Tuesday, October 10, 2017

5 Benefits to Having Students Grade Their Own Homework

By Rejoice Mudzimiri, Contributing Editor, University of Washington Bothell

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!

How to let students grade their own work?
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 Nelta M. Edwards, 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.

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.

Benefits of Having Students Grade their Own Homework
There are several benefits to letting students grade their homework, and the following are my top five:
  1. Helps student reflection. 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.

  2. Offers immediate and relevant feedback. Students value identifying their own mistakes shortly after making them. 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.

  3. Reduces instructor grading time. 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.

  4. Shifts attention away from grades. In addition to the 6 Ways to Upend the Focus on Good Grades, 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 Edwards, 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.

  5. Provides students with another learning opportunity. Having students grade their own work can help provide them with another opportunity to learn concepts they might have missed. Sadler and Good 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.”

Edwards, N. M. (2007). Student Self-Grading in Social Statistics. College Teaching, 55 (2), 72-76.

Sadler & Good (2006). The Impact of Self- and Peer Grading on Student Learning. Educational Assessment, 11(1), 1-31.

Weimer Maryellen (2009). Benefits of a Student Self Grading Model. Faculty Focus. https://www.facultyfocus.com/articles/educational-assessment/benefits-of-a-student-self-grading-model/.

Tuesday, September 26, 2017

5 Ways to go Beyond Recitation

By E. Fuller, WVU Mathematics (guest blogger)

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?

Here are a few approaches you can take to change your students’ experiences during recitation.

1) Focus on getting students to do the work instead of doing it for them. 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.

2) Incorporate group work into your sessions. Build teams and leverage peer instruction (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.

3) Get students to communicate what they understand to each other and to the class. Research 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.

4) Have students relate mathematics to their own experiences. To develop a connection with mathematical ideas, students can investigate how mathematics is related to their futures or how multiple levels of mathematics show up in their day to day experiences. Connecting ideas like contour maps to real world activities like hiking can bring even more advanced concepts into life.

5) Cultivate an environment where failure is ok and experimentation is encouraged. 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 (even incorrect ones) helps support a growth mindset among the students, especially important if the classroom is student-centered and they are doing and explaining the mathematics that is happening.

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.

Tuesday, September 12, 2017

Language matters: 5 Ways Your Language Can Improve Your Classroom Climate

Rachel Levy, Contributing Editor, Harvey Mudd College

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 unconscious biases through language, we can recognize them and find ways to reduce their impact on our students.

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.

Here are five ways you can modify your language to improve your classroom climate:

1. Convey explicitly in your syllabus that you believe that mathematics belongs to everyone and that everyone can be a math doer. Share with your students that making and discussing mistakes are a normal part of learning (and being human). See this tool for surveying your syllabus and course design for examples of inclusive syllabus language.

2. Be intentional about encouraging questions. 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 Teaching Tidbits have concrete suggestions, such as ways to engage your students through reflective writing; your responses to incorrect answers; office hours; and inquiry-based learning.

3. When they suggest an answer to a question, ask students to justify that answer, whether is it right or wrong. 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 Russian pedagogy. It allows you to better see how your students are thinking and where they might have gone awry. Students may also sort out their own errors as they argue their point.

4. Avoid perpetuating mathematical language that fails to acknowledge the challenge of learning, such as "clearly, " "only” and “obviously.” 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.”

5. Aim to use inclusive and unbiased language. 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.”

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 opportunities for feedback, students will let us know when they experience an ouch because of some way we communicated.

Related Links Karp, Alexander, and Bruce Ramon Vogeli. Russian mathematics education: Programs and practices. Vol. 2. World Scientific, 2011.

Tuesday, August 29, 2017

6 Ways to Upend the Focus on Good Grades

By Chad Topaz, Williams College; and Jude Hidgon, Bennington College (guest bloggers)

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.”

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.

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.

1. Design a multifaceted assessment scheme. For the sake of example, consider two different schemes for determining a student’s final grade.

Scheme I: two midterm exams worth 30% each and a final exam worth 40%.

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.

Additionally, students benefit from frequent, ongoing assessment because it provides feedback on their learning 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.

2. Use a drops policy. 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.

3. Allow corrections. 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.

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.

4. Structure grades as formative feedback. 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.

5. Make mathematics verbal. 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 (written or oral) 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 correlated with mastery goal orientation.

6. Discourage (or even abolish) discussions about grades or points. 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.”

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.

Tuesday, April 25, 2017

Read the 3 Most Popular Teaching Tidbits Posts of the Year

By Lew Ludwig (Editor-in-Chief), Denison University

As the academic year comes to a close, Teaching Tidbits 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:
While the blog is on summer holiday, we encourage you to seek out other sources of good teaching tips, like attending the ‘Encouraging Effective Teaching Innovation’ contributed paper session at this year’s MAA MathFest in Chicago this summer. We also welcome your suggestions of topics or ideas for future posts by contacting: teachingtidbits@maa.org. Enjoy your summer and see you in the fall.

-The Teaching Tidbits Team

Tuesday, April 11, 2017

Want to Give Your Teaching Style a Makeover This Summer? Here’s How.

By Dana ErnstContributing Editor, Northern Arizona University

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.

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 Conference Board of the Mathematical Sciences 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:

  • students deeply engage in meaningful problems, and 
  • students collaboratively process ideas. 
According to education research, these "twin pillars" of IBL are at the core of most IBL implementations.

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.”

Workshops and conferences
  • Head to Chicago for MAA MathFest in July and attend a number of sessions dedicated to active learning and/or IBL. 
  • Inquiry-Based Learning Conference: 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.
  • IBL Workshops: 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: 
    • DePaul University, Chicago Illinois: June 20-23, 2017 
    • Cal Poly State University, San Luis Obispo, California: June 27-30, 2017 
    • Nazareth College, Upstate New York: July 18-21, 2017
Summer Reading List
Other resources 
  • Math Ed Matters: 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. 
  • IBL SIGMAA: There is a newly-formed Special Interest Group of the MAA (SIGMAA) devoted to IBL. 
  • The IBL Blog 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. 
  • #mathchat: 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.

Tuesday, March 28, 2017

3 Ways to Engage Your Students in Reflective Writing

Rachel Levy, Contributing Editor, Harvey Mudd College

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 metacognition. Written reflections can also help professors get to know their students, both personally and mathematically.

Three ways I engage my students in reflective writing:

  1. 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.

  2. 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 Teaching Tidbits post.

  3. Direct students to complete an “exit ticket” 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.
Keep reading for more sample questions.

Connectedness Often Translates to Engagement
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.

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.

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.

I recommend searching on the terms “math” and “metacognition” for related reading opportunities. Start with the reference linked at the end of this post.

Sample Questions
These questions are from my Spring 2016 differential equations course in-class quizzes.

  • 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.” 
  • 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: 
  • If you had a magic wand and could change one thing about our college, what would you change? 
  • What’s something you are looking forward to this summer? (Write something or draw something.)
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!

Related Links:

Schoenfeld, A. H. (1987). What's all the fuss about metacognition? In A. H. Schoenfeld (Ed.), Cognitive Science and Mathematics Education (pp. 189-215). Hillsdale, NJ: Lawrence Erlbaum Associates.