Have you checked out the Mathematical Association of America’s Math Values blog? The site includes posts about inclusivity, community, communication, teaching and learning, and more. Please join me on a blog tour highlighting some Math Values posts that I find noteworthy.
“Calculus and Virtual Reality” by Katie Haymaker
For this post, Haymaker interviewed Nick Long and Jeremy Becnel, both of Stephen F. Austin University in Texas. They discussed the Calculus and Virtual Reality (CalcVR) project.
“Often the largest hindrances to student success in multivariable calculus courses are the student’s inability to visualize the curves, surfaces, and vector fields, as well as the disconnect that this causes between the geometric interpretation and the algebraic calculation. While there are many great tools that are freely available (like CalcPlot3D) to help students understand these multivariable objects, the rendering is still a two-dimensional picture of a three-dimensional object. In order to show these objects with visual depth, we created a virtual reality app that is available for free on smartphones (Android or iPhone) and requires less than $5 in additional hardware costs for students. We have created interactive lessons and demos for multivariable calculus topics with the ability for the user to input their own expressions and explore the related figures with inexpensive integrated Bluetooth controllers,” the researchers told Haymaker.
Also within the post, Long and Becnel shared with Haymaker how the project has impacted students, advice for other researchers applying for NSF DUE grants, and more.
“Do Math and Chess Make You a Better Problem Solver? Teaching Math for Life in a Wicked World” by Keith Devlin
You have probably heard the buzz before: playing chess supposedly helps people become better problem-solvers. “Does taking a logic course at college make you a better reasoner? How about algebra? Or calculus? Or playing chess?” Devlin asked.
“Despite being a mathematician who concentrated on mathematical logic for my Ph.D. studies and many years of research thereafter, I always had my doubts. I harbored a suspicion that a course on, say, history or economics would (if suitably taught) serve better in that regard. Turns out my doubts were well founded,” he wrote. He shares a potentially controversial idea: that learning mathematics is “ideal preparation for, well, doing mathematics; but [is] not, on its own, particularly conducive to success in solving problems in other domains.”
He then explains the difference between “kind problems,” which can be solved by choosing and applying rule-based procedures, and “wicked problems,” which fall outside the bounds of that approach. He closes with a list of suggestions for providing students with what they need to grapple with wicked problems, beginning with putting together diverse teams of students so they can tackle problems together.
“Questioning Final Exams” by David Bressoud
With many folks on winter break, it seems timely to mention this post. Bressoud also asked readers to share their thoughts on exams here.
He begins by discussing Chapter 8 of The Years that Matter Most: How College Makes or Breaks Us by Paul Tough. I haven’t read the book, but it seems like one I should add to my reading list. Bressoud highlights a major issue with final exams. In his words? “The problem that I have is how much depends on that final exam.”
He explains his rationale for usually restricting final exams to no more than 10% of a student’s grade (“there are no options for allowing students to improve a grade on a final exam”), then discusses how he builds “at least three major projects into each course.” It’s important that students receive detailed feedback early on in the course of these projects, he noted. He discusses how to provide this feedback, especially if class sizes are large.
“Equal vs. Fair” by Dave Kung
Kung’s post begins with a scene from 10 years ago in which he asked students to find a partner for an activity. “As the room buzzed to life with students pairing up, most people quickly found someone,” he wrote. “But I watched as the one black student in the back corner slowly made his way past already-partnered-up students, eventually meeting up with the other lonely soul: a 40-year-old former carpenter returning for his degree,” he noted. Kung analyzes the difference between equal and fair treatment of students. He then shares how awareness of these issues, along with focusing on inclusion, can help us create a more just mathematical community.