with some additional sections that explain the importance of evidence-based instructional practices. Karen Keene and Beth Burroughs served as lead writers for the Design Practices and Hortensia Soto was a project team member and co-editor of the MAA IP Guide.</span></span><br /><i><span style="font-family: cambria;"><br /></span></i><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-sGEwkpGNWrI/Wti_2LykfuI/AAAAAAAALGM/KBHNNUr7b2UhHkcutxkxtdt8VNRDkQGxACLcBGAs/s1600/GettyImages-668043722.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1067" data-original-width="1600" height="266" src="https://3.bp.blogspot.com/-sGEwkpGNWrI/Wti_2LykfuI/AAAAAAAALGM/KBHNNUr7b2UhHkcutxkxtdt8VNRDkQGxACLcBGAs/s400/GettyImages-668043722.jpg" width="400" /></a></div><span id="docs-internal-guid-afe24975-8b7a-07ab-89c5-bc050d91bb7c"><br /></span></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 4pt; margin-top: 0pt; text-align: justify;"><span id="docs-internal-guid-afe24975-8b7a-07ab-89c5-bc050d91bb7c"><span style="font-family: "cambria"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">College professors have been planning for their classroom instruction for as long as universities have existed. Planning for instruction is one facet of the practice of design. The MAA IP Guide addresses design practices as</span></span></div><span id="docs-internal-guid-afe24975-8b7a-07ab-89c5-bc050d91bb7c"><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 4pt; margin-left: 36pt; margin-top: 0pt; text-align: justify;"><span style="font-family: "cambria"; font-size: 12pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">“the plans and choices instructors make before they teach and what they do after they teach to modify and revise for the future. Design practices inform the construction of the learning environment and curriculum and support instructors in implementing pedagogies that maximize student learning.”</span></div><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 4pt; margin-top: 0pt; text-align: justify;"><span style="font-family: "cambria"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">Design practices include planning for the content, but much more as well. Designing to maximize student learning requires professors to consider many things as they plan, but also to use the results of teaching to continue to revise and modify teaching in the future. Consideration of what is known about teaching practices and how students learn is necessary for all parts of the design. The design practices </span><a href="https://www.dropbox.com/s/42oiptp46i0g2w2/MAA_IP_Guide_V1-2.pdf?dl=0" style="text-decoration-line: none;"><span style="color: #1155cc; font-family: "cambria"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">chapter</span></a><span style="font-family: "cambria"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;"> of the IP Guide includes questions that instructors could ask themselves while designing instruction (i.e., how can I be sure to be inclusive in my instruction?), as well as many suggestions that focus on designing cognitive and affective learning goals, developing tasks and other ideas for instruction, and creating learning environments. To focus on student learning, instructors need to design the learning environments, the tasks and the homework based on the student learning objectives. </span></div><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 4pt; margin-top: 0pt; text-align: justify;"><span style="font-family: "cambria"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">In the design practices </span><a href="https://www.dropbox.com/s/42oiptp46i0g2w2/MAA_IP_Guide_V1-2.pdf?dl=0" style="text-decoration-line: none;"><span style="color: #1155cc; font-family: "cambria"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">chapter</span></a><span style="font-family: "cambria"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">, the authors offer design principles and considerations, educational research, and real examples provided by faculty in the field. Readers can access the chapter for a quick planning idea, or to consider making bigger instructional changes that focus on student learning; both are exciting and possible.</span></div><div><span style="font-family: "cambria"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div></span>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-51011912153759616632018-03-20T10:30:00.000-04:002018-04-19T12:03:40.937-04:00Three Ways to Help Teach Growth Mindset<i style="background-color: white; color: #222222; font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 13.2px;">By <a href="https://apps.carleton.edu/profiles/dhaunspe/" target="_blank">Deanna Haunsperger</a>, <a href="https://www.carleton.edu/" target="_blank">Carleton College</a> and MAA President</i><br /><br /><br /><br />Every fall I teach a differential calculus course at Carleton College that is five days a week instead of our usual three-days-per-week format. This course is designed to give students a review of algebra and pre-calculus and trigonometry skills just-in-time as I’m teaching the calculus material. It’s the lowest entry point we have for students who want or need to learn calculus, and it is where I introduce students to the idea of a growth mindset. <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-GJZi3EOdOF4/Wti9U12yE4I/AAAAAAAALF0/WSdxb_xnyRMfJtZvmHhdtYg1Xxr1SDb-QCLcBGAs/s1600/GettyImages-484766846%2B%25281%2529.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1068" data-original-width="1600" height="265" src="https://3.bp.blogspot.com/-GJZi3EOdOF4/Wti9U12yE4I/AAAAAAAALF0/WSdxb_xnyRMfJtZvmHhdtYg1Xxr1SDb-QCLcBGAs/s400/GettyImages-484766846%2B%25281%2529.jpg" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>On their mathematical autobiography cards that students write for me the first day of class, they often admit to feeling unsuccessful in their previous math class, being nervous about the material, and worried they’re not smart enough to succeed this time. What I enjoy most about these students is that they are in my class on the first day, regardless of background or perceived ability, ready to learn. <br /><br />I know from day one that one of my biggest responsibilities as a mathematician is to give my students the confidence to be successful. They need to come at this material with a fresh start, open their notebooks to a fresh page, and use a new mindset: a growth mindset. <br /><br /><a href="https://www.mindsetworks.com/science/" target="_blank">Growth mindset</a>, as defined by psychologist Carol Dweck, is the belief that mathematical (or any) ability is not something you’re born with, but something that can be developed through dedication, hard work, and good strategies. She and her colleagues have shown that students who believe in a fixed mindset – that you’re either born with a certain ability or intelligence or you’re not – are defeated by mistakes because they don’t think they are capable of improving. Growth mindset students, however, take mistakes as a challenge to work harder or dig in more deeply. They believe they can grow their brains to understand more. <br /><br />Of course we want our math students to have a growth mindset so that when they face problems they don’t know how to solve, they engage with the problem and persevere. But how do we teach growth mindset? Here are my three ways:<br /><br /><ol><li><b>Tell them.</b> I was talking to the director of our Learning and Teaching Center a few years ago over coffee. I wasn’t seeking advice at the time, I was just kvetching about my students and the things I thought they should know about being a successful student. “How can they not know that being in class is important? How can they not know that getting enough sleep and eating well helps? How can they not know that if they work at something long and hard and try different strategies they’ll get better at it?” He looked at me and said, “Well, have you told them?” No, I had to admit, I hadn’t. I don’t know why, but it had never occurred to me than in addition to teaching math, I needed to teach my students how to learn math.<br /><br />So now on day one I tell them that showing up to class well-rested and well-nourished is important. I tell my students that finding study buddies is important and that keeping up with their homework is important. I also tell them all about growth mindset and how they can be successful if they engage the material and persevere. In fact, I have a handout I give them on <a href="http://maa.org/sites/default/files/pdf/Succeeding%20in%20the%20College%20Mathematics%20Classroom.pdf" target="_blank">“How to be Successful in a College Math Classroom”</a> that contains these and other suggestions.</li><li><b>Remind them.</b> Before the first exam, I bring up these tips for success again. Not everyone is fully listening the first day of class, so it is important to continue to remind students of the expectations I have of them. This time, I tell them a personal story; this is not difficult for me because having a growth mindset helped me survive graduate school. My first year of graduate school, I took graduate abstract algebra without having had undergraduate abstract algebra. It turns out this was not a good idea. I felt defeated after one term, redoubled my efforts the second term, dug in even deeper the third term, and I ended up passing my algebra prelim at the end of the year on my first attempt. The material in that course did not come to me through divine intervention. I worked very hard to learn it, and I put in the hours and the focus to develop a growth mindset.</li><li><b>Use growth mindset-appropriate words throughout the term.</b> I am, sincerely, very proud of the efforts that the students put in throughout the term, and I love being their cheerleader. I don’t commend their talent or intelligence, though. Instead, I write “Great improvement; I can see you studied a long time for this exam!” “Excellent work!” on their exams. I acknowledge the hard work their brains are doing during class and over time, they are building new stronger connections between the neurons in their brains, and that’s why they need adequate rest and nutrition. Exams are not meant to judge students. Exams assess how much students have learned and indicate whether students have put in enough work to master the material.</li></ol>Of course, not all students are successful in this class that meets every day; it’s a lot of hard work. But a couple years ago, a student who had dropped the course one fall, signed up for it again the next fall. He went from failing one year to earning A’s the next year. “What’s different?,” I asked him. “I learned how to work hard and focus,” he replied. Now I make sure to slip that story into the class each year as well. <br /><br />Once they understand the growth mindset, students also feel slightly more in control of their own grades in the class, since they are seeing a more direct correlation between their time on task and their grade in the class. <br /><br />This made such a positive change in my calculus class, that I brought it into all the classes I teach now. I see a difference in my classes, especially in the attitude of some women. If this change in frame of mind improves the classroom experience for even a few students each term, it’s well worth the extra few minutes in class. <br /><br />Editor’s note: For more on the Growth Mindset in the math classroom, please see the MAA <a href="https://www.maa.org/programs-and-communities/curriculum%20resources/instructional-practices-guide" target="_blank">Instructional Practices Guide</a> sections on classroom practices as well as the equity in practice section. Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-45657763307191069592018-03-06T08:35:00.000-05:002018-03-06T08:35:20.113-05:00Fostering Student Engagement through Enhanced Classroom Practices<br /><div> <div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">By guest writers April Strom </span><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><a href="https://www.scottsdalecc.edu/"><span style="color: #1155cc; font-family: "Cambria",serif;">Scottsdale Community College</span></a></span><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"> and James Álvarez </span><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><a href="https://www.uta.edu/uta/"><span style="color: #1155cc; font-family: "Cambria",serif;">University of Texas at Arlington</span></a><o:p></o:p></span></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><br /></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 5.0pt;"><i><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">This is the third and final installment of Teaching Tidbits highlighting the new Instructional Practices Guide (</span></i><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><a href="https://www.maa.org/programs-and-communities/curriculum%20resources/instructional-practices-guide"><i><span style="color: #1155cc; font-family: "Cambria",serif;">IP Guide</span></i></a></span><i><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">) from the Mathematical Association of America (</span></i><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><a href="https://www.maa.org/"><i><span style="color: #1155cc; font-family: "Cambria",serif;">MAA</span></i></a></span><i><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">). This evidence-based guide is a complement to the </span></i><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><a href="https://www.maa.org/sites/default/files/pdf/CUPM/pdf/CUPMguide_print.pdf"><i><span style="color: #1155cc; font-family: "Cambria",serif;">Curriculum Guide</span></i></a></span><i><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">published in 2015. The guide provides significant resources for faculty focused on teaching mathematics using ideas grounded in research. Many thanks to April Strom and James Álvarez , lead writers for the Classroom Practices section, for providing this post.</span></i><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 5.0pt;"><i><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"><br /></span></i></div><div class="separator" style="clear: both; text-align: left;"><a href="https://1.bp.blogspot.com/-GShJa9Mkers/Wp6Yx6fg6FI/AAAAAAAALDQ/rKqqOeDsfh0cC7bVjOnZKdHx_X0EpgFHgCLcBGAs/s1600/dreamstime_m_39316670.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1067" data-original-width="1600" height="265" src="https://1.bp.blogspot.com/-GShJa9Mkers/Wp6Yx6fg6FI/AAAAAAAALDQ/rKqqOeDsfh0cC7bVjOnZKdHx_X0EpgFHgCLcBGAs/s400/dreamstime_m_39316670.jpg" width="400" /></a></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 5.0pt;"><br /></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Have you wondered how to increase student engagement in your courses or searched for ideas to help curious colleagues enhance their classroom practices? Well, the Mathematical Association of America’s Instructional Practices Guide (MAA IP Guide) may be an answer for you! The MAA IP Guide is purposefully written for all college and university mathematics faculty and graduate students who wish to enhance their instructional practices. A valuable feature of the MAA IP Guide is that it doesn't need to be read from cover to cover. Rather readers can begin, depending on their interests, with any chapter. The MAA IP Guide contains 4 main chapters: Classroom Practices, Assessment, Design Practices, and Cross-cutting Themes (such as Technology and Equity). In this post, we take a deeper dive into the Classroom Practices chapter of the MAA IP Guide, which can be downloaded in full for free </span><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><a href="https://www.maa.org/programs-and-communities/curriculum%20resources/instructional-practices-guide"><span style="color: #1155cc; font-family: "Cambria",serif;">here</span></a></span><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">. </span><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><br /></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">The Classroom Practices chapter is partitioned into two primary sections: (1) fostering student engagement and (2) selecting appropriate mathematical tasks. Moreover, the chapter is designed such that quick-to-implement instructional practices are presented upfront in the chapter followed by ideas that require more preparation to fully implement. The message is clear: we want to embrace, encourage, and support active learning strategies in the teaching and learning of collegiate mathematics!