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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Inquiry-Oriented Instruction: What It Is and How We Are Trying to Help

By Estrella Johnson, Assistant Professor of Mathematics Education at Virginia Tech University, Karen Keene, Associate Professor of Mathematics Education at North Carolina State University, and Christy Andrews-Larson, Assistant Professor of Mathematics Education at Florida State University

Making fundamental changes to the way you teach is a difficult task. However, with a growing number of students leaving STEM majors, instructors’ dissatisfaction with student learning outcomes, and research indicating positive avenues for improving undergraduate mathematics instruction, some instructors are ready and eager to try something new. In this post, we describe some promising research-based curricular materials, briefly identify specific challenges associated with implementing these materials, and describe a recently funded NSF project aimed at addressing those challenges.

Teaching Inquiry-Oriented Mathematics: Establishing Supports (TIMES) is an NSF-funded project (NFS Awards: #143195, #1431641, #1431393) designed to study how we can support undergraduate instructors as they implement changes in their instruction. A pilot is currently being conducted with a small group of instructors. In the next two years, approximately 35 math instructors will be named TIMES fellows and will participate in the project as they change their teaching of differential equations, linear algebra, or abstract algebra. As project leaders, we will study how to best support these instructors, as well as how their instructional change affects student learning. More details about the project follow later in this blog post.

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The Power of Undergraduate Researchers

By Audrey St. John, Associate Professor of Computer Science at Mount Holyoke College

When I first started teaching, I was mystified (and, frankly, at times panicked) at the thought of having undergraduates work with me on research. I realized this was part of the job, part of my institution’s mission, but I just couldn’t figure out how it would be effective. Sure, these students were bright, eager and motivated to learn, but how much could they contribute with such limited time? A typical research experience might be 8-10 weeks during the summer (full time) or 10 hours a week during a semester; best case, I might find a student who would work with me for a couple years in this way. I had just finished six years in grad school and still felt like I knew nothing. On top of that, my research is at the intersection of computer science and math with applications in the domains of engineering and biology – would I be able to find students with experience in even two of these fields? As it turns out, I would soon discover how powerful research with undergraduates can be, and I’d like to share some of the lessons I’ve learned over the years. Continue reading

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Creating the 2015 CUPM Curriculum Guide

by Martha J. Siegel, Professor, Towson University

I serve as chair of the Mathematical Association of America’s (MAA’s) Committee on the Undergraduate Program in Mathematics (CUPM). Approximately every ten years, CUPM publishes a new curriculum guide, with the primary goal of assisting mathematics departments with their undergraduate offerings. Over five years in the making, the 2015 Curriculum Guide to Majors in the Mathematical Sciences encourages departments to engage in a process of review and renewal, by examining their own beliefs, interests, resources, mission, and particularly their own students in designing or revising a major in mathematics or, more generally, in the mathematical sciences. In the remainder of this blog post, we discuss the history, development, process, and key characteristics and recommendations of the 2015 Guide. Continue reading

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One Reason Fractions (and Many Other Topics) Are Hard: Equivalence Relations Up and Down the Mathematics Curriculum

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

Why are fractions hard to learn for so many people?  There are many reasons for this, but I like to think about one in particular, a mathematical idea hiding in plain sight, from elementary school to college: equivalence relations.  Consider the fraction sum 2/3 + 1/5, which we of course compute by using 2/3=10/15 and 1/5=3/15, arriving at an answer of 13/15.  This raises a whole host of fundamental questions about equality:  If 2/3 equals 10/15, why can we use one but not the other in evaluating the sum?  Does this mean something is wrong with our idea of “equals”?  Could we have used something else besides 10/15; or, in the other extreme, should we always use 10/15?  This shows that often when we say “equals”, what we really mean is “equivalent”.  Equivalence introduces a number of useful mathematical connections, but we must be careful in how we handle it with our students who just want to know, for instance, how to add two fractions.

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Mathematical education of teachers Part II: What are we doing about Textbook School Mathematics?

By Hung-Hsi Wu

This two-part series is a summary of the longer paper, Textbook School Mathematics and the preparation of mathematics teachers.

TSM (Textbook School Mathematics) has dominated school mathematics curriculum and assessment for the past four decades, yet, in mathematics education, TSM is still the elephant in the room that everybody tries to ignore.

We will look at three examples of this phenomenon. Continue reading

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Mathematical Education of Teachers, Part I: What is Textbook School Mathematics?

By Hung-Hsi Wu

This two-part series is a partial summary of the longer paper, Textbook School Mathematics and the preparation of mathematics teachers.

School mathematics education has been national news for at least two decades. The debate over the adoption of the Common Core State Standards for Mathematics (CCSSM) even became a hot-button issue in the midterm elections of 2014. This surge in the public’s interest in math education stems from one indisputable fact:  school mathematics is in crisis.

From the vantage point of academia, two particular aspects of this crisis are of pressing concern: School textbooks are too often mathematically flawed, and in spite of the heroic efforts of many good teachers, the general level of math teaching in school classrooms is below acceptable.

Mathematicians like to attack problems head-on. To us, the solution is simple: Just write better school textbooks and design better teacher preparation programs. I will concentrate on the latter for now and will not return to the textbook problem until the end of Part 2. Continue reading

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