What I Wish I Had Learned More About in College Mathematics

By Sabrina Schmidt, Data Manager at Time, Inc. and former undergraduate mathematics major at Vassar College

Editor’s note: The editorial board believes that in our discussion of teaching and learning, it is important to include the authentic voices of current and former undergraduate students reflecting on their experiences with mathematics.

When I graduated from Vassar College in 2010 with degrees in math and Italian, I wasn’t sure what was next for me. I applied for math-related jobs at my favorite media companies. Ultimately, Time Inc. offered me a position as a Data Analyst, a job which has been an ideal blend of my mathematical and entertainment interests. I manage store-level distributions for three magazines, Us Weekly, Rolling Stone, and Men’s Journal, all published by Wenner, a primary client. I determine how many copies of every issue go into each store by using formulas based on the store’s available checkout pockets and average sales. At Time Inc., I have been impressed and surprised by the variety of math-related projects. There is a Shopper Insights group that has developed an eye-tracking system that follows the movement of a consumer’s pupils while shopping and helps optimize magazine placement in stores. The Research divisions work on projects that include using subscriber data to help expand the reach of our brands and analyzing historical data to create new pricing strategies. They are doing a zone- pricing test for People magazine, where they are removing the cover price and setting different prices for different regions. In this blog post, I use examples from my work experience over the last five years to suggest ways in which undergraduate mathematics majors can be better prepared for math-related positions in companies. I discuss how I wish I had learned more about applications, computer science, statistics, and connections to other STEM fields.

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(Don’t?) Make ’em Laugh

By Art Duval, Contributing Editor, University of Texas at El Paso

When I started teaching, I wanted to be the very best teacher.  Not just “the best teacher I could be”, but the very best teacher, the one students would tell their friends about and remember fondly years later, the kind of teacher they might imagine being the hero in a movie.  I don’t know what your movie hero teacher looks like, but mine is beloved by all the students (more Robin Williams than John Houseman).  So naturally, I wanted all the students to like me.  I also wanted them to share my love of mathematics, and see it as a joyful endeavor, not just a requirement to be checked off.  As a result, I started including more humor in my classes.  What I eventually realized, and had to confront, was that at least some of what I was doing was more about making me look like that movie hero teacher, or about making the class fun, than about helping my students learn mathematics.

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Number Theory and Cryptography: A Distance Learning Course for High School Students

By Matt Baker, Professor of Mathematics, Georgia Institute of Technology

Last year, I began offering an online Number Theory and Cryptography course for gifted high school students through Georgia Tech.  Fourteen high school seniors from metro Atlanta took the course in Fall 2014, and overall I would say it was a big success.  We will be offering the course again in Fall 2015 and are expecting roughly double the number of students.  After describing the structure of the course, I will relate some of my experiences and describe some of the things I learned along the way.  I hope this article stimulates others to think outside the box about using technology in education without necessarily following the standard “MOOC” model. Continue reading

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We Started a Directed Reading Program (And So Can You!)

By Steve Balady, graduate student, University of Maryland – College Park

What’s the Directed Reading Program?

“The Directed Reading Program (DRP) pairs undergraduates with mathematics graduate student mentors for semester-long independent study projects.”

This mission statement isn’t mine — it was the consensus of a group of graduate students at the University of Chicago in 2003. Since then, programs with this mission have been started at Rutgers, UConn, Maryland, MIT, UT-Austin, and UC-Berkeley. I was an undergraduate participant in the program at Chicago, and I founded the Maryland DRP in 2011. Since then our committee has overseen more than a hundred projects — freshmen through seniors, projects on areas as diverse as logic and finance, with student talks ranging from how to multiply complex numbers to a showcase of original research on nonlinear dimension reduction. Continue reading

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Attending to Precision: A Need for Characterizing and Promoting Careful Mathematical Work

By Elise Lockwood, Contributing Editor, Oregon State University

My research focus is on undergraduate students’ solving of counting problems, and I have worked toward better understanding students’ combinatorial thinking. Counting problems provide excellent opportunities for students to engage in meaningful mathematical tasks and to experience tangible beynefits of being precise and meticulous in their work. In this post, I draw on my experience studying undergraduate students’ combinatorial reasoning to offer examples of “careful” work. There is likely little debate that it is important for students to be organized, precise, and careful as they engage in mathematical activities. Although some students turn in homework assignments that are detailed, organized, and well thought out, others pass over details or do not properly represent ideas. What makes some students (and not others) willing to invest time and effort in detailed and methodical work? How can we help students more amenable to being careful and precise? I believe that these are important questions to consider, and in this post I suggest moving toward emphasizing and characterizing this kind of behavior. In this post, I offer three contrasting examples of students’ solutions to counting problems, which highlight characteristics of careful and precise work.