</span><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><br /></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><b><i><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Fostering Student Engagement: </span></i></b><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Classroom practices aimed to foster student engagement can build from the research-based idea that students learn best when they are engaged in their learning (e.g., Freeman, et al., 2014). Consistent use of active learning strategies in the classroom also provide a pathway for more equitable learning outcomes for students with demographic characteristics who have been historically underrepresented in science, technology, engineering, and mathematics (STEM) fields (e.g., Laursen, Hassi, Kogan, & Weston, 2014). In this section we illustrate what it means to be actively engaged in learning and offer suggestions to foster student engagement. </span><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><br /></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">To foster student engagement, the MAA IP Guide promotes the notion of building a classroom community from the first day of class. Community and sense of belonging are more likely to flourish in classrooms where the instructor incorporates student-centered learning approaches (c.f. Slavin, 1996; Rendon, 1994). Thus, establishing norms for active engagement or taking steps to increase a student’s sense of belonging to the classroom community also impacts the quality of student engagement in the classroom. We begin by providing suggestions on how to build a classroom community and then describe quick-to-implement strategies (e.g., wait time after questioning and one-minute papers), followed by more elaborate strategies that may require more preparation (e.g., collaborative learning strategies, flipped classroom, just-in-time teaching). </span><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><br /></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Of course, fostering student engagement through active learning strategies requires thoughtful consideration of the mathematical tasks that will support the work you want to accomplish with your students. In the next section, we focus on part 2 of the MAA IP Guide: </span><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><br /></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><b><i><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Selecting Appropriate Mathematical Tasks: </span></i></b><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Stein, Grover, and Henningsen (1996) define a mathematical task as a set of problems or a single complex problem that focuses student attention on a particular mathematical idea. Selecting appropriate mathematical tasks is critical for fostering student engagement because the tasks chosen provide the conduit for meaningful discussion and mathematical reasoning. But, how does an instructor know when a mathematical task is appropriate? There does not appear to be one single idea of what constitutes appropriateness in the research literature or in practice. Rather, appropriateness appears to be determined from a linear combination of a number of factors. The successful selection of an appropriate mathematical task seems to involve two related ideas: </span><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><br /></div><ol start="1" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; mso-list: l0 level1 lfo1; tab-stops: list .5in; vertical-align: baseline;"><span style="font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-fareast-font-family: "Times New Roman";">The <b>intrinsic appropriateness </b>of the task, by which we mean the aspects of the task itself that lend itself to effective learning; and </span><span style="font-family: "Arial",sans-serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></li><li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; mso-list: l0 level1 lfo1; tab-stops: list .5in; vertical-align: baseline;"><span style="font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-fareast-font-family: "Times New Roman";">The <b>extrinsic appropriateness </b>of the task, by which we mean external factors involving the learning environment that affect how well students will learn from the task. </span><span style="font-family: "Arial",sans-serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></li></ol><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><br /></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">In this section we elaborate on <b>group-worthy tasks</b>, which provide opportunities for students to develop deeper mathematical meaning for ideas, model and apply their knowledge to new situations, make connections across representations and ideas, and engage in higher-level reasoning where students discuss assumptions, general reasoning strategies, and conclusions. Group-worthy tasks can be characterized in terms of the cognitive demand required and they are often considered as high-level cognitive demand (see Stein et al. (1996) for a discussion on low-level and high-level cognitive demand). </span><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><br /></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">When implementing active learning strategies in the classroom, it is important to keep in mind the notion of communication: reading, writing, presenting, and visualizing of mathematics. The MAA IP Guide leverages the Common Core Standards for Mathematical Practice, specifically the idea of SMP3: constructs viable arguments and critiques the reasoning of others, where students are expected to justify their thinking publicly through verbal and written mathematics. Students construct viable arguments as they engage in mathematical problem solving tasks by articulating their reasoning as they demonstrate their solution to the problem. These arguments can be made for solutions to abstract problems and proofs as well as for mathematical modeling and other problems with real world connections. Students should come to interpret the word “viable” as “possible” so that during presentations students recognize that they are considering a possible solution which requires analysis in order to determine its mathematical worthiness. </span><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><br /></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><b><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Impact on Teaching Evaluations</span></b><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Whenever new teaching strategies are implemented in the classroom, faculty take a risk that student feedback surveys of their teaching may not accurately reflect the positive changes made or the deep learning achieved. Although the use of student feedback surveys as the only tool for evaluating teaching is highly problematic, in such cases it is important that faculty communicate their efforts. Documenting significant efforts to implement new strategies and collecting evidence of positive change can support this communication. Some possible ways to do this include:</span><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><br /></div><ol start="1" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; mso-list: l1 level1 lfo2; tab-stops: list .5in; vertical-align: baseline;"><span style="font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Keep notes; use them to write a brief summary of the changes made and the rationale for the changes to be shared with administrators or tenure and promotion committees.<o:p></o:p></span></li><li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; mso-list: l1 level1 lfo2; tab-stops: list .5in; vertical-align: baseline;"><span style="font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Document positive student feedback and comments, especially regarding their learning experience.<o:p></o:p></span></li><li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; mso-list: l1 level1 lfo2; tab-stops: list .5in; vertical-align: baseline;"><span style="font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Put negative comments into perspective. For example, if students make negative comments about working on open-ended problems, provide a rationale and explanation for the implementation of these types of tasks. <o:p></o:p></span></li><li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; mso-list: l1 level1 lfo2; tab-stops: list .5in; vertical-align: baseline;"><span style="font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Save examples of student work that represent the quality of the mathematical work and learning taking place and include or explain this in the summary of changes to the course delivery. <o:p></o:p></span></li></ol><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><br /></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Although negative student feedback surveys of teaching may be discouraging, it is important to put the survey feedback into context and to remember that implementing new strategies and techniques takes practice (i.e., don’t give up after the first time you try it). Students also need time and practice to acclimate to new ways of learning, so having several courses that require active engagement may also affect the way they react to active engagement in your course. Bringing these issues to the attention of the person or committee that evaluates your teaching and collecting evidence of your efforts to supplement student feedback surveys may help mitigate possible apprehension in trying new strategies to encourage active engagement in the classroom. </span><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><br /></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">To learn more about Classroom Practice, </span><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><a href="https://www.maa.org/programs-and-communities/curriculum%20resources/instructional-practices-guide"><span style="color: #1155cc; font-family: "Cambria",serif;">download</span></a></span><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"> the MAA IP Guide and use it as a resource to increase student engagement. And don’t forget to share broadly with others! </span><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><br /></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><b><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">References</span></b><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., & Wenderoth, M. P. (2014). Active learning increases student performance in science, engineering, and mathematics. <i>Proceedings of the National Academy of Sciences, 111</i>(23), 8410-8415. </span><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><br /></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Laursen, S. L., Hassi, M. L., Kogan, M., & Weston, T. J. (2014). Benefits for women and men of inquiry-based learning in college mathematics: A multi-institution study. <i>Journal for Research in Mathematics Education</i>, <i>45</i>(4), 406-418. </span><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><br /></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Rendon, L. I. (1994). Validating culturally diverse students toward a new model of learning and student development. <i>Innovative Higher Education</i>, <i>19</i>(1), 33. </span><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><br /></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Slavin, R. W. (1996). Research on cooperative learning and achievement: What we know, what we need to know. <i>Contemporary Educational Psychology, 21</i>, 43-69. </span><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><br /></div><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;"><span style="color: black; font-family: "Cambria",serif; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. <i>American Educational Research Journal</i>, <i>33</i>(2), 455-488. </span><span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></div></div>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-72604863715803079472018-02-20T11:51:00.000-05:002018-02-20T11:51:02.340-05:004 Ways to Promote Gender Equity in Your Classroom<i style="background-color: white; color: #222222; font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 13.2px;">By <a href="http://math.wvu.edu/~deshler/" target="_blank">Jessica Deshler</a>, <a href="https://www.wvu.edu/" target="_blank">West Virginia University</a></i><br /><br />There is something beautiful about the structure of mathematics that we can all appreciate, but it’s equally beautiful because it can be creative and messy. So is the teaching of mathematics. As mathematicians, we know and understand the complexities involved in our discipline, but sometimes overlook the underlying complexities of our classroom environment when preparing to teach. <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-4bRcKCkVAP8/WoxQ5S7uPOI/AAAAAAAALCc/a632zXJJvSQEgKC7rT78ttqS0dVfeSpvgCEwYBhgL/s1600/Femalecollegestudents.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1067" data-original-width="1600" height="266" src="https://2.bp.blogspot.com/-4bRcKCkVAP8/WoxQ5S7uPOI/AAAAAAAALCc/a632zXJJvSQEgKC7rT78ttqS0dVfeSpvgCEwYBhgL/s400/Femalecollegestudents.jpg" width="400" /></a></div><br />You’ve likely heard about the leaky pipeline – the phenomenon that describes the loss of women from STEM fields at various points in the academic pipeline. Because many undergraduate women leave the STEM pipeline <a href="http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0157447" target="_blank">after taking a mathematics course</a>, our discipline can especially benefit from classroom practices known to help retain and support these students. <br /><br />You might wonder whether the gender breakdown in our classes or variation in our students’ cultural and social backgrounds matter. We posit that these do matter, and that they can impact whether students are comfortable contributing to discussions, volunteering to present work on the board, or seeking help during office hours. We have some control, though, over how social interactions affect learning in our classrooms. Below are several ways you can support gender equity in your classroom. These techniques are meant to be inclusive and support all students, but are particularly important and empowering for undergraduate women in our classrooms. Links are included for suggestions that have appeared in previous <i>Teaching Tidbits</i> posts.<br /><br /><ul><li><b>Don’t be the Authority in the Classroom.</b> Help your students find ways to stop relying on you as the expert, and use the authority inherent in mathematics to become the experts. Through collaborative activities, students can express themselves and their mathematical ideas to their peers, developing self-reliance and focusing on <i>the mathematics</i>, not <i>what the instructor says</i>. </li></ul><ul><li><b> Language Matters.</b> Research has shown that even in elementary school, acknowledging the gender of our students <a href="https://www.tolerance.org/magazine/fall-2005/good-morning-boys-and-girls" target="_blank">reinforces stereotypes</a>. While we might not be saying ‘boys and girls’ in our Calculus classes, we are certainly using language that affects our students. This recent <a href="http://maateachingtidbits.blogspot.com/2017/09/language-matters-5-ways-your-language.html" target="_blank"><i>Teaching Tidbits</i> post</a> provides several ways for us to use language inclusively to support our students’ identities as mathematicians including statements like “When a mathematician approaches this problem, she…” or “When you explain it like that, you are really thinking like a mathematician.” </li></ul><ul><li><b> Don’t Lecture.</b> If you’re reading <i>Teaching Tidbits</i>, chances are you are interested in doing more than lecturing to your students. However, lecturing is still the <a href="https://www.maa.org/sites/default/files/pdf/cspcc/InsightsandRecommendations.pdf" target="_blank">preferred teaching method</a> of many mathematics instructors. Research has shown us <a href="http://science.sciencemag.org/content/332/6034/1213?ijkey=749dbce76a1159231d475879cb14f81dbad34dae&keytype2=tf_ipsecsha" target="_blank">over</a> and <a href="http://aapt.scitation.org/doi/abs/10.1119/1.2162549" target="_blank">over</a> that interactive teaching is one of the best ways to reduce the gender gap in achievement, and a <a href="http://www.pnas.org/content/111/23/8410.full" target="_blank">2014 report</a> told us just how much we were neglecting all students when using only lecture in our classrooms. Moving from ‘sage on the stage’ to ‘guide on the side’ is a powerful way to give all students, especially women, the opportunity to engage in classroom activities and discussions. One technique for providing this type of classroom experience is through Inquiry Based Learning, described in a recent post with some resources <a href="http://maateachingtidbits.blogspot.com/2017/04/want-to-give-your-teaching-style.html" target="_blank">here</a>.</li></ul><ul><li><b>Know Your Own Biases.</b> One of the most important social interaction factors that can play out in our classroom is implicit bias. Before we can address any bias we see in our students, we need to understand our own biases. These freely accessible <a href="https://implicit.harvard.edu/implicit/selectatest.html" target="_blank">Implicit Association Tests</a> allow us to face biases we might not know we’re carrying with us and help us to become more equitable instructors.</li></ul><br /><br />Additional related resources:<br /><br /> Deshler, J. & Burroughs, E., (2013). Teaching Mathematics with Women in Mind, Notices of the <i>American Mathematical Society</i>, <a href="http://www.ams.org/notices/201309/rnoti-p1156.pdf">http://www.ams.org/notices/201309/rnoti-p1156.pdf</a>.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-4bRcKCkVAP8/WoxQ5S7uPOI/AAAAAAAALCc/gmIn3gIk9Kg4JkJutXBJ_kUpTwUIZrmmgCLcBGAs/s1600/Femalecollegestudents.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1067" data-original-width="1600" height="213" src="https://2.bp.blogspot.com/-4bRcKCkVAP8/WoxQ5S7uPOI/AAAAAAAALCc/gmIn3gIk9Kg4JkJutXBJ_kUpTwUIZrmmgCLcBGAs/s320/Femalecollegestudents.jpg" width="320" /></a></div>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-52998598158478453752018-02-06T07:30:00.000-05:002018-02-06T07:30:05.799-05:00MAA IP Guide – Assessment<i style="background-color: white; color: #222222; font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 13.2px;">By <a href="http://www.babson.edu/Academics/faculty/profiles/Pages/Cleary-Richard.aspx" target="_blank">Rick Cleary</a> (guest blogger), <a href="http://www.babson.edu/Pages/default.aspx" target="_blank">Babson College</a></i><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-702yAPVCNbI/WnSY3NHtrxI/AAAAAAAALB4/AnukIiIOSAwi1rT8EiRzaFIi_8sHA3DLwCLcBGAs/s1600/GettyImages-871203952.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1068" data-original-width="1600" height="266" src="https://3.bp.blogspot.com/-702yAPVCNbI/WnSY3NHtrxI/AAAAAAAALB4/AnukIiIOSAwi1rT8EiRzaFIi_8sHA3DLwCLcBGAs/s400/GettyImages-871203952.jpg" width="400" /></a></div><blockquote class="tr_bq"><b>A note from the Editors:</b> This semester <i>Teaching Tidbits</i> will have several posts highlighting the new Instructional Practices Guide (<a href="https://www.maa.org/programs-and-communities/curriculum%20resources/instructional-practices-guide" target="_blank">IP Guide</a>) from the Mathematical Association of America (<a href="https://www.maa.org/" target="_blank">MAA</a>). The MAA has a long tradition of reporting what content should be taught in the mathematics classroom through its <a href="https://www.maa.org/sites/default/files/pdf/CUPM/pdf/CUPMguide_print.pdf" target="_blank">Curriculum Guide</a>; now the new IP Guide addresses how things could be taught in the mathematics classroom, how one could to design that experience, and how one could assess that experience. The suggested practices are well grounded in research on student learning. In our first post about the IP Guide, we dive deeper into the Assessment Practices section of the guide. Thanks to Rick Cleary, a lead writer for this section, for providing this post.</blockquote>The opening statement of the Assessment chapter of the MAA Instructional Practices guide makes the following claim: Effective assessment occurs when we clearly state high-quality goals for student learning, give students frequent informal feedback about their progress toward these goals, and evaluate student growth and proficiency based on these goals. The chapter details some of the ways that effective assessment can be implemented in various types of courses. Many of the same assessment principles apply, whether you are from a big or small school, whether you teach large or small numbers of students, no matter what your lecture/active learning balance, on or off-line, developmental courses through graduate seminars. This portion of the IP Guide is designed to get colleagues thinking and talking about grounding both formative assessments that take place throughout the course and summative assessments at the end of a course in appropriate learning goals. <br /><br />There is a fine line between assessments that are challenging and assessments that are discouraging. Once students become discouraged, it is hard to get them back on track. For example, traditional lecture-based instruction methods have been associated with traditional summative assessment procedures such as timed exams with questions in very specific formats. Recent research in mathematics education recommends classroom practices that provide ongoing lower stakes assessment to promote student engagement. New technology such as clickers and online polls or quizzes can help faculty provide these types of opportunities. Through vignettes grounded in the experience of the writers, the IP Guide illustrates these developments, providing instructors the tools they need to be creative as they design appropriate and equitable assessments for their courses. <br /><br />The IP Guide chapter on Assessment provides both a research framework and practical tips needed to implement effective assessments that encourage, rather than discourage, student learning. It considers ways to make assessment consistent with course design and practice to promote effective learning for all students. Rather than seeing assessment as a mandate from an administration or an accrediting agency, the IP guide shows there is great value in creating a positive culture of assessment for students, faculty and departments. <br /><br />Download a copy of the <a href="https://www.dropbox.com/s/xpvkni52tkf0wgt/MAA_IP_Guide_V1-1.pdf?dl=0">MAA Instructional Practices Guide</a> today. <br /><br />Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-44521948687258562112018-01-23T08:00:00.000-05:002018-01-23T08:00:02.427-05:00The One Question Calculus Final<i style="background-color: white; color: #222222; font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 13.2px;">By <a href="http://maateachingtidbits.blogspot.com/p/meet-authors.html" target="_blank">Lew Ludwig</a> (Editor-in-Chief), <a href="http://denison.edu/" target="_blank">Denison University</a></i><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-yh8QfsSdyGY/WmIeq2lpd7I/AAAAAAAALA0/q5d2SMAKKdcYoZUNVGeO-E2enMBlbtASACLcBGAs/s1600/Lew_Calculus_image1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="636" data-original-width="635" height="400" src="https://2.bp.blogspot.com/-yh8QfsSdyGY/WmIeq2lpd7I/AAAAAAAALA0/q5d2SMAKKdcYoZUNVGeO-E2enMBlbtASACLcBGAs/s400/Lew_Calculus_image1.JPG" width="398" /></a></div><br />As the semester begins and we prep for classes, the practice of <a href="http://languages.oberlin.edu/blogs/ctie/2017/02/26/backward-design-from-course-to-class/" target="_blank">backward course design</a> is a powerful way to get the most of the learning experience for our students. With this in mind, I thought I would share one of my favorite exam questions for a first semester calculus course, which appears below. I call it “the one question calculus final.” Now of course this is tongue-in-cheek, as the one question has over 15 questions. Nonetheless, this one question tour de force covers the full range of a first semester calc course. To substantiate this bold claim, I found a comprehensive list of typical topics in such a course at <a href="http://mathworld.wolfram.com/classroom/classes/CalculusI.html" target="_blank">Wolfram Mathworld Classroom</a>. The chart below cross-references each alphabetically listed topic with its specific question. While some questions touch on a range of topics, the cross-referencing refers to the primary reference. <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-l9ssBvKIUik/WmIdfYR-_ZI/AAAAAAAALAk/NGHAutsfvHQB2Ze8rdsTT7hpYmatteuVACLcBGAs/s1600/TeachingTidbits_CalculusFinal.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="305" data-original-width="749" height="162" src="https://4.bp.blogspot.com/-l9ssBvKIUik/WmIdfYR-_ZI/AAAAAAAALAk/NGHAutsfvHQB2Ze8rdsTT7hpYmatteuVACLcBGAs/s400/TeachingTidbits_CalculusFinal.JPG" width="400" /></a></div><br /><b>Why I like this question:</b><br />I really like this question because it requires students to problem-solve, not just memorize a procedure. For example, instead of providing a typical composite function and asking for the derivative, my students must understand that the function in question (f) is a composition, know how to apply the chain rule, then read the graph to fill in the missing values. While I admit that question (m) may be a stretch for a Riemann sum, question (p) helps students realize the a definite integral is just a question about area. I especially like questions such as (j) and (k) that help students intuitively use important results like the intermediate value theorem or the mean value theorem. Finally, I like this question because no piece of technology can do the work for you. I can safely permit graphing calculators during my final without the fear of some CAS (computer algebra system) making short work of my exam. <br /><br /><b>How I use this question:</b><br />Please do not unleash this question on your students without prior exposure! My students have been working with this type of question for the whole semester. The beginning of the semester would focus more on limit questions like (a)-(e). By the second test of the semester, my students work on questions like (f) and (g) to understand the with mechanics of differentiation. By the third test, we get practice with applications of the derivative with questions such as (h)-(l). And by the end of the semester, questions of the type (m)-(p) test students’ understanding of the definite and indefinite integral. To make sure students do not forget prior material, my tests include questions from previous tests. Cognitive psychologists refer to this technique as <a href="https://www.scientificamerican.com/article/the-interleaving-effect-mixing-it-up-boosts-learning/" target="_blank">interleaving</a>. <br /><br /><b>How I grade this question:</b><br />Since this question has so many parts, I only count each sub-question for one point out of a 100-point final exam. Okay, I do ask other questions beside this one! I grade each question as right or wrong, no partial credit. While this may seem harsh, by giving each question a small point value, a student can miss a few of these questions without serious detriment to the overall grade. Moreover, past tests have shown a student’s exam score tracks fairly closely with performance on this question. <br /><br /><b>How to modify this question:</b><br />Of course there is a myriad of ways this question could be modified. For one, change the graph. When I initially developed this question, I would make sketches of the graph by hand. Now the online graphing program <a href="https://www.desmos.com/calculator" target="_blank">Desmos</a> helps me produce graphs that are easy to read and export into LaTex or word processing programs. Students can contribute by creating their own questions for a graph you provide. Or you can turn that on end and have students provide a graph based on questions you provide. However you use it, you will find this focused cumulative approach will help deepen your students understanding of calculus. <br /><br /><iframe height="480" src="https://drive.google.com/file/d/0BwrEr4CXDpSIdmdqS05mMVlocU0/preview" width="640"></iframe>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-84284476616789348782017-12-12T07:25:00.000-05:002017-12-20T11:25:30.688-05:00Use the MAA Instructional Practices Guide to Maximize Student Engagement with Math<i>By guest bloggers Martha Abell, <a href="http://www.georgiasouthern.edu/" target="_blank">Georgia Southern University</a>, and Linda Braddy, <a href="https://www.tccd.edu/" target="_blank">Tarrant County College</a></i><br /><i><br /></i>If you enjoy <i>Teaching Tidbits</i>, be sure to get an electronic copy of the Mathematical Association of America Instructional Practices Guide, which is chock full of great ideas to help you and your students. The guide is available as a <a href="https://www.maa.org/programs/faculty-and-departments/ip-guide" target="_blank">free download on the MAA website</a>. The MAA IP Guide is intended for all instructors of mathematics:<br /><ul><li>New graduate teaching assistants </li><li>Experienced senior instructors </li><li>Contingent faculty member at a two-year institution </li><li>New faculty member at a doctoral-granting institution </li><li>Instructors who want to transform their own teaching </li><li>Mathematicians delivering professional development to colleagues</li></ul>The guide boldly responds to challenges articulated in the <a href="https://www.maa.org/sites/default/files/NGenIOuS_full_report.pdf" target="_blank">2014 INGenIOuS</a> report and the <a href="https://www.maa.org/sites/default/files/pdf/CommonVisionFinal.pdf" target="_blank">2016 Common Vision</a> report, which both call for transformation within the mathematical sciences community toward deeper, more meaningful learning experiences. The MAA IP Guide was written by faculty from a wide range of institutions and professional associations. It supports the use of evidence-based instructional strategies to actively engage students in the learning process by providing “how to” suggestions. The supporting research focuses on effective teaching, deep student learning and student engagement with the mathematics both inside and outside the classroom. <br /><br />The content organization is based on three interconnected foundations of effective teaching: classroom practices, assessment practices, and course design practices. It also addresses two key cross-cutting themes, technology and equity, that permeate all three practice areas.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-ekNwgcTsXfE/Wi7nF0UFcRI/AAAAAAAAK_I/ldkkkaG5AY4HaWO2XRX68kwM6l-Iwsu2QCLcBGAs/s1600/IP_Guide.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="255" data-original-width="375" src="https://4.bp.blogspot.com/-ekNwgcTsXfE/Wi7nF0UFcRI/AAAAAAAAK_I/ldkkkaG5AY4HaWO2XRX68kwM6l-Iwsu2QCLcBGAs/s1600/IP_Guide.JPG" /></a></div><br />The <b>Classroom Practices</b> chapter provides multiple entry points to help instructors implement practices that foster student engagement. Topics include building community within the classroom, using collaborative learning strategies, developing persistence in problem-solving, and selecting appropriate tasks. <br /><br />The <b>Assessment Practices</b> chapter offers guiding principles to assess student learning through both summative and formative assessments. Most instructors routinely employ summative assessments such as quizzes and exams, but some may not be as familiar with formative assessment practices which can inform their decisions during the course regarding “next steps” in instruction based on students’ current needs. <br /><br />The <b>Design Practices</b> chapter guides instruction planning and revision to maximize student learning. Each chapter includes vignettes, practical tips, and references to research-based studies that support the effectiveness of the practices. Each chapter also offers strategies for trying new instructional methods and avoiding common pitfalls. <br /><br />The MAA IP Guide will be a topic of discussion at the Joint Mathematics Meetings in San Diego in January 2018, most notably at the <a href="http://jointmathematicsmeetings.org/meetings/national/jmm2018/2197_program_mipac.html#title" target="_blank">MAA Invited Paper Session</a> on this topic, Thursday from 8:00-10:50. The writing team is excited to present this resource to the community in support of deep, meaningful experiences for all instructors and students. We promote the use of engaging instructional practices in your own department by sharing this resource with your colleagues! <br /><br /><br /><br />Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-18965619194107288902017-11-28T07:07:00.000-05:002017-11-29T10:07:00.629-05:00“I’m Worried About My Grade.” How to Pre-empt the End of Semester Panic<i>By <a href="http://maateachingtidbits.blogspot.com/p/meet-authors.html" target="_blank">Julie M. Phelps</a>, Contributing Editor, <a href="http://valenciacollege.edu/" target="_blank">Valencia College</a></i><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-IOrrTintxMg/Wh14id4kFrI/AAAAAAAAK-4/jwA-LgmV5IEgqXYmuvlcl94-EgZCfVwVACLcBGAs/s1600/GettyImages-607927560.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1067" data-original-width="1600" height="266" src="https://3.bp.blogspot.com/-IOrrTintxMg/Wh14id4kFrI/AAAAAAAAK-4/jwA-LgmV5IEgqXYmuvlcl94-EgZCfVwVACLcBGAs/s400/GettyImages-607927560.jpg" width="400" /></a></div><br />As the end of the semester nears, educators brace for the inevitable student questions about their final grades. If you are anything like me, this can be distracting from my goal of the class: to teach mathematics and make a difference in student lives. Sometimes I find myself dreading the last couple weeks because many students are stressed and solely focused on the final grade, not on learning ways to utilize mathematics in their major. <br /><br />This year I decided to try something new and pre-empt student questions about their grades by having them reflect on their class work and engagement. To do so, I showed a YouTube video called “<a href="https://www.youtube.com/watch?v=G07r0yIlRJo&t=17s" target="_blank">I am worried about my grade</a>” to my College Algebra students at the beginning of the semester (just before the first test). While very basic, the video goes over the many ways we educators evaluate student performance, and how we make time for students to approach us outside of class. <br /><br />After showing the video, I asked the student to reflect on it and write a brief essay about what they saw in the video. Here are the themes from their essays that you can use to set course expectations early in the semester (and pre-empt the end of semester panic):<br /><b><br /></b><b>1. I need to be a responsible college student/adult.</b><br /><ul><li>Ask for help/ask questions/make sure I understand/go to tutoring. </li><li>Always try to improve your work/use the resources. </li><li>Turn in assignments on time/don’t procrastinate. </li><li>Come to class/participate. </li><li>Passing the class is up to the student. </li><li>Take your education seriously/have good work ethic/don’t be lazy/take the initiative/have a good attitude. </li><li>Learn from your mistakes. </li><li>Manage your time. </li><li>Taking this class is not about a grade but about learning mathematics.</li></ul><b>2. There are plenty of opportunities to get help.</b><br /><div><ul><li>Go to office hours.</li><li>When the professor takes time to be flexible within your schedule, make sure to show up.</li><li>Go to tutoring.</li></ul><b>3. The professor is there to help!</b></div><div><ul><li>Establish a connection with the professor.</li><li>"Professors have a lot of students, so if they offer to help...accept it!"</li><ul></ul></ul></div><br />Three notable quotes from student essays on being responsible and engaged students:<br /><ul><li>“OMG… I’m the bear… you’re talking directly to me aren’t you? Don’t drop me… I get it! I need to make a schedule, study, and ask for help immediately. Thanks for the wake-up call.”