The Role of Mathematics Departments in the Mathematical Preparation of Elementary Teachers

By Diana White, Contributing Editor, University of Colorado Denver

Mathematics departments have long provided the bulk of the mathematics content training for both practicing teachers and those studying to be teachers.  This is a tremendous responsibility, and one that presents a variety of challenges and opportunities.  In this post, we start early in the mathematical spectrum – with elementary teachers and how mathematics departments impact their mathematical preparation. Continue reading

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Do mathematicians need new journals about education?

By Priscilla Bremser, Contributing Editor, Middlebury College.

In the past nine months, I’ve heard colleagues at three different meetings—an AMS sectional meeting in Louisville, the Joint Mathematics Meetings in Baltimore, and the Contemporary Issues in Mathematics Education workshop at the Mathematical Sciences Research Institute—identify a need for journals focused on publishing useful refereed articles for mathematicians about mathematics education. This raises several questions that get at fundamental issues in the complicated and sometimes uneasy relationships among research mathematicians, mathematics education specialists, and those with interests in both areas (I put myself in the last category). Continue reading

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On being a friendly mathematician

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

Almost fifteen years later, Lucy Michal still remembers the exact words Phil Daro told the leaders of the El Paso Collaborative for Academic Excellence as they were preparing to launch the K-16 Mathematics Alