by Janet Barnett, Colorado State University – Pueblo; Dominic Klyve, Central Washington University; Jerry Lodder, New Mexico State University; Daniel Otero, Xavier University; Nicolas Scoville, Ursinus College; and Diana White, Contributing Editor, University of Colorado Denver
Mathematics faculty and educational researchers are increasingly recognizing the value of the history of mathematics as a support to student learning. The expanding body of literature in this area includes recent special issues of Science & Education and Problems, Resources and Issues in Undergraduate Mathematics Education (PRIMUS), both of which include direct calls for the use of primary historical sources in teaching mathematics. Sessions on the use of primary historical sources in mathematics teaching at venues such as the Joint Mathematics Meetings regularly draw large audiences, and the History of Mathematics Special Interest Group of the Mathematical Association of America (HOMSIGMAA) is one of the largest of the Association’s twelve special interest groups. In this blog post, which is adapted from a recent grant proposal, we explore the rationale for implementing original sources into the teaching and learning of undergraduate mathematics, and then describe in detail one method by which faculty may do so, namely through the use of Primary Source Projects (PSPs).
By Ryota Matsuura, Assistant Professor of Mathematics at St. Olaf College and North American Director of Budapest Semesters in Mathematics Education.
Home to eminent mathematicians such as Paul Erdős, John von Neumann, and George Pólya, Hungary has a long tradition of excellence in mathematics education. In the Hungarian approach to learning and teaching, a strong and explicit emphasis is placed on problem solving, mathematical creativity, and communication. Students learn concepts by working on problems with complexity and structure that promote perseverance and deep reflection. These mathematically meaningful problems emphasize procedural fluency, conceptual understanding, logical thinking, and connections between various topics. Continue reading
By Reinhard Laubenbacher, Center for Quantitative Medicine, University of Connecticut Health Center, and Jackson Laboratory for Genomic Medicine
Job opportunities for graduates with degrees in the mathematical sciences have never been better, as the world is being viewed through increasingly quantitative eyes. While standard statistical methods remain the work horse for data analytics, new methods have appeared that help us look for all sorts of hidden patterns in data. Examples include statistical methods inspired by tools from abstract algebra, geometric data analysis based on methods from algebraic topology, and new machine learning methods, such as deep neural nets, combined with novel optimization methods. Most importantly, perhaps, an eye trained for the discovery of patterns can go beyond standard analysis approaches through ad hoc data interrogation. Mathematics can be viewed as the science of (non-obvious) patterns, so it is not surprising that a solid mathematics education makes for excellent training in data analysis. It is now more widely known than ever that mathematics is the key enabling technology for the solution of the most difficult scientific problems facing humankind. Human health is arguably at the top of this list. I will focus here on data analytics in healthcare, a field growing by leaps and bounds, although one can make similar statements about the need for mathematical scientists in many other areas. Continue reading
By Priscilla Bremser, Contributing Editor, Middlebury College
Somehow, over the last 600 years or so, mathematics has moved from the core of the liberal arts disciplines to entirely outside. We’re all used to this; a “liberal arts math” course is understood to serve non-STEM majors, for example. The reasons for this shift are interesting to ponder (see  and ), but in this post I suggest that we consider some of its unfortunate present-day implications. It’s also worth considering the broader aim of a liberal arts approach, which transcends disciplinary boundaries. Continue reading
By Elise Lockwood, Contributing Editor, Oregon State University.
When I teach classes for pre-service teachers, I typically have the students read and discuss a math education article about the teaching or learning of content they may eventually teach. This may include research articles (in journals such as Journal for Research in Mathematics Education, which typically report on research studies), or practitioner articles (in journals such as Mathematics Teacher, which offer practical insights without necessarily being rooted in rigorously conducted research).
Recently, however, I have also started to have students in more traditional postsecondary mathematics classes (not just those designed for pre-service teachers) read math education articles. Last term, for instance, after discussing counting problems in an advanced mathematics course, I had my students read an article by Batanero, Navarro-Pelayo, and Godino (1997) about effects of implicit combinatorial models on students’ solving of counting problems. Through such readings, my students can be exposed to research on students’ thinking about the very postsecondary content they are learning. I am always pleasantly surprised by the rich discussion such readings stimulate, and this made me reflect on the value of having students read such articles, even in their “pure” mathematics classes.
Both research and practitioner papers about math education can elicit valuable ideas and points of discussion from which math students can benefit. In this post, I make a case for three potential benefits of having students occasionally read math education articles in their math courses. Continue reading
By Sarah E. Andrews and Justin R. Crum, undergraduate Mathematics majors at Northern Arizona University, and Taryn M. Laird, graduate student in Mathematics at, and 2014 graduate of, Northern Arizona University.