</li><li>“By showing me this example, Dr. Phelps showed me that grades aren’t given, they’re earned. After realizing this, I’m going to utilize every resource that is available to me to show that I have the potential to get passing grade and higher, and that I have the capacity to be good at math and enjoy the work that I do in the class and in the other math classes.”</li><li>“The video that we watched in class shows in a very droll way a conversation between a student and a teacher. I identify his [the students’] attitude as a student from high school or a middle school, since they only want to pass the year, not to learn things for the future, they can’t see the utility of their learning.”</li></ul>Because of this activity, I am now able to focus on what the end-of-term should be about: teaching mathematics for long-term use and retention. At the end of the semester, we educators only have a few more classes to make an impact on our students, and our students only have a few more class meetings to get the most out of the semester-long experience. I encourage you to have this conversation with your students before the end of the semester so everyone can have productive class time. <br /><br /><br />Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-73231314058156256002017-11-07T12:51:00.001-05:002017-11-07T12:51:27.957-05:00The Role of Failure and Struggle in the Mathematics Classroom<i>By <a href="http://maateachingtidbits.blogspot.com/p/meet-authors.html">Dana Ernst</a>, Contributing Editor, <a href="https://nau.edu/">Northern Arizona University</a></i><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-yKSElwKCvIU/WgHyiQmP0_I/AAAAAAAAK-M/sPecCrmXPdAwLMB3X9fBD6oAcKw40A9OgCLcBGAs/s1600/GettyImages-171385688.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1067" data-original-width="1600" height="266" src="https://2.bp.blogspot.com/-yKSElwKCvIU/WgHyiQmP0_I/AAAAAAAAK-M/sPecCrmXPdAwLMB3X9fBD6oAcKw40A9OgCLcBGAs/s400/GettyImages-171385688.jpg" width="400" /></a></div><br /><i>The purpose of this post is to generate discussion and to get us thinking deeply about our teaching practices. This post introduces teaching concepts that researchers and educators developed to promote student success.</i><br /><br />In an attempt to understand who is successful and why, psychologist <a href="https://angeladuckworth.com/" target="_blank">Angela Duckworth</a> has spent years studying groups of people in a variety of challenging situations. Over and over again, one characteristic surfaced as a significant predictor of success: grit. <a href="https://angeladuckworth.com/qa/#faq-125" target="_blank">According to Duckworth</a>, grit is passion and perseverance for long-term goals. One of the big open questions in cognitive psychology is how to develop grit. <br /><br /><b>Growth Mindset </b><br /><a href="https://www.edutopia.org/resilience-grit-resources" target="_blank">Research suggests</a> that one of the key ingredients to fostering grit is adopting a <a href="https://www.mindsetworks.com/science/" target="_blank">growth mindset</a>. Psychologist <a href="https://mindsetonline.com/abouttheauthor/" target="_blank">Carol Dweck</a> defines growth mindset as the view that intelligence and abilities can be developed with effort. In contrast, a fixed mindset is the belief that one's talent, intelligence, and abilities are fixed traits with little room for improvement. <a href="https://www.mindsetworks.com/Science/Impact" target="_blank">Dweck has found</a> that:<br /><blockquote class="tr_bq"> "People’s theories about their own intelligence had a significant impact on their motivation, effort, and approach to challenges. Those who believe their abilities are malleable are more likely to embrace challenges and persist despite failure." </blockquote> The claim is that those with a fixed mindset will tend to avoid challenges, while those with a growth mindset will embrace challenges. <a href="https://www.edutopia.org/neuroscience-brain-based-learning-neuroplasticity" target="_blank">Research has shown</a> that effort has the potential to physically alter our brains, strengthening neural pathways and essentially making one smarter. <br /><br />A growth mindset increases potential. Teachers who have a growth mindset about their students can help share this perspective and reap its benefits. Views like "some people just aren't good at mathematics," or "not everyone is cut out to be a math major" exhibit a fixed mindset and may severely limit the potential of our students. <br /><br /><b>Productive Failure</b><br />At the core of the growth mindset paradigm is the notion of <a href="http://manukapur.com/productive-failure/" target="_blank">productive failure</a>. While mistakes and failure are part of the learning process, productive failures provide an opportunity to learn and grow. According to <a href="https://qz.com/535443/the-best-way-to-understand-math-is-learning-how-to-fail-productively/" target="_blank">Manu Kapur</a>, productive failure activates parts of the brain that trigger deeper learning. Unfortunately, failure and mistakes are stigmatized in our culture, especially in many mathematics classrooms. <br /><br />One of the key ingredients to a successful active learning classroom is getting the students on board. One approach is to explain the concept of productive failure to our students and go out of our way to point out when we see it happen in class (this is a part of being more <a href="http://maateachingtidbits.blogspot.com/2017/10/how-transparency-improves-learning.html" target="_blank">transparent in the classroom</a>). Some teachers even make productive failure <a href="http://theiblblog.blogspot.com/2014/06/productive-failure-pf.html" target="_blank">part of the course grade</a>. <br /><br />If we want students to feel comfortable taking risks, making mistakes, and failing, then we need to provide an environment where this type of behavior is encouraged. I'm not suggesting that we lower standards (or allow wrong or inadequate answers to be sufficient), but give space for tinkering and failure along the way. Our assessment and grading practices need to jive with our philosophy of productive failure. I think that it is important to build opportunities for failure into our everyday structure. <br /><br /><b>Productive Struggle</b><br />Due to the negative connotation of the word "failure,” I started referring to productive failure as <a href="http://interactivestem.org/wp-content/uploads/2015/08/EDC-RPC-Brief-Productive-Struggle.pdf" target="_blank">productive struggle</a>, thinking that these two phrases meant the same thing. However, over time, I have come to view these two concepts as related but not identical. Let's do a little experiment. Take a minute to look at the following list of word pairs, but do not write anything down. <br /><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-HOaA8NB98u8/WgHv01Zeh4I/AAAAAAAAK94/Y7CjkkQX4D8SzUekn5Eqap_ag2uCpibPQCLcBGAs/s1600/productivestruggle_1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="267" data-original-width="500" src="https://1.bp.blogspot.com/-HOaA8NB98u8/WgHv01Zeh4I/AAAAAAAAK94/Y7CjkkQX4D8SzUekn5Eqap_ag2uCpibPQCLcBGAs/s1600/productivestruggle_1.JPG" /></a></div><br />Now, without looking at the list of words, write down as many pairs as you can. You do not need to remember where any missing letters were nor which column a pair was in. Next, looking at the table below, count how many pairs you found in column A versus column B. <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-13rSA8RamVY/WgHwNP-U6wI/AAAAAAAAK-A/sPYl9Q5LGCoKlagarE6-HhxqZZsZHa0kQCLcBGAs/s1600/productivestruggle_2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="293" data-original-width="500" src="https://3.bp.blogspot.com/-13rSA8RamVY/WgHwNP-U6wI/AAAAAAAAK-A/sPYl9Q5LGCoKlagarE6-HhxqZZsZHa0kQCLcBGAs/s1600/productivestruggle_2.JPG" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><br />This list of words is from <i><a href="http://thetalentcode.com/" target="_blank">The Talent Code</a></i> by Daniel Coyle (although I've rearranged the order a bit). According to Coyle, studies show that on average people remember three times as many pairs in column B, the one with missing letters. The claim is that a moment of struggle (<a href="http://mathematicaltasks.weebly.com/cognitive-demand-defined.html" target="_blank">cognitive demand</a>) makes all the difference. I regularly utilize this exercise on the first day of class as part of my <a href="http://danaernst.com/teaching/SettingTheStage.pdf" target="_blank">Setting the Stage activity</a>, the purpose of which is to get students on board with an active learning approach. The point of the exercise is to have students experience in a simple, yet profound way, the value of productive struggle. <br /><br />This exercise does an excellent job of distinguishing the difference between productive failure and productive struggle. The key to success here is the struggle, not failure. This exercise also helps pinpoint the "productive" part. Imagine we removed most of the letters from the words in column B. As more letters are removed, the less productive one will be in figuring out what the pairs are. It is important to keep this in mind when designing tasks for our students to engage in. There is a "Goldilocks zone" (related to the <a href="https://en.wikipedia.org/wiki/Zone_of_proximal_development" target="_blank">zone of proximal development</a>), where struggle will be most productive. How much scaffolding we should provide our students will depend greatly on who our students are. <br /><br /><b>The Goldilocks Zone </b><br />The following images, taken from <a href="http://rault.faculty.arizona.edu/" target="_blank">Patrick Rault</a>, provide an analogy for productive struggle and productive failure.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/--tuMWhAtKng/WgHvX73NilI/AAAAAAAAK9s/7bdatP7kzn8blFiDv7oCFm_GZUuFb4CEACLcBGAs/s1600/productivestruggle_3.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="143" data-original-width="500" src="https://4.bp.blogspot.com/--tuMWhAtKng/WgHvX73NilI/AAAAAAAAK9s/7bdatP7kzn8blFiDv7oCFm_GZUuFb4CEACLcBGAs/s1600/productivestruggle_3.JPG" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><br />All three images are meant to represent a challenge or task. In Figure A, all the obstacles have been removed; struggle is minimized, and failure is unlikely. There is no opportunity to develop grit, and we have provided too much scaffolding for our students. This is what happens when teachers demonstrate a certain type of problem and then ask students to do problems using the demonstrated method. Certainly a useful skill, but we want more. <br /><br />In Figure B the rocks are slippery, and the path is not clear; the risk of failure is high, and most attempts to cross the river will involve a tremendous amount of struggle. Whether the failure and struggle are productive depends on how agile the person is crossing the river. For many, the risks may be too high. Perhaps only a few make it across. This is what happens when we only provide students with tasks that are mostly beyond their current reach. <br /><br />Figure C is meant to represent the Goldilocks zone. The path across the river isn't trivial, but hopefully the risk of failure and amount of struggle isn't too great. As students become more proficient at crossing the river, the rocks in Figure C should be moved further apart, and potentially introduce a maze of rocks for students to navigate. Ultimately, we want students to have developed enough grit to strive for crossing the river in Figure B. It's possible that eventually the stepping stones in Figure B become the new Goldilocks zone. <br /><br /><a href="http://theiblblog.blogspot.com/" target="_blank">Stan Yoshinobu</a> says that the right question to ask is "how are my students intelligent," as opposed to "how intelligent are my students?" What the Goldilocks zone looks like for one group of students may be wildly different for another group of students. In fact, the ideal set of stepping stones is different for each student. This may make the task of providing this experience for our students sound too daunting, but we would be lying to ourselves if we thought the problem went away by not providing the opportunity. Being forced to confront these issues is a feature, not a bug. <br /><br />Here are some questions to ponder. We welcome respectful dialogue in the comments section.<br /><br /><ul><li>To what extent is grit necessary or sufficient for a student (or even a research mathematician) to be successful in mathematics? </li><li>How do we go about fostering a growth mindset and altering a fixed mindset? </li><li>How do we provide a classroom environment where risk-taking is encouraged, mistakes and failures are valued as part of the learning process, and high standards are maintained? </li><li>How can we identify productive versus nonproductive failure and struggle? In particular, how can we locate the Goldilocks zone for a given set of students?</li></ul><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-78590981539761344592017-10-24T07:00:00.000-04:002017-10-24T07:00:03.293-04:00How Transparency Improves Learning<i>By <a href="https://www.hmc.edu/about-hmc/hmc-experts/yong-darryl/" target="_blank">Darryl Yong</a>, guest blogger, <a href="https://www.hmc.edu/" target="_blank">Harvey Mudd College</a></i><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-3GclMMSv_bE/We5hB2ljxFI/AAAAAAAAK8E/kN6SU44xTkwGYYeWW_Axgv8Bdn5rpNlfQCLcBGAs/s1600/GettyImages-155773349.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1067" data-original-width="1600" height="266" src="https://4.bp.blogspot.com/-3GclMMSv_bE/We5hB2ljxFI/AAAAAAAAK8E/kN6SU44xTkwGYYeWW_Axgv8Bdn5rpNlfQCLcBGAs/s400/GettyImages-155773349.jpg" width="400" /></a></div><br />When we clearly communicate to students the rationale behind our instructional choices, they are more likely to do what we intend, be more motivated to learn, and be more successful. It is an idea that is so simple and obvious and yet often overlooked. <br /><br />Recent <a href="https://www.unlv.edu/provost/teachingandlearning" target="_blank">research</a> suggests that being more transparent with our students can improve their learning. In <a href="http://www.aacu.org/peerreview/2016/winter-spring/Winkelmes" target="_blank">one study</a>, conducted at the University of Nevada, Las Vegas (UNLV), first-year students who took introductory-level courses from instructors trained to be more transparent were more likely to enroll the subsequent year (a 90 percent retention rate compared with the prevailing 74 percent rate for first-time, full-time, first-year students). <br /><br /><a href="https://www.unlv.edu/people/mary-ann-winkelmes" target="_blank">Mary-Ann Winkelmes</a> and her colleagues at UNLV have developed a useful framework for making our teaching more transparent.<br /><ul><li>Be more transparent about the <i>purpose</i> of your course content and activities. What knowledge and skills will students get out of the course and how do those things connect to their lived experiences and personal goals? (Examples: If you have students give oral presentations to the class, explain what they will gain by honing that skill. Connect what students are learning in your class to what they have learned and will learn in future courses.)</li><br /><li>Be more transparent about the <i>tasks</i> that students have to complete. What is the first step that students need to take on an assignment? How can students get themselves unstuck? How can students complete those tasks to get the most out of them? How can students complete those tasks efficiently? (Examples: Describe common errors that students tend to make and how to avoid them. Require students to visit your office hours or your school’s drop-in tutoring center at least once, so that they become familiar with how to get help on their work.)</li><br /><li>Be more transparent about the <i>criteria</i> for success in your class. What do you expect good work in your class to look like? What does bad work look like? (Example: I give students this <a href="http://www.math.hmc.edu/~dyong/goodwritingbadwriting.pdf" target="_blank">handout</a> by MAA Past President Francis Su with annotated examples of good and bad homework problem write-ups. Francis gives this <a href="https://www.math.hmc.edu/~su/math-writing.pdf" target="_blank">version</a> to students in lower division courses.