Tuesday, May 15, 2018

Farewell from the Teaching Tidbits Blog

Thank you for visiting the Teaching Tidbits blog, hosted by the Mathematical Association of America, 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 MAA IP Guide was being developed.

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.

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.

Thank you for your support!

Tuesday, May 8, 2018

Teaching Tidbits Blog 5 Most Popular Posts

As 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.

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 MAA Instructional Practices Guide is available, 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.

Of our 34 posts over the last two years, these are the 5 most popular posts:

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!

Tuesday, May 1, 2018

5 Reasons Math Modeling Should have a Place in your Undergraduate Curriculum

by Rachel Levy, Harvey Mudd College

I believe students should see mathematical modeling in school because this way of engaging mathematics can be both inclusive and personally empowering.

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.

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 M3 Challenge or MCM/ICM or in the workplace. I believe this can start as early as kindergarten, though of course here we focus on undergraduate education.

Mathematical modeling is a topic of increased visibility in the education system. First, it appears in the US Common Core Standards for Mathematical Practice (CCSSM-MP4) 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.

Here are 5 characteristics of mathematical modeling that can make it inclusive and personally empowering:

1. Mathematical modeling involves genuine choices. 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.

2. Students learn how objective functions and assumptions/constraints matter. 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.

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.

3. Mathematical modeling can draw on interdisciplinary ideas and ways of knowing. 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?

4. Real world problems help students see that mathematics is everywhere. 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.

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.

5. Mathematical Modeling is a team sport that focuses on process as much as product. 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.

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.

Here are three ways to make mathematical modeling available to your students:
  •  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.
  • 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.
  • 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.
To learn more about the teaching and learning of mathematical modeling, see these free downloadable reports: