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
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
By Keith Weber, associate professor of Mathematics Education at Rutgers’ Graduate School of Education. Dr. Weber is one of the faculty in Rutgers’ Proof Comprehension Research Group.
The advanced proof-oriented courses for mathematics majors are typically taught in a lecture format, where much of the lecture is comprised of presenting definitions, theorems, and proofs. There is a general perception amongst mathematicians and mathematics educators that these lectures are not as effective as they could be. However, the issues of why these lectures are not effective and how they might be improved are not discussed often in the mathematics education literature. In my research, I have sought to address this issue. Through task-based interviews with students and discussions about pedagogy with mathematicians, as well as observations of lectures and students’ reactions to them, I have found that mathematics professors and mathematics majors have different expectations of lectures and these different expectations lead to barriers in communication. By expectations, I am referring to (i) what a student is supposed to learn from, or “get out of”, a lecture and (ii) how students should engage in the lecture to understand this content. As a consequence of these different expectations, students do not gain what mathematicians hoped they would from the lectures they attend. Below I describe four such differing expectations and how they might inhibit lecture comprehension, with the hope that discussing these differing expectations might help us improve the teaching of proof at the undergraduate level. Continue reading
By: Sarah Blackwell, mathematics major, Saint Louis University; Rose Kaplan-Kelly, mathematics major, Bryn Mawr College; and Lilly Webster, mathematics major, Grinnell 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 undergraduate students reflecting on their experiences with mathematics. We thank Ms. Blackwell, Ms. Kaplan-Kelly, and Ms. Webster for contributing their essay. The American Mathematical Society maintains a list of summer mathematics programs for undergraduates and has published Proceedings of the Conference on Promoting Undergraduate Research in Mathematics as a resource for mathematicians interested in similar programs.
We were participants in the Summer Math Program for Women Undergraduates (SMP) at Carleton College, a program with the goal of encouraging and supporting women undergraduates in their study of mathematics during their first two years of college. For four weeks we took math classes, listened to math talks, went to problem sessions, and talked about math for fun. We had the opportunity to meet many mathematicians from across the country. The people we met did not fit into the mold of the solitary eccentric that popular culture would have us believe. We met mathematicians who defied negative stereotypes often attributed to people in STEM areas and especially to women who are interested in math. Learning about their projects and interests helped us to see ourselves as capable of becoming mathematicians as well. In talking to them, we started to see what our lives could be like if we pursued math as a career and learned that there was no single “correct” type of person we would need to become. SMP was also an opportunity to meet mathematicians who worked outside of academia, mainly in applied math, which was not an area many of us had been exposed to before. This expanded our view of what being a mathematician might be like and what we could achieve. Continue reading
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