</li></ul>One interesting finding from the work by Winkelmes and her colleagues is that while all students had improved learning outcomes in more transparent classes, the effect was greater for underrepresented students. <br /><br />Why might that be? One possible explanation is that transparency creates a more level playing field for everyone. Let’s face it: students don’t walk into our classes equally prepared to learn. For example, first-generation students tend not to ask for help because they’ve not learned how, or they have coped for so long on their own that they are ashamed to ask for help. And we, because of our mathematical skill, experience, and wisdom, tend to leave a lot of things unsaid because we take them for granted. Those two things combine to confer advantages to students who have mastered the hidden curriculum of our institutions. <br /><br />The key to being more transparent is to learn to see your classroom from each student’s vantage point. What would they find bewildering or frustrating or alienating? One of the best ways to do this is to ask your non-STEM colleagues to look at your syllabus and assignments. Ask them what questions and frustrations they would have. <br /><br />Being more transparent with our students is not the same as coddling them. There are certain aspects of your class that is designed to engage your students in a productive struggle: that challenging proof, difficult derivation, or multi-step computation. There are other aspects of your class that you probably don’t want to cause struggle, like: what you mean when you say you want their work to be “rigorous,” how to find more example problems when the ones in the book just aren’t working for them, or whether they truly belong in your class because they couldn’t follow a calculation that you said was “obvious.” <br /><br />Even if you already say things to your students during class to be more transparent, it is also important to write them down on your syllabus, assignments, and handouts. Why? Students are far too likely to miss important details that are just spoken during class instead of being written down. Also, English language learners and students with learning disabilities will appreciate having the information presented to them in multiple ways. <br /><br />The amount of transparency that you provide to students depends on their maturity and the level of the course. There are times when you don’t want to be explicit about everything. For example, you don’t want to constrain their creativity by priming them with examples, you want them to struggle with figuring out what the first step should be, or you want them to be more independent in their learning. However, even then you can be transparent about your intentional vagueness. For example: “I have given you problems that may have extraneous information or missing information (like the thermal diffusivity of steel) that you will need to look up. I’m doing this to help you acclimate to what it will be like to solve problems in an industrial engineering environment.” <br /><br />A few more suggestions on how to be transparent in your mathematics classroom:<br /><ul><li>The verb “simplify” is ambiguous and overused in mathematics. The context of a calculation determines the form of the answer that is “simplest,” but students often don’t have that intuitive sense when they’re new to the subject. Either help them develop that intuition to know what is “simplest” given the context of the material or problem or be more specific (e.g., say “express the answer as a single fraction with denominator factored as much as possible”).</li><br /><li>At what point are students allowed to use tools like Wolfram Alpha, Symbolab, or Maple? If those tools are allowed, explain how to use those tools in a way that maximizes their learning.</li><br /><li>Share your rationale for how you’ve chosen to assess their learning. (That is, why a final project? Why a written exam? Why is the exam timed or untimed?) Have compelling reasons for those choices that connect with your learning outcomes. Collect strategies that successful students have used to prepare for your assessments and share them with your students. If you assign writing in your class and will use a rubric to assess it, then share that rubric with your students. Consider sharing examples of good writing, annotated in a way that refers to your rubric.</li><br /><li>If you teach via inquiry, explain to students why. This wonderful <a href="http://danaernst.com/setting-the-stage/" target="_blank">activity</a> by Dana Ernst will help students understand how inquiry-based learning can help them develop independence, curiosity, and persistence.</li><br /><li>In my partial differential equations class, I start every class by highlighting a current area of research and the people who are doing it. I acknowledge our field’s lack of inclusivity in the past and that I intentionally showcase women and people of color in these highlights to engage in counter-stereotyping.</li></ul>Unspoken expectations set us up for disappointment and others for frustration. I know that I could be more transparent in my teaching and I invite you to comment below with your strategies and ideas for promoting transparency. <br /><br /><br />Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-23399645063849736372017-10-10T12:16:00.001-04:002017-10-10T14:45:45.986-04:005 Benefits to Having Students Grade Their Own Homework<i>By <a href="http://maateachingtidbits.blogspot.com/p/meet-authors.html" target="_blank">Rejoice Mudzimiri</a>, Contributing Editor, <a href="https://www.uwb.edu/" target="_blank">University of Washington Bothell</a></i><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-mZEPWms2blc/WdzyNKtWkPI/AAAAAAAAK7g/MNgUR7PVY2MmzFUsKUCLJcGlJY5V8YNIACLcBGAs/s1600/GettyImages-858273256.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1067" data-original-width="1600" height="266" src="https://4.bp.blogspot.com/-mZEPWms2blc/WdzyNKtWkPI/AAAAAAAAK7g/MNgUR7PVY2MmzFUsKUCLJcGlJY5V8YNIACLcBGAs/s400/GettyImages-858273256.jpg" width="400" /></a></div><br />Do you have a hard time keeping up with your grading? Do you have to cut back on your homework assignments to make grading manageable? Have you ever considered making your students grade their own homework? Well, if you answered yes to any of these questions, this post is for you! Having students grade their own homework is valuable, saves teachers time, and enhances student learning. I had always hesitated to have my students grade their work, however, when I could not keep up with my grading, I decided to give it a shot. I wish I had considered doing this sooner! <br /><br /><b>How to let students grade their own work?</b><br />Please note that I do not let my students grade all their homework. Personally, I grade every other homework assignment, starting with the first one, so that they get used to my grading style. There is more than one way you can have students grade their work. Some instructors, like <a href="http://www.tandfonline.com/doi/abs/10.3200/CTCH.55.2.72-76" target="_blank">Nelta M. Edwards</a>, hand out a key at the beginning of the lesson on the day the homework is due and let the students grade themselves with the key. If a student is absent, they do not get credit. <br /><br />I go over all the homework problems with my students and then let them assign themselves points depending on what they missed. Then I collect the homework to check on their grading and enter grades. The first time I tried this, I was surprised by how many points my students took off their work. They graded harsher than I would have. Also, they were surprisingly honest about what they did wrong. <br /><br /><b>Benefits of Having Students Grade their Own Homework</b><br />There are several benefits to letting students grade their homework, and the following are my top five:<br /><ol><li><b>Helps student reflection.</b> When I grade my students’ homework, they seem to care more about their grade than what they did wrong. They would not even bother trying to do corrections on their own. However, when I have them grade, they do their corrections as we are going over the homework. This is a valuable learning experience that gives them an opportunity to reflect on their own thinking.</li><br /><li><b>Offers immediate and relevant feedback.</b> <a href="https://www.facultyfocus.com/articles/educational-assessment/benefits-of-a-student-self-grading-model/" target="_blank">Students value identifying their own mistakes shortly after making them</a>. When students grade their work, they get immediate feedback on what exactly they missed, rather than waiting for the instructor days after their homework was turned in for grading.</li><br /><li><b>Reduces instructor grading time.</b> Perhaps an important benefit for instructors, having students grade their homework could reduce their own time spent on grading. If you decide to have your students grade every other homework assignment, that is a 50 percent reduction in your grading time. Since most of our precalculus and calculus classes tend to have high enrollments, a 50 percent reduction in your homework grading is a welcome relief.</li><br /><li><b>Shifts attention away from grades.</b> In addition to the <a href="http://maateachingtidbits.blogspot.com/2017/08/6-ways-to-upend-focus-on-good-grades.html" target="_blank">6 Ways to Upend the Focus on Good Grades</a>, having students grade their homework also refocuses their attention away from grades. Instead, they focus more on why they got the problems wrong, thereby allowing them to take responsibility for their own learning. It also eliminates the need for any grade-related discussions with students as they know exactly how they were graded. According to <a href="http://www.tandfonline.com/doi/abs/10.3200/CTCH.55.2.72-76" target="_blank">Edwards</a>, having students grade their own work “alleviates student anxiety and, subsequently, eases student-teacher conflict by demystifying the grading process and making students feel that they have control over their own evaluation.” When my students ask questions while grading, they are usually more concerned about how many points should be taken off for certain kinds of errors.</li><br /><li><b>Provides students with another learning opportunity.</b> Having students grade their own work can help provide them with another opportunity to learn concepts they might have missed. <a href="https://www.cfa.harvard.edu/sed/staff/Sadler/articles/Sadler%20and%20Good%20EA.pdf" target="_blank">Sadler and Good</a> looked at the correlation of grades by comparing self- and peer-grading with the test grades that a seventh-grade science teacher assigned to 101 students in four classes. They also measured the impact on learning by analyzing students’ performance on an unannounced second administration of the test a week after self- or peer-grading. They noted that “students who graded their peers’ tests did not gain significantly more than a control group of students who did not correct any papers but simply took the same test again,” however “those students who corrected their own tests improved dramatically.”</li></ol><br /><b>References </b><br />Edwards, N. M. (2007). <a href="http://www.tandfonline.com/doi/abs/10.3200/CTCH.55.2.72-76" target="_blank">Student Self-Grading in Social Statistics</a>. <i>College Teaching</i>, 55 (2), 72-76.<br /><br />Sadler & Good (2006). <a href="https://www.cfa.harvard.edu/sed/staff/Sadler/articles/Sadler%20and%20Good%20EA.pdf" target="_blank">The Impact of Self- and Peer Grading on Student Learning</a>. <i>Educational Assessment</i>, 11(1), 1-31. <br /><br />Weimer Maryellen (2009). Benefits of a Student Self Grading Model. <i>Faculty Focus</i>. <a href="https://www.facultyfocus.com/articles/educational-assessment/benefits-of-a-student-self-grading-model/" target="_blank">https://www.facultyfocus.com/articles/educational-assessment/benefits-of-a-student-self-grading-model/</a>. <br /><br />Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-79764453995898510842017-09-26T07:15:00.000-04:002017-09-26T07:15:02.922-04:005 Ways to go Beyond Recitation<i style="background-color: white; color: #222222; font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 13.2px;">By <a href="http://math.wvu.edu/~ef/" target="_blank">E. Fuller</a>, WVU Mathematics (guest blogger)</i><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-gQ6yIwGzWOg/WcPl-xDYfUI/AAAAAAAAK6M/3iQk92MvJMENlnWL4GJBf5kmT7jzXfa0gCLcBGAs/s1600/GettyImages-640924184.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1067" data-original-width="1600" height="266" src="https://3.bp.blogspot.com/-gQ6yIwGzWOg/WcPl-xDYfUI/AAAAAAAAK6M/3iQk92MvJMENlnWL4GJBf5kmT7jzXfa0gCLcBGAs/s400/GettyImages-640924184.jpg" width="400" /></a></div><br />Students at almost every institution of higher education will encounter a recitation as part of their mathematics class at some point, part of the class time set aside to repeat foundational mathematical equations. Graduate teaching assistants (GTAs) are frequently called on to lead these smaller groups of students through the basics of finding the roots of a quadratic equation or computing derivatives using the chain rule. Recitation time is often left for practice of the techniques students learn in lecture. But what if we could do more during this class time? What would that look like? <br /><br />Here are a few approaches you can take to change your students’ experiences during recitation. <br /><b><br /></b><b>1) Focus on getting students to do the work instead of doing it for them. </b>Homework problems are great and it’s sometimes easiest for us to go to recitation prepared to work out many variations of problems we‘ve done ahead of time. The problem is that we already know how to do them. We are better served, as are the students, by providing the space to let them work through the content with guidance. This is perhaps the easiest way to stay true to the content of the class while creating student-focused time. Use inquiry and questioning to get students to tell you how to do the problems instead of the other way around. <br /><br /><b>2) Incorporate group work into your sessions.</b> Build teams and leverage <a href="https://en.wikipedia.org/wiki/Peer_instruction" target="_blank">peer instruction</a> (a method that allows students quick to understand a method or solution to help his or her peers through the problem) so that they can become teachers themselves. Empowering students is always a good thing. <br /><br /><b>3) Get students to communicate what they understand to each other and to the class. </b><a href="http://science.sciencemag.org/content/323/5910/122" target="_blank">Research</a> shows that students need to explain what they understand to really master a topic. This practice forces them to rethink concepts as they try to convey knowledge to someone else. Writing prompts such as ‘Explain why this procedure works…’ or ‘Evaluate this solution and determine if there are errors’ force students to think through ideas and develop reasoning to support conclusions. <br /><b><br /></b><b>4) Have students relate mathematics to their own experiences.</b> To develop a connection with mathematical ideas, students can investigate how <a href="http://c.ymcdn.com/sites/www.amatyc.org/resource/resmgr/Summer_Reading_2015/Pedagogy-Sept2014.pdf?hhSearchTerms=%22deshler%22" target="_blank">mathematics is related to their futures</a> or how multiple levels of mathematics show up in their <a href="https://ed.ted.com/series/?series=math-in-real-life" target="_blank">day to day experiences</a>. Connecting ideas like contour maps to real world activities like <a href="https://ed.ted.com/series/?series=math-in-real-life" target="_blank">hiking</a> can bring even more advanced concepts into life. <br /><br /><b>5) Cultivate an environment where failure is ok and experimentation is encouraged.</b> Students need to learn that trying is important even if it doesn’t lead to the (correct) answer the first time. Making your classroom safe for exploring ideas (<a href="http://maateachingtidbits.blogspot.com/2016/09/5-ways-to-respond-when-students-offer.html" target="_blank">even incorrect ones</a>) helps support a <a href="https://www.youcubed.org/category/teaching-ideas/growing-mindset/" target="_blank">growth mindset</a> among the students, especially important if the classroom is student-centered and they are doing and explaining the mathematics that is happening. <br /><br />It’s important to keep in mind that you can start small - you don’t need to do these things in every meeting. You can pick some manageable topics to try something new with and build from there. It can be hard work and takes time and practice, but your students will benefit from it, and you will find that those recitation sessions can lay the groundwork for some pretty amazing mathematical discoveries for the students. <br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-46991297362900445942017-09-12T12:15:00.001-04:002017-09-12T12:47:34.011-04:00Language matters: 5 Ways Your Language Can Improve Your Classroom Climate<i><a href="https://www.math.hmc.edu/~levy/" target="_blank">Rachel Levy</a>, Contributing Editor, <a href="http://hmc.edu/">Harvey Mudd College</a></i><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-Eclxu4WOH0E/WbgIAUaLjwI/AAAAAAAAK5s/_RddW1su5gsXBJVq--kdpXLWPOCQjXO3ACLcBGAs/s1600/GettyImages-188123530.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="298" src="https://1.bp.blogspot.com/-Eclxu4WOH0E/WbgIAUaLjwI/AAAAAAAAK5s/_RddW1su5gsXBJVq--kdpXLWPOCQjXO3ACLcBGAs/s400/GettyImages-188123530.jpg" width="400" /></a></div><br />The language we use in our classes extends beyond mathematical content. We communicate subtle (and not so subtle) messages about who belongs in the classroom and in our profession. Signals transmit through our level of enthusiasm, quizzical looks at incorrect or convoluted statements, and focus of our attention through eye contact, time to speak, and personal interactions. To avoid perpetuating our <a href="http://cte.virginia.edu/wp-content/uploads/2016/05/Inclusion-by-Design-Survey-Your-Syllabus-Brantmeier-Broscheid-Moore-.pdf" target="_blank">unconscious biases</a> through language, we can recognize them and find ways to reduce their impact on our students. <br /><br />Even when we are careful, at some point our language will likely cause unintended ouch for one of our students. Hopefully we can create feedback mechanisms and classroom environments where they can let us know. But as long as we give grades and write letters of recommendation, the power dynamic in the classroom is unavoidable. This may make it hard for students to speak up and let us know. We hold the responsibility to create a welcoming environment for all of our students. <br /><br />Here are five ways you can modify your language to improve your classroom climate: <br /><br /><b>1. Convey explicitly in your syllabus that you believe that mathematics belongs to everyone</b> and that everyone can be a math doer. Share with your students that <b>making and discussing mistakes are a normal part of learning (and being human)</b>. See <a href="http://cte.virginia.edu/wp-content/uploads/2016/05/Inclusion-by-Design-Survey-Your-Syllabus-Brantmeier-Broscheid-Moore-.pdf" target="_blank">this tool</a> for surveying your syllabus and course design for examples of inclusive syllabus language. <br /><br /><b>2. Be intentional about encouraging questions.