Editor’s note: The editorial board believes that in our discussion of teaching and learning, it is important to include the authentic voices of undergraduate students reflecting on their experiences with mathematics. We thank Ms. Andrews, Mr. Crum, and Ms. Laird for contributing their essay. More information regarding inquiry based learning can be found at http://www.inquirybasedlearning.org/.
Inquiry based learning (IBL) classes inspired each of us to believe that we could go into mathematics. That we belonged. We may be able to prove something important or make an impact in the lives of other budding mathematicians. IBL classes have given us this confidence to believe in ourselves, and to have fun trying to discover for ourselves what math is and where it will lead us. It was not only this sense of being able to discover, however, it was also learning how to collaborate with others. Mathematics is not an isolated endeavor, but rather a concentrated attempt by groups of people working toward their common goal. In normal lecture-based classes, we would talk to our friends, and if we got stuck, we might ask one another what to do next. In the IBL classes, we would talk to each person in the class. Students would ask each other questions willingly. We would make new friends, and ask more questions, until each of us decided we were satisfied — we understood the material now. Continue reading
By Dick Stanley, Professional Development Program, University of California at Berkeley
The notion of one quantity being proportional to another is certainly a very basic part of an understanding of mathematics and of its applications, from middle school through calculus and beyond. Unfortunately, the picture of proportionality that tends to emerge in school mathematics in this country is narrow and confused. Everyone learns the procedure of setting up and solving a proportion, but the connection of this to the idea of one quantity being proportional to another is tenuous.
In support of this statement, I summarize below the results of participant responses given in a workshop attended by teachers, mathematics educators, and mathematicians. The surprisingly shallow responses show a striking lack of a common, mathematically coherent understanding in this audience of the subject of proportionality. Continue reading
By Benjamin Braun, Editor-in-Chief, University of Kentucky
The 2014 American Mathematical Society (AMS) Committee on Education (CoE) meeting took place on October 16-18 in Washington, D.C. I attended as a member of the AMS CoE. In addition to the committee members, there were many attendees from academic institutions, government, other professional societies, and the private sector. Like the recent CBMS forum that Diana White discussed in a blog post earlier this month, the focus of the CoE meeting this year was the first two years of postsecondary mathematics education. In this post, I will reflect on some of the key themes that stood out to me during the CoE meeting. Continue reading
By Diana White, Contributing Editor, University of Colorado Denver
In early October, approximately 150 educators and policy makers gathered together in Reston, Virginia for the fifth Conference Board of the Mathematical Sciences (CBMS) Forum entitled The First Two Years of College Mathematics: Building for Student Success. Participants came from almost every state in the country and represented higher education institutions ranging from two-year colleges to top-ranked research universities. We spent two days reflecting, learning, and in some cases planning how to improve the last year of high school mathematics and the first two years of college mathematics.
As is often my reaction at these types of conferences, I found the two days both sobering and energizing — sobering because of the sometimes harsh realities and challenges we face, energizing because of the good work participants report on and the many people gathered together who care so passionately and who dedicate so much of their time and energy to moving us forward. For those who could not join us in Virginia, this blog post will present a few key highlights from the Forum, in an effort to open a broader conversation about the future of the first two years of collegiate mathematics instruction. Continue reading
By Morgan Mattingly, undergraduate double-major in STEM Education and Mathematics at the University of Kentucky.
Comment from the Editorial Board: We believe that in our discussion of teaching and learning, it is important to include the authentic voices of undergraduate students reflecting on their experiences with mathematics. This article is our first such contribution. We feel it provides a window into many of the subtle challenges students face as they transition to advanced postsecondary mathematics courses, and that it mirrors many of the themes discussed in previous posts. We thank Ms. Mattingly for being the first student to contribute an essay to our blog.
In previous math classes, I was the quiet worker who kept to herself and didn’t know when or how to ask questions. After improving my skills in a problem solving class, that has changed. The group work we did each day allowed me to be around other people who think significantly differently than I do. Being in this environment was difficult at first because I actually had to work through problems with other people, which was somewhat unfamiliar to me. My classmates and I were not just sitting down and reading information about specific math problems. We had to analyze and make sense of the best methods and strategies to use and present our ideas to each other. Confusion would set in when other students introduced different approaches. The only way I could understand their ways of thinking was to ask them to explain. Asking questions in math initially intimidated me, especially because my questions had to be directed to my peers. I did not want them to think that I could not keep up with the material or that I did not belong in the class. But I also did not want to misunderstand major mathematical concepts as a consequence of not asking questions. So I started asking my group members each week what strategies they used in their solutions. Although it may have seemed repetitive to them or obnoxious to have to explain their approaches, it helped me immensely. Through my question asking, I was able to talk and think about math in a unique way. I could compare my peers’ techniques to my own, which further stimulated my interest in the particular subjects that were covered in the class. This skill has been and will continue to be essential in my future relationship with mathematics. Continue reading