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The First Year of “On Teaching and Learning Mathematics”

By Benjamin Braun, Editor-in-Chief, University of Kentucky

It has been one year since On Teaching and Learning Mathematics launched, so it seems an appropriate time for reflection.  As I re-read the 36 articles we have published over the past twelve months, five prominent themes emerged that I will discuss below: teaching practices; bridges between K-12 and postsecondary education; expanding visions of mathematics education; the voices of students; and research, communication, and policy.  If you have not had a chance to read all of our articles during the past twelve months, or if you have done so and would like to revisit them from a new perspective, this is my guide to the first year of our blog. Continue reading

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Collective Action: Why the Future is Brighter for Undergraduate Teaching in the Mathematical Sciences

By Karen Saxe, Professor, Macalester College, and Principal Investigator “A Common Vision for the Undergraduate Mathematics Program in 2025” [NSF DUE-1446000]

A remarkable event took place a few weeks ago at the Alexandria, Virginia headquarters of the American Statistical Association. Leaders from five professional associations whose missions include teaching in the mathematical sciences came together to guide future progress to incrementally improve education in our fields. It is the first time that all five — the American Mathematical Association of Two-Year Colleges (AMATYC), the American Mathematical Society (AMS), the American Statistical Association (ASA), the Mathematical Association of America (MAA), and the Society of Industrial and Applied Mathematics (SIAM) — are working together. Our focus is the collection of credit-bearing mathematics courses a student might take in the first two years of college. We examine the undergraduate program using a wide-angle lens, inclusive of modeling, statistics, and computational mathematics as well as applications in the broader mathematically based sciences. Continue reading

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In Math as in Dance, Don’t Miss a Step, or Else You May Fall

By A.K. Whitney, journalist.  In 2009, Whitney went back to school to find out, once and for all, if journalists really are as bad at math as they fear they are; her blog about the experience, Mathochism, runs on Medium three days a week.

When you return to the classroom as an adult student, a big perk is that what seemed like an unreasonable demand back then from the instructor suddenly makes sense, because maturity means you’re better able to fit it into the bigger picture.  For me, a longtime journalist who decided to retake high school math at a community college after decades of hating and fearing it, that demand was “show your work.” As a teen, I’d always sighed when the teacher marked me down for not showing how I’d worked out a problem on an exam or in the homework. Why was it necessary to take eight steps to show a triangle’s angles added up to 180? What a bore.

But 20 years later, going from pre-algebra to calculus, I finally understand why, and I credit dance.

Huh? Let me explain. Continue reading

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Famous Unsolved Math Problems as Homework

By Benjamin Braun, Editor-in-Chief, University of Kentucky

One of my favorite assignments for students in undergraduate mathematics courses is to have them work on unsolved math problems.  An unsolved math problem, also known to mathematicians as an “open” problem, is a problem that no one on earth knows how to solve.  My favorite unsolved problems for students are simply stated ones that can be easily understood.  In this post, I’ll share three such problems that I have used in my classes and discuss their impact on my students. Continue reading

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Taming the Coverage Beast

By Priscilla Bremser, Contributing Editor, Middlebury College

By the end of every workshop and conference session on Inquiry-Based Learning that I’ve attended, someone has raised a hand to ask about coverage. “Don’t you have to sacrifice coverage if you teach this way?” Of course coverage took center stage for many of my professional conversations long before I tested the IBL waters; it’s important. But an equally important question is this: What do we sacrifice when coverage dominates? It may well be conceptual understanding; it’s possible to cover more ground, albeit thinly, if we settle for procedural understanding instead. More than once I’ve settled for even less, delivering a quick lecture just so that my students will have “seen” a particular idea. How do we strike a balance between coverage and other considerations when we are so practiced at reducing a course description to a list of topics? Continue reading

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