</b> Pay attention to which students in the class feel empowered to speak and provide a variety of ways for students to communicate with us and with each other. Many of the <i>Teaching Tidbits</i> have concrete suggestions, such as ways to engage your students through <a href="http://maateachingtidbits.blogspot.com/2017/03/5-reflective-exam-questions-that-will.html" target="_blank">reflective writing</a>; <a href="http://maateachingtidbits.blogspot.com/2016/09/5-ways-to-respond-when-students-offer.html" target="_blank">your responses to incorrect answers</a>; <a href="http://maateachingtidbits.blogspot.com/2017/02/theyre-in-my-office-now-what-3-tips-for.html" target="_blank">office hours</a>; and <a href="http://maateachingtidbits.blogspot.com/2017/04/want-to-give-your-teaching-style.html" target="_blank">inquiry-based learning</a>. <br /><br /><b>3. When they suggest an answer to a question, ask students to justify that answer, whether is it right or wrong.</b> For example, let students know if they don’t provide a justification you will ask “And why would you say that?” This is a technique common in <a href="http://www.worldscientific.com/worldscibooks/10.1142/7892" target="_blank">Russian pedagogy</a>. It allows you to better see how your students are thinking and where they might have gone awry. Students may also <a href="http://maateachingtidbits.blogspot.com/2016/09/5-ways-to-respond-when-students-offer.html" target="_blank">sort out their own errors</a> as they argue their point. <br /><br /><b>4. Avoid perpetuating mathematical language that fails to acknowledge the challenge of learning, such as "clearly, " "only” and “obviously.”</b> These words tend to cue the audience that the speaker thinks the work is trivial. The problem is that even when ideas are taught well, they may not be at all simple for new learners. They also may carry an underlying assumption that all students have had access to the same prerequisite information. Since students enter with a range of previously acquired knowledge and experience, it can be more welcoming to say “the rest requires algebra” instead of “the rest is *just* algebra.” <br /><br /><b>5. Aim to use inclusive and unbiased language.</b> For example, privately request students’ preferred pronouns and preferred names and use them. Pay attention to how you use humor, encouragement and analogies while teaching. Small comments can have a big positive impact. For example, “When a mathematician approaches this problem, she…”. or “When you explain it like that, you are really thinking like a mathematician.” <br /><br />Unintended ‘ouch’ happens. What one person finds funny, another finds offensive. What one person finds welcoming, another finds off putting. We are not perfect and we can’t please everyone all the time. But my hope is that when we establish a constructive classroom climate with <a href="http://maateachingtidbits.blogspot.com/2017/03/3-ways-to-engage-your-students-in.html" target="_blank">opportunities for feedback</a>, students will let us know when they experience an ouch because of some way we communicated. <br /><br />Related Links Karp, Alexander, and Bruce Ramon Vogeli. <i><a href="http://www.worldscientific.com/worldscibooks/10.1142/7892">Russian mathematics education: Programs and practices</a></i>. Vol. 2. World Scientific, 2011. <br /><br /><br /><br /><br /><br />Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-62924115265103245132017-08-29T11:51:00.000-04:002017-08-30T11:26:36.061-04:006 Ways to Upend the Focus on Good Grades<i style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;">By <a href="https://chadtopaz.com/" target="_blank">Chad Topaz</a>, Williams College; and <a href="https://www.linkedin.com/in/judehigdon/" target="_blank">Jude Hidgon</a>, Bennington College (guest bloggers)</i><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-v-NrhBCNKXE/WaWNXud9qDI/AAAAAAAAK5M/tHCsTGy_w-sTHSnzdBXT-HxW0VSKjP1PgCLcBGAs/s1600/GettyImages-537006210.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="483" data-original-width="724" height="266" src="https://3.bp.blogspot.com/-v-NrhBCNKXE/WaWNXud9qDI/AAAAAAAAK5M/tHCsTGy_w-sTHSnzdBXT-HxW0VSKjP1PgCLcBGAs/s400/GettyImages-537006210.jpg" width="400" /></a></div><br />As a math educator, there is a good chance this thought has crossed your mind: “All my students care about is grades. They don’t seem to care about learning the material.” <br /><br />In the parlance of educational psychology, this complaint suggests a tension between mastery goal orientation (e.g., “I want to understand the material”) and performance goal orientation (e.g., “I want to get a good grade”). Research suggests that learning is optimized when learners have high levels of both mastery and performance orientations. However, the structure of higher education arguably stresses performance over mastery. We assign grades, grades get used by educational institutions and by society, and there’s little wonder that students care about the grade more than mastering the material. <br /><br />Grades remain relevant, and we certainly do not advocate their abolition. But it is important to balance an attention to grades with emphasis on mastering course material. Here are six strategies we have implemented that we have found to support this balance. <br /><br /><b>1. Design a multifaceted assessment scheme.</b> For the sake of example, consider two different schemes for determining a student’s final grade. <br /><br />Scheme I: two midterm exams worth 30% each and a final exam worth 40%. <br /><br />Scheme II: 10 homework assignments worth 2% each, daily informal reflective writing assignments worth 20% total, 5 unit tests worth 8% each, and a final exam worth 20%. In this second scheme, the high frequency of assessments renders each one lower stakes. <br /><br />Additionally, <a href="https://www.nap.edu/read/9853/chapter/10">students benefit from frequent, ongoing assessment because it provides feedback on their learning</a> and more opportunities to correct misconceptions as they are forming, rather than once they are baked into students’ brains. Frequent assessments need not be labor-intensive. When available, TA’s could perform the grading, and/or an instructor could use online assessments with automatic grading as needed. For items such as informal writing assignments, one could also use a low-labor point allocation system, for instance, 0 = assignment not turned in; 1 = assignment turned in but of low quality; 2 = assignment completed at a satisfactory level. <br /><br /><b>2. Use a drops policy. </b>For example, if there are 12 weekly homework assignments during the term, tell students that the lowest two homework grades are automatically dropped. However, insist that they benefit from this privilege only if they turn in all assignments completed fully. This system provides a sense of security to students that they can struggle in good faith and perhaps not “get it” right away, but it also discourages them from simply not doing the work. <br /><br /><b>3. Allow corrections.</b> Consider letting students make corrections to quizzes and exams to earn back half of the points they missed. This opportunity encourages students to think about the errors they made, and emphasizes that the midterm is a learning opportunity. <br /><br />For added learning opportunities, ask students to add to their corrections a discussion of what they got wrong, why their corrected answers or analyses are better than their original, and how they will integrate what they’ve learned to avoid similar errors in the future. This procedure models good scientific inquiry (when we get something wrong, it’s a beginning, not an ending) and tells the student that what you value is that they’ve learned, not that they are perfect. If written corrections are too onerous, an instructor or TA could allow students to perform corrections oral exam style during a designated time period. <br /><br /><b>4. Structure grades as formative feedback.</b> Don’t merely give numerical grades. A numerical grade says to a student “the number or letter assigned to you is the most important thing.” On the other hand, written feedback can correct mathematical misconceptions, and it provides a metacognitive moment in which students can reflect on their level of understanding of the material. We encourage you, however, not to just tell students the correct answer; instead, point to errors, make suggestions, and then encourage students to correct their own work. To reduce any additional grading load, consider leveraging technology to offer audio feedback. If giving feedback to every student individually is not feasible, hold a single class meeting or discussion section to go over common mistakes, and require students who want to drop their lowest grade (strategy 1 above) or to submit corrections (strategy 3 above) to attend in order to be eligible. <br /><br /><b>5. Make mathematics verbal.</b> Ask learners to discuss what they understand and don’t understand in words, not just in calculations. Encourage learners to consider the application of your course concepts to real-world scenarios, to other courses, or to the students’ lives outside of school. Find ways to encourage student self-talk (<a href="http://maateachingtidbits.blogspot.com/2017/03/3-ways-to-engage-your-students-in.html" target="_blank">written</a> or <a href="http://maateachingtidbits.blogspot.com/2017/02/engage-your-students-in-60-seconds-or_28.html" target="_blank">oral</a>) about what they are learning. This can be done via a simple blog post, or as a “think, pair, share” opportunity at the start of class. Invigilate these sessions through a Socratic approach; randomly call on two groups from a larger class to report on what they discussed to help ensure that they focus on the task at hand. These activities encourage metacognition, which has been <a href="http://psycnet.apa.org/record/1988-29536-001" target="_blank">correlated with mastery goal orientation</a>. <br /><br /><b>6. Discourage (or even abolish) discussions about grades or points.</b> We believe that it is our responsibility as instructors to constantly direct our students’ focus to be on learning. In our syllabi, we use a statement like this, and we stick by it, referring students back to the policy as needed: “The purpose of grades is to provide formative feedback that aids your learning. I keep course grades in the online gradebook, so you can always check them there. But what matters is learning. I’ll enthusiastically talk to you about your learning anytime and I encourage discussions in which we go over the work you have completed. These conversations let me hear about your challenges and questions, and provide important learning opportunities. However, my rule is that we shouldn’t talk (and especially haggle) about the points or letter grade assigned unless I have made a clerical error.” <br /><br />We recognize that some of the suggestions above create more work for instructors; we have offered a few options for helping to reduce this additional load in instructional settings with large class sizes but without the benefit of TAs or grading support. We’ve found that having more (but lower-stakes) graded items, allowing students to make corrections and giving more corrective feedback all contribute to an environment where the focus is on learning. Just as we would tell our students that more time studying will help their learning, we believe more time spent on these grading activities will help strengthen the learning-focused culture we want. <br /><br /><br /><br /><br /><br />Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-66998580988858402452017-04-25T07:10:00.000-04:002017-04-26T09:53:27.165-04:00Read the 3 Most Popular Teaching Tidbits Posts of the Year <i style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;">By <a href="http://maateachingtidbits.blogspot.com/p/meet-authors.html" target="_blank">Lew Ludwig</a> (Editor-in-Chief), <a href="http://denison.edu/" target="_blank">Denison University</a></i><br /><br />As the academic year comes to a close, <i>Teaching Tidbits </i>is headed for summer vacation. We hope you enjoyed the inaugural year of the blog and found it useful for your classroom. As you prepare for next year’s classes, be sure to read our posts from the last year, particularly our three most popular posts:<br /><ul><li><a href="http://maateachingtidbits.blogspot.com/2016/09/5-ways-to-respond-when-students-offer.html" target="_blank">5 Ways to Respond When Students Offer Incorrect Answers</a></li><li><a href="http://maateachingtidbits.blogspot.com/2016/10/how-to-deal-with-math-anxiety-in.html" target="_blank">How to Deal with Math Anxiety in Students</a> </li><li><a href="http://maateachingtidbits.blogspot.com/2017/03/5-reflective-exam-questions-that-will.html" target="_blank">5 Reflective Exam Questions That Will Make You Excited About Grading</a> </li></ul>While the blog is on summer holiday, we encourage you to seek out other sources of good teaching tips, like attending the ‘<a href="http://www.maa.org/meetings/mathfest/program-details/2017/contributed-paper-sessions" target="_blank">Encouraging Effective Teaching Innovation</a>’ contributed paper session at this year’s <a href="http://www.maa.org/meetings/mathfest-2017" target="_blank">MAA MathFest</a> in Chicago this summer. We also welcome your suggestions of topics or ideas for future posts by contacting: <a href="mailto:teachingtidbits@maa.org">teachingtidbits@maa.org</a>. Enjoy your summer and see you in the fall.<br /><br />-The <i>Teaching Tidbits</i> TeamMathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-14315647267802811752017-04-11T07:02:00.000-04:002017-04-17T16:36:17.911-04:00Want to Give Your Teaching Style a Makeover This Summer? Here’s How.<i style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;">By <a href="http://maateachingtidbits.blogspot.com/p/meet-authors.html" style="color: #888888; text-decoration-line: none;" target="_blank">Dana Ernst</a>, </i><i style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;">Contributing Editor,</i><i style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;"> <a href="https://nau.edu/" style="color: #888888; text-decoration-line: none;" target="_blank">Northern Arizona University</a></i><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-wjR7ZpDEO-k/WOvy9Lmv36I/AAAAAAAAK0c/CFlLQM0xj0kfu8M0v_kyHEj1OgQMME8WwCLcB/s1600/GettyImages-468988149.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="266" src="https://4.bp.blogspot.com/-wjR7ZpDEO-k/WOvy9Lmv36I/AAAAAAAAK0c/CFlLQM0xj0kfu8M0v_kyHEj1OgQMME8WwCLcB/s400/GettyImages-468988149.jpg" width="400" /></a></div><br />Active learning is all the rage these days, and with good reason. As teachers embrace active learning, students are building problem solving skills that promote analysis and evaluation of the content they are given in the classroom. Read on to learn how active learning can give your teaching style a makeover.<br /><br />Active learning has been gaining traction over the past few years, aided in part by public approval from several entities, including the 15-member society presidents of the <a href="http://www.cbmsweb.org/Statements/Active_Learning_Statement.pdf" target="_blank">Conference Board of the Mathematical Sciences</a> in 2016. Active learning comes in several shapes and sizes, and inquiry-based learning (IBL) is just one of many forms. In particular, the IBL community has grown up to be very active and supportive in the past few decades. Loosely speaking, IBL is a pedagogical framework characterized by two essential principles:<br /><br /><ul><li>students deeply engage in meaningful problems, and </li><li>students collaboratively process ideas. </li></ul>According to <a href="http://www.colorado.edu/eer/research/steminquiry.html" target="_blank">education research</a>, these "twin pillars" of IBL are at the core of most IBL implementations.<br /><br />Here I have summarized a few resources for learning more about IBL and active learning, and how to get started. This list is certainly not exhaustive and is not intended to be a "how-to guide.” <br /><br /><b>Workshops and conferences</b><br /><ul><li>Head to Chicago for <a href="http://mathfest.maa.org/" target="_blank">MAA MathFest</a> in July and attend a number of sessions dedicated to active learning and/or IBL. </li><li><a href="http://www.inquirybasedlearning.org/ibl-conference/" target="_blank">Inquiry-Based Learning Conference</a>: As the name implies, this annual summer conference is devoted to IBL. It's also my favorite conference. It's inspiring to be surrounded by so many educators that are devoted to engaging and empowering students. The conference is also run in conjunction with MAA MathFest, so participants can get even more out of this double meeting.