The Secret Question (Are We Actually Good at Math?)

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

“How many of you feel, deep down in your most private thoughts, that you aren’t actually any good at math? That by some miracle, you’ve managed to fake your way to this point, but you’re always at least a little worried that your secret will be revealed? That you’ll be found out?”

Over half of my students’ hands went into the air in response to my question, some shooting up decisively from eagerness, others hesitantly, gingerly, eyes glancing around to check the responses of their peers before fully extending their reach.  Self-conscious chuckling darted through the room from some students, the laughter of relief, while other students whose hands weren’t raised looked around in surprised confusion at the general response.  

“I want you to discuss the following question with your groups,” I said.  “How is it that so many of you have developed negative feelings about your own abilities, despite the fact that you are all in a mathematics course at a well-respected university?”

If this interaction took place in a math course satisfying a general education requirement, I don’t think anyone would be surprised.  Yet this discussion repeats itself semester after semester in my upper-level undergraduate courses, for which the prerequisites are at least two semesters of calculus and in which almost every student is either a mathematics major or minor.  I’ve had similar interactions with students taking first-semester calculus, with experienced elementary school teachers in professional development workshops, with doctoral students in pure mathematics research seminars, and with fellow research mathematicians over drinks after dinner.  These conversations are about a secret we rarely discuss, an invisible undercurrent of embarrassment and self-doubt that flows through American mathematical culture, shared by many but revealed by few.  At every level of achievement, no matter what we’ve done, no matter how much we’ve accomplished, many of us believe that we’re simply not good at math. Continue reading

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Why high-impact educational practices (despite being so labor–intensive) keep me coming for more

By Maria Mercedes Franco, Coordinator for Undergraduate Research & Associate Professor, Mathematics & Computer Science, Queensborough Community College-The City University of New York (CUNY)

By the time I was finishing graduate school, I had done much soul-searching and had come to realize that I have a passion for teaching and a strong commitment to the mission of public education. With my new awareness came the opportunity to interview for (and soon after accept) a position at Queensborough Community College, where I was encouraged early on to incorporate innovative pedagogies into my teaching. Now on my tenth year at the college, I look back and say without hesitation that High-Impact Educational Practices have brought me closer to larger and more diverse groups of learners – and closer to my ideals for higher education – than any other practice. Continue reading

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Let Your Students Do Some Grading? Using Peer Assessment to Help Students Understand Key Concepts

By Elise Lockwood, Contributing Editor, Oregon State University

On many occasions when I grade my students’ proofs, or when I read their solution to a particularly interesting problem, I am surprised by something I read. Sometimes I am surprised because I am disappointed with a given argument or a hand-wavy proof, but often I am surprised because I am impressed by a clever insight or an eloquent way of expressing an argument. Indeed, there have been occasions when I have learned something through the experience of grading my students’ work. Also, seeing the sheer variety of solution strategies that my students offer helps me to appreciate various mathematical approaches and makes me more attuned to their respective mathematical ways of thinking.

In this post I will discuss an activity that I call peer grading, by which I mean having students provide formative, written feedback on their classmates’ assignments. This involves giving students the opportunity to engage with and analyze work that their classmates have done. Peer grading has been used by other teachers (see the references at the end of this post), and my personal reflections on the value of engaging in the process of grading have convinced me that students can similarly benefit from grading other students’ work.

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Start Small, Think Big: Making a Difference Through K-12 Mathematics Outreach

By Kathleen Fowler, Professor of Mathematics, Department of Mathematics and Computer Science, Clarkson University

Since starting my career as a faculty member in 2003, I jumped right in to K-12 Outreach and have never looked back. I was motivated by my strong connection to my community, which is located in St. Lawrence County, a geographically isolated, rural part of upstate New York. All K-12 districts in this county share the same problems of limited resources, significant poverty rates, and a “high needs” population. My choice to become involved in K-12 Outreach was a personal one. I had a very nonlinear path to becoming a mathematician. I was raised by a single mom who sold cars and told me I could do anything I wanted to if I hunkered down and worked hard. I went to three different colleges, changed majors three times, and took five years to get my undergraduate degree—waitressing for the last three years to support myself. I only had one female math teacher in 8th grade and one female math professor—but not until graduate school. My point is, I didn’t have many female STEM role models, but honestly not much of this occurred to me until I started to get involved in K-12 Outreach. However, I quickly understood that these experiences are not the norm and that not every child has an encouraging support system to motivate them. Even for students who do have strong family support, a lack of opportunities for resume building activities or enrichment such as Robotics or Science Olympiad or even an AP Physics class means they are not even competitive when they apply to colleges. I am raising two daughters in this community—they and their peers deserve the same opportunities as students in affluent suburbs scattered across “downstate” New York and elsewhere.

Feedback I’ve received from faculty from a variety of Universities that do K-12 Outreach imply that a common thread is a feeling of wanting to “give back” or to honor a K-12 teacher that made a difference in their lives. The bottom line is that this sort of service to the broader community is a win-win situation. In times of major budget cuts in education, new curriculum and assessments, exhausted teachers, overworked parents, and a new generation of students who need STEM problem solving skills more than ever, it feels great to help out in any possible way. In this article, I’ll describe what K-12 Outreach is and share examples about how mathematics faculty can get involved on a variety of levels. My hope is that, as mathematicians, we can share our expertise with and also learn from the K-12 community to strengthen STEM education through collaboration. Continue reading

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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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