</li><li><a href="http://www.inquirybasedlearning.org/workshops/" target="_blank">IBL Workshops</a>: The NSF-sponsored IBL Workshops are practical, hands-on, and interactive workshops for college math instructors interested in teaching via IBL or hybrid IBL. There are three workshops offered during the summer of 2017: </li><ul><li>DePaul University, Chicago Illinois: June 20-23, 2017 </li><li>Cal Poly State University, San Luis Obispo, California: June 27-30, 2017 </li><li>Nazareth College, Upstate New York: July 18-21, 2017</li></ul></ul><b>Summer Reading List</b><br /><ul><li>There are a variety of <a href="http://store.maa.org/site/index.php?app=cms&ns=display&sid=s5l6a2r9j6itbzhbc3dwb4pb14jippy8" target="_blank">MAA textbooks</a> that are designed for an active learning approach, for example: </li><ul><li><a href="http://www.maa.org/press/ebooks/number-theory-through-inquiry" target="_blank"><i>Number Theory Through Inquiry</i></a>, David C. Marshall, Edward Odell, and Michael Starbird </li><li><a href="http://www.maa.org/press/books/distilling-ideas-an-introduction-to-mathematical-thinking" target="_blank"><i>Distilling Ideas: An Introduction to Mathematical Thinking</i></a>, Brian P. Katz and Michael Starbird </li><li><i><a href="http://www.maa.org/press/ebooks/beyond-lecture" target="_blank">Beyond Lecture: Resources and Pedagogical Techniques for Enhancing the Teaching of Proof-Writing Across the Curriculum</a></i>, Rachel Schwell, Aliza Steurer, and Jennifer F. Vasquez (editors). While not a textbook, this book describes pedagogical techniques in proof-based courses that extend beyond standard lecture.</li></ul><li><a href="http://www.jiblm.org/" target="_blank"><i>Journal of Inquiry-Based Learning in Mathematics</i></a>: JIBLM publishes course materials that are designed to be used in courses that utilize IBL. All of the materials are professionally refereed, classroom-tested, and free to download. Materials are available for a wide variety of courses, from calculus through proof-based courses. </li><li><a href="http://www.artofmathematics.org/" target="_blank">Discovering the Art of Mathematics</a>: The DAoM library includes 11 inquiry-based books freely available for classroom use. These texts can be used as semester-long content for themed courses (e.g. geometry, music and dance, the infinite, games and puzzles), or individual chapters can be used as modules to supplement typical topics with classroom tested, inquiry-based approaches.</li></ul><b>Other resources </b><br /><ul><li><a href="http://maamathedmatters.blogspot.com/" target="_blank">Math Ed Matters</a>: This MAA-sponsored column explores topics and current events related to undergraduate mathematics education. Posts will aim to inspire, provoke deep thought, and provide ideas for the mathematics—and mathematics education—classroom. Most of the posts address IBL in some way. </li><li><a href="http://www.maa.org/community/sigmaas" target="_blank">IBL SIGMAA</a>: There is a newly-formed Special Interest Group of the MAA (SIGMAA) devoted to IBL. </li><li><a href="http://theiblblog.blogspot.com/" target="_blank">The IBL Blog</a> by Stan Yoshinobu (Cal Poly): This blog focuses on promoting the use of IBL methods in the classroom at the college, secondary and elementary school levels. </li><li><a href="https://twitter.com/hashtag/mathchat?lang=en" target="_blank">#mathchat</a>: This is active Twitter hashtag that is used by teachers, educators, students, or anyone else interested in math and math education to highlight conversations related to math education.</li></ul><br /><br />Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-63405471169314918452017-03-28T09:59:00.001-04:002017-03-28T10:01:06.725-04:003 Ways to Engage Your Students in Reflective Writing <i><a href="https://www.math.hmc.edu/~levy/" target="_blank">Rachel Levy</a>, Contributing Editor, <a href="http://hmc.edu/">Harvey Mudd College</a></i><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-nyFF2swvuz4/WNpsNNIWQDI/AAAAAAAAKzc/N9VKKQFcH-cMQMYMC6CPiDGBBRcr1koEQCLcB/s1600/GettyImages-184298794.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="266" src="https://1.bp.blogspot.com/-nyFF2swvuz4/WNpsNNIWQDI/AAAAAAAAKzc/N9VKKQFcH-cMQMYMC6CPiDGBBRcr1koEQCLcB/s400/GettyImages-184298794.jpg" width="400" /></a></div><br />Contemplation and reflective writing can be powerful tools for teaching and learning. Students benefit from considering the way that they learn and do mathematics (in addition to thinking directly about the subject matter). This intellectual activity is often called <a href="https://www.amazon.com/Cognitive-Science-Mathematics-Education-Schoenfeld/dp/0805800573" target="_blank">metacognition</a>. Written reflections can also help professors get to know their students, both personally and mathematically. <br /><br /><b>Three ways I engage my students in reflective writing:</b><br /><br /><ol><li>Have students write periodically in a physical journal. Assignments could be very general, such as “How’s it going in this class?” to more structured prompts, such as “Describe your process for solving one of the homework problems you found challenging” or “Name three strategies you employ when you get stuck on a problem.” When the journal is a physical book, I collect and return the posts with a smiley face, sticker or small comment so students know I looked. I used to use the old fashioned bluebooks created to administer exams because they only cost $0.10. You could use an online submission process. Paper is nice, because students seem more likely to doodle fun pictures.</li><br /><li>Ask students to answer a question or two (for credit) at the end of a quiz or exam. I like this approach because it communicates that I value the writing and I will already be in “grading” mode when I look at the result. On the downside, students might be more stressed and less attentive to the task during a quiz. Francis Su has outlined his approach to reflective exam questions in a previous <a href="http://maateachingtidbits.blogspot.com/2017/03/5-reflective-exam-questions-that-will.html" target="_blank"><i>Teaching Tidbits </i>post</a>.</li><br /><li>Direct students to complete an “<a href="http://maateachingtidbits.blogspot.com/2016/11/did-they-catch-that-need-for-exit.html" target="_blank">exit ticket</a>” or “minute paper” at the end of class. A prompt might ask what the student found most interesting or confusing that day. Sometimes I encourage students to pose a “what if” question. You could use slips of paper or a web form for these end of class questions. Web forms can make it easier to skim and manage comments from a large class.</li></ol>Keep reading for more sample questions. <br /><b><br /></b><b>Connectedness Often Translates to Engagement </b><br />The more you know about your students, the easier it can be to choose a combination of strategies that promote teaching, learning, transfer and affective gains. <br /><br />In their reflective writing, my students have shared their hobbies, preferences/likes/dislikes, hopes and dreams, difficulties and triumphs in the course, questions about the subject matter, personal challenges, undiagnosed or unreported learning disabilities and general feedback on their experience in the course. I often indirectly learn about my students’ preparation for the course, attitude, culture, maturity, life pressures and personal goals. <br /><br />A big caveat: some faculty do not want to know these kinds of things about their students. It is a personal choice, of course, and faculty should be aware that they are opening the door to some potentially heavy topics. Some students will want to share very personal information. Others will not. With this in mind, I try to ask relatively unobtrusive questions (such as the ones above) that students can answer many ways. Even the question, “How’s it going in this class?” has started conversations leading to decades-long connections with former students. <br /><br />I recommend searching on the terms “math” and “metacognition” for related reading opportunities. Start with the reference linked at the end of this post. <br /><b><br /></b><b>Sample Questions</b><br />These questions are from my Spring 2016 differential equations course in-class quizzes.<br /><br /><ul><li><i>What is something that you do that gives you joy and rejuvenates you? Try to think of something that you don’t judge yourself about - something that makes you happy whether or not you do it “well.” </i></li><li><i>When I encounter mathematics that challenges me, I use these strategies to get unstuck (circle the letters of everything you try): (a) go to office hours (b) sleep on it (c) go to peer tutoring (d) look online (e) read a textbook (f) take a break (g) go over my notes (h) eat/drink a snack (i) watch a DE video (j) ask a friend (k) other: </i></li><li><i>If you had a magic wand and could change one thing about our college, what would you change? </i></li><li><i>What’s something you are looking forward to this summer? (Write something or draw something.)</i></li></ul>When my colleague and I forgot to put a journal question on one quiz we were surprised that some of our students wrote their own questions and answered them! <br /><b><br /></b><b>Related Links: </b><br /><br />Schoenfeld, A. H. (1987). What's all the fuss about metacognition? In A. H. Schoenfeld (Ed.), <i><a href="https://www.amazon.com/Cognitive-Science-Mathematics-Education-Schoenfeld/dp/0805800573" target="_blank">Cognitive Science and Mathematics Education</a></i> (pp. 189-215). Hillsdale, NJ: Lawrence Erlbaum Associates. Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-33328731079735766312017-03-13T07:27:00.000-04:002017-03-13T09:14:53.232-04:005 Reflective Exam Questions That Will Make You Excited About Grading<i><a href="https://www.math.hmc.edu/~su/" target="_blank">Francis Su</a>, Guest Blogger, <a href="http://hmc.edu/">Harvey Mudd College</a></i><br /><i>Want to read more blogs like this? Subscribe to our email list in the right sidebar.</i><br /><blockquote class="tr_bq" style="text-align: left;"></blockquote><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-v8jxpVgX4CA/WML-DEB1D8I/AAAAAAAAKzI/iitIUKm3plM21579biAzVWHQGBkQPIkTwCLcB/s1600/GettyImages-622042632.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="205" src="https://1.bp.blogspot.com/-v8jxpVgX4CA/WML-DEB1D8I/AAAAAAAAKzI/iitIUKm3plM21579biAzVWHQGBkQPIkTwCLcB/s400/GettyImages-622042632.jpg" width="400" /></a></div><br /><blockquote class="tr_bq" style="text-align: left;">“To doubt everything, or, to believe everything, are two equally convenient solutions; both dispense with the necessity of reflection.” -Henri Poincare, <i>Science and Hypothesis</i> </blockquote>Do your exams accurately represent what you value in your course? Only after many years of teaching did I begin to ask that question.<br /><br />For instance, one of the goals for my upper division courses is for students to be able to articulate what mathematicians do. Another goal I have is for students to learn to generate their own questions for further investigation. Even though I might have seen a student exhibit such skills in the occasional conversation, the tools that I greatly valued were not showing up regularly in how I evaluated student progress.<br /><br /><b>Why Use Reflective Exam Questions </b><br />To give students opportunities to demonstrate these reflective skills, I began to assign reflection exercises as exam questions. There are certainly other ways to elicit such information--for instance, you could assign research papers or reflection journals--but I was interested in something that wouldn’t be additional work. Putting a question on an exam was a simple way to signal to students that I cared about their ability to process and reflect on what they were learning, in addition to the mathematical reasoning I expected them to demonstrate.<br /><br />What I didn’t anticipate was the benefit reflective exam questions would have for me!<br /><br />First of all, these questions made exams much more interesting to grade. (If you know me, you know that while I love teaching, I have never enjoyed grading. The monotony!) Now I say to myself: ‘if you grade all the other questions, then you get to read the reflections!’ Without reflective questions, the exams show very little of my students’ personalities. Having reflective questions helps me see the unique ways my students are thinking and feeling, and that gives me joy.<br /><br />The second reason for adding reflective questions to my exams is that I often learn things from my student responses that help me become a better teacher. Sometimes students will explain an idea in a way that I had not considered. For instance, in reflecting about the importance of definitions in mathematics, one student described a definition as a choice of what conversation you are going to have with the material. That’s a metaphor that I now use in my own teaching!<br /><br /><b>Assigning Points to Reflective Exam Responses </b><br />My advertised grading system for such questions is simple: give me a thoughtful answer, and you’ll get full points. Less thoughtful responses get slightly fewer points, but students rarely fail to give thoughtful answers. That also makes my heart happy! Depending on the question, you may wish to give your students the question in advance, so they will have time to think of thoughtful answers and they can reflect on it as they study for their exam.<br /><br />Below are five examples of questions I have used in the past, and some actual responses I have received.<br /><br /><ol><li><b>What three theorems did you most enjoy from the course, and why? Choose one theorem of moderate difficulty and reconstruct its proof. </b><br /><br />I like this question, because the answers often surprise me. What I think is interesting is not always what they think is interesting. <br /><br />One student responded: <i>The moment in class where I was truly blown away was when we applied Van Kampen’s Theorem on the torus to derive its fundamental group...the simplicity of its application is a moment I will never forget. </i></li><br /><li><b>Formulate a research question related to the course material that you would like to answer. (You do not have to answer the question. Just ask a good question whose answer is unknown to you, and doesn’t have an obvious answer based on what you know from the course.) </b><br /><br />One student responded: <i>Is there a classification theorem for 3-manifolds? </i>(This came after we had discussed the classification of surfaces.) <br /><br />The main value of this question is that you signal to students that you value question-asking and conjecture-making. But students often rediscover questions of historical significance that lead to important conjectures or theorems. In such cases I have an opportunity to affirm the student’s intuition for asking a good question, as well as to answer it.</li><br /><li><b>Reflect on your overall experience in this class by describing an interesting idea that you learned, why it was interesting, and what it tells you about doing or creating mathematics. </b><br /><br />One student responded: <i>One interesting thing I learned from the class was the equivalence of open-cover compactness and subsequential limit compactness. Both of the definitions are quite abstract, but both end up being extremely significant in their consequences. I think this seeming disconnect between definition and consequence emphasizes the importance of definitions in mathematics. Definitions essentially frame the type of conversation you are going to have--some definitions that seem different produce conversations with similar results. Many definitions lead to conversations with results that are hard to predict.</i><br />What a thoughtful answer! I learned a new way to explain the importance of definitions from this response.</li><br /><li><b>How did the ideas of this course enlarge your sense of what it means to do mathematics? </b><br /><br />One student responded: <i>This class gave me a much better understanding of what it means to do mathematics than I had in the past. Most of our problem sets in other classes were applying theorems that we learned in class, and the problems were roughly of comparable difficulty. However, with this class, we did much of the learning on our own, through results that we proved. In addition, some of the problems were relatively straightforward, but there were several very challenging problems, where my group didn’t even have a clear idea where to start. This seems much more realistic to the life of a mathematician, where problems don’t present themselves in homogeneous sets. </i><br /><br />From this response, I could see that my student was able to articulate what mathematicians do. Goal accomplished.</li><br /><li><b>I have emphasized the importance of struggling in mathematics: that it’s normal and part of the process of learning. Describe an instance, so far in this course, where you struggled with a problem or concept, and initially had the wrong idea, but then later realized your error. In this instance, in what ways was a struggle or mistake valuable to your eventual understanding? </b><br /><br />This is one of the best reflective questions I have used. The prompt helps my students recall specific struggles that have helped them, and reinforces a theme I have emphasized in class. If you’d like to see a wonderful response to this question, you might enjoy my MAA FOCUS magazine article “<a href="http://digitaleditions.walsworthprintgroup.com/publication/index.php?i=307612&p=20" target="_blank">The Value of Struggle</a>.” <br /><br />I’m sure you can think of other reflective questions that can advance your goals for your courses. Student reflections will help your students grow as learners and will help you grow as a teacher too.</li></ol>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-89988085870346941522017-02-28T09:30:00.000-05:002017-02-28T16:38:43.382-05:00Engage Your Students in 60 Seconds or Less<i style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;">By <a href="http://maateachingtidbits.blogspot.com/p/meet-authors.html" target="_blank">Lew Ludwig</a> (Editor-in-Chief), <a href="http://denison.edu/" style="text-decoration: none;" target="_blank">Denison University</a></i><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-DYqe7OdCrp4/WLSSerFAjxI/AAAAAAAAKxw/HF2f0fee70IzHEwReERWTkCIPm3kn6TWwCPcB/s1600/Bueller.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="163" src="https://4.bp.blogspot.com/-DYqe7OdCrp4/WLSSerFAjxI/AAAAAAAAKxw/HF2f0fee70IzHEwReERWTkCIPm3kn6TWwCPcB/s400/Bueller.gif" width="400" /></a></div><br />Ever feel like the teacher from the movie "Ferris Bueller's Day Off,” asking a question and just getting silence back? We’ve all had those moments in the classroom. You pose a well-crafted question to the class, and no one responds.<br /><br /> Several years ago, I watched <a href="https://www.ma.utexas.edu/users/starbird/" target="_blank">Dr. Michael Starbird</a> of the <a href="http://www.utexas.edu/" target="_blank">University of Texas – Austin</a> employ a simple technique that has forever changed my own teaching. After you pose your question to the class, pause, then state a slightly rephrased version of the same question. After this, ask your students to take two minutes to discuss with a nearby neighbor.<br /><br />I saw Dr. Starbird use this technique at a national convention with 300 attendees in the room. After two minutes, the room of strangers was vibrating with engaging discussion. Dr. Starbird could then point to a person and ask, “What did your neighbor say?” Not only did this technique prompt active discussion and engagement, but avoids the risk of embarrassment when putting someone on the spot.<br /><br />For those familiar with this technique, it is a variation on the Think-Pair-Share model that can help learners of all ages. In this method, the students might first reflect individually on a question, maybe for several minutes writing notes or solving a math problem (Think). Next, the students would turn to a nearby neighbor to discuss their work (Pair). Finally, the instructor calls on students to report (Share).<br /><br />I have slightly modified this technique to assure a varied discussion: every week I randomly assign students to a pair. These pairs have to physically sit next to each other for that week. When I ask the class to discuss something with a neighbor, they know exactly where to turn. <br /><br />Does it work? First, the weekly pairing creates a notable community within the classroom as students get to better know each other over the course of the semester. This is very apparent by mid-semester when I walk into the classroom to see students actually chatting with one another as opposed to being absorbed in their own thoughts. Second, students often highlight this technique in the course evaluations. They appreciate the opportunity to test out ideas in a low-stakes environment. Lastly, the class discussion is much richer. Since we have a variety of ideas and viewpoints being shared, the discussion goes much deeper and broader than when only one student answers my well-crafted question. <br /><br />The “talk to a neighbor” technique is extremely easy to employ, and the time required is very flexible. Sometimes I will give them as little as 30 seconds to compare ideas while longer exercises might call for as much as ten minutes. I circulate the room nudging discussions and gauging understanding. In a given 50-minute class period I use this technique three to ten times, depending on the topic and the mood of the class. I highly recommend you give it a try in your next class. You will be amazed at how quickly your students catch on and become engaged in their learning. <br /><br /><b>Recommended app:</b> Poll Everywhere <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-oF6KQzQAsyg/WLST3fdfYwI/AAAAAAAAKx4/75KxSQ7lhGgJVB8fETeYWf14bp8Dt_fhwCPcB/s1600/poll%2Beverywhere.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-oF6KQzQAsyg/WLST3fdfYwI/AAAAAAAAKx4/75KxSQ7lhGgJVB8fETeYWf14bp8Dt_fhwCPcB/s320/poll%2Beverywhere.JPG" width="254" /></a></div>This semester, <i>Teaching Tidbits</i> will focus on useful and engaging apps. A helpful app for the "talk to your neighbor” technique is <a href="https://www.polleverywhere.com/" target="_blank">Poll Everywhere</a>. Give students a link to respond to your question in the app via mobile phone, Twitter, or web browser. Responses are posted online or in a Powerpoint presentation. <br /><br />This app has many of the same advantages of "talk to your neighbor" but functions more like a clicker system because students can provide their responses anonymously. This makes it a valuable tool for formative assessment and quick checks on difficulty level, pacing and retention. <br /><br />The free version allows for up to 40 users with a variety of question types and displays. Upgrades allow for more users and additional reporting and tracking options. <br /><br />Pose a question, visualize responses via Poll Everywhere, and let the discussions begin! Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-64072501186469713532017-02-14T07:32:00.000-05:002017-02-14T07:32:01.542-05:00They’re in My Office - Now What? 3 Tips for Productive Office Hours<i>By <a href="http://maateachingtidbits.blogspot.com/p/meet-authors.html" target="_blank">Jessica Deshler</a>, </i><i>Contributing Editor, </i><i><a href="http://www.wvu.edu/" target="_blank">West Virginia University</a></i><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-h8qcKzALD_4/WKI2hz1B8sI/AAAAAAAAKxY/SsUzIDOtP-Y0nktcWakNlrec4Hkt99QqgCLcB/s1600/GettyImages-465010196.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="213" src="https://4.bp.blogspot.com/-h8qcKzALD_4/WKI2hz1B8sI/AAAAAAAAKxY/SsUzIDOtP-Y0nktcWakNlrec4Hkt99QqgCLcB/s320/GettyImages-465010196.jpg" width="320" /></a></div><br />For students, office hours can be an opportunity to catch up or gain additional insight to coursework that challenges them. Recently, we posted about “<a href="http://maateachingtidbits.blogspot.com/2017/01/5-successful-ways-to-get-students-to.html" target="_blank">5 Successful Ways to Get Students to Office Hours</a>,” but what do we do when they come? How do we make the most out of that time so that it’s productive for faculty and students? Here are a few tips you can try to help your students during office hours:<br /><ol><li><b>Tell them your expectations.</b> Let students know early in the semester what your expectations are for office hours. Do you expect them to bring their attempts at working out problems with them to see you? Do they have to keep and bring a journal? What type of pre-meeting preparation do you require of them? Ideally, these expectations should be outlined in the syllabus and during your first class. Be specific and repeat your expectations throughout the semester.<br /></li><li><b>Once you have expectations set, stick to them.</b> Reserve the right to reschedule a meeting if a student shows up completely unprepared to engage in a productive conversation. This is fair to students who have put in the expected effort ahead of time and come to your office with specific questions. Specifically, if students have not done the readings or assignments, or have missed class, give them an additional “assignment” of reviewing another student’s class notes before coming back to you to ask for clarification (and bringing those notes with them so you know they did it - it was an assignment after all).<br /></li><li><b>Let them do the work.</b> Much like class time, the time spent in office hours is most effective if your students spend it working through the mathematics instead of watching you do problems on the board. Your goal as an instructor is not to show them how to solve questions, but to teach them how to go about solving questions and how to think while problem solving. Leading students through the work is incredibly valuable. Questions like “How would you get started on this one?” and “What have you tried so far?” are ways to help students talk to you about their troubles in working through problems. </li></ol><b>Recommended tools:</b>Check out these two tools to help you schedule office hours: <a href="http://youcanbook.me/">youcanbook.me</a> and a cool little setting in <a href="https://support.google.com/calendar/answer/190998?hl=en" target="_blank">Google calendar</a>. Both of these allow you to set aside specific blocks of time in your calendar for students, and allows them to book just part of that time. They’ll get reminders (always helpful for students) and you’ll know that they’re actually going to show up! Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-734282906725806669.post-67567302820032615152017-01-31T09:00:00.000-05:002017-01-31T09:18:54.644-05:005 Successful Ways to Get Students to Office Hours<i>By <a href="http://maateachingtidbits.blogspot.com/p/meet-authors.html" target="_blank">Rejoice Mudzimiri</a>, Contributing Editor, <a href="https://www.uwb.edu/" target="_blank">University of Washington Bothell</a></i><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-oNvwyrOj0Ko/WJCcxFs_P7I/AAAAAAAAKvg/iN7If53WxS8aSOj9mQJ_NzYQ-biNvufawCLcB/s1600/GettyImages-511024264.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="213" src="https://4.bp.blogspot.com/-oNvwyrOj0Ko/WJCcxFs_P7I/AAAAAAAAKvg/iN7If53WxS8aSOj9mQJ_NzYQ-biNvufawCLcB/s320/GettyImages-511024264.jpg" width="320" /></a></div><br />Are you tired of sitting alone during your office hours waiting for students to show up? I used to feel the same way, until this past fall quarter when my students came to office hours in better numbers than ever. What changed?<br /><br />Studies show that office hour visits are <a href="http://www.tandfonline.com/doi/abs/10.1080/15512169.2013.835554" target="_blank">positively correlated</a> to academic performance (Guerrero & Rod, 2013). More so, they are an important opportunity for faculty-student communication and interaction. So how can you get students to attend your office hours?<br /><ol><li><b>Timing.</b> When it comes to office hours, timing is everything. The best ways to schedule office hours include:</li><ul><br /><li><i>Avoiding conflicts with other classes</i>. If office hours are scheduled during times that most students have classes, chances are very few students will be able to find time to attend your office hours. As part of <a href="http://www.facultyfocus.com/articles/teaching-professor-blog/office-hours-redux/" target="_blank">scheduling your office hours</a>, you should find out peak times when most of your students are available.</li><br /><li><i>Eliciting student input</i>. One of my colleagues who has had success with getting students to come for office hours administers a survey the first day of class to elicit student input on the times that work best for them. She then schedules her office hours depending on the times that most of the students are available. Using <a href="https://www.polleverywhere.com/" target="_blank">Poll Everywhere</a> provides a quick way to survey students on their preferred times.</li></ul><br /><li><b>Location.</b> Some students are not comfortable with meeting in their instructor’s office. Alternative office hour locations include:</li><ul><br /><li><i>Public Places</i>. Holding office hours in public areas such as a student lounge or conference room may be more relaxing for students. A colleague of mine holds her office hours in our “foyer” because her office is very far away from the building where she teaches and this makes it convenient for students to attend her office hours. I hold my office hours in the conference room right next to my office - with big white boards - that provide a lot of working space for a number of students. This allows me to accommodate more students at the same time. Students worked either individually or in groups during my office hours.</li><br /><li><i>Virtual Office Hours</i>. Holding some of your office hours online gives your students flexibility. One study on undergraduate millennial students’ perceptions of office hours suggests that they preferred virtual communication with their professor over face-to-face. Another colleague holds evening virtual office hours using the app <a href="https://guides.instructure.com/m/4152/l/40302-what-are-conferences-for-instructors" target="_blank">Canvas Conference</a>. In addition to audio, video and screen sharing options, this conference feature allows students to upload PDF files of their work so that the instructor can give feedback while talking with them. My colleague allows his students to schedule one-on-one appointments with him for these virtual sessions.<br /><br />Interestingly, some students reach out for help during these virtual sessions who never attend traditional office hours. The main advantage of virtual office hours is that office hours can be scheduled at flexible times such as the evenings or weekends. To avoid back and forth emails on availability and double booking, an instructor can use free online resources such as <a href="https://appoint.ly/">https://appoint.ly</a> or <a href="https://youcanbook.me/">https://youcanbook.me/</a>. Both of these add the appointments directly to your calendar.</li><br /></ul><li><b>Make Homework Assignments Due During Office Hours.</b> Two of my colleagues who have had a good office hour turnout have their students turn in their written homework during office hours. They do this strategically so that students must attend office hours and can get help with their homework.</li><br /><li><b>Educating Students about the Benefits of Office Hours.</b> Some students don’t attend office hours because they do not know what the purpose of this time. In addition to having office hours listed on the course syllabus and announcing them regularly in class, <a href="http://www.tandfonline.com/doi/abs/10.1080/87567555.2014.896777" target="_blank">instructors need to educate students</a> about them. Let students know what office hours are for and the kind of things they can expect or benefit from taking advantage of them.<br /><br />As an international graduate student, I did not know anything about office hours since I grew up in a school system where lectures were accompanied by one-hour tutorials. When I struggled with my math class, one of my friends suggested that I visit my professor during office hours and that was the end of all my struggles! My professor had assumed that as graduate students, we would know about this already.</li><br /><li><b>Make Office Hour Visits an Assignment.</b> <a href="https://chroniclevitae.com/news/1167-make-your-office-hours-a-requirement" target="_blank">Gooblar</a> suggests actually making office hour visits one of the course assignments, because giving students feedback face-to-face is easier than written comments. Gooblar believes that “if you make them [students] come in once, they may start dropping by on their own.” I usually encourage students who did not do well on an exam to make an appointment with me to go over the exam. As they go over the exam with me, I sometimes give them points back as they explain to me their thinking. In addition, we talk about what they could do differently next time and how I could be of help to them. A fellow editor, Jessica Deshler, sometimes makes visiting the tutoring center a course assignment so that students become more comfortable with seeking help and talking about homework problems.</li></ol><br /><b>Related Links </b><br /><br />Edwards, J. T. (2009). Undergraduate Millennial Students’ Perceptions of Virtual Office Hours. <i>International Journal of Instructional Technology and Distance Learning</i>. 6(4) Retrieved from <a href="http://www.itdl.org/Journal/Apr_09/article05.htm" target="_blank">http://www.itdl.org/Journal/Apr_09/article05.htm </a><br /><br />Gooblar, D. (2015). "Make your Office Hours a Requirement." Retrieved from <a href="https://chroniclevitae.com/news/1167-make-your-office-hours-a-requirement" target="_blank">https://chroniclevitae.com/news/1167-make-your-office-hours-a-requirement </a><br /><br />Griffin, W., Cohen, S. D., Berndtson, R., Burson, K.M., Camper, M., Chen, Y ,Margaret Austin Smith, M. A. (2014). 62 <a href="http://www.tandfonline.com/doi/abs/10.1080/87567555.2014.896777" target="_blank">Starting the Conversation: An Exploratory Study of Factors That Influence Student Office Hour Use</a>. <i>College Teaching</i>. 62(3), 94-99 <br /><br />Guerro, M. & Rod, A. B. (2013). <a href="http://www.tandfonline.com/doi/abs/10.1080/15512169.2013.835554" target="_blank">Engaging in Office Hours: A Study of Student-Faculty Interaction and Academic Performance</a>. <i>Journal of Political Science Education</i>. 9(4), 403-416. <br /><br />Weimer, M (2015). Office Hour Redux. <i>Faculty Focus</i>. Retrieved from <a href="http://www.facultyfocus.com/articles/teaching-professor-blog/office-hours-redux/" target="_blank">http://www.facultyfocus.com/articles/teaching-professor-blog/office-hours-redux/ </a><br /><br /><br /><br /><br /><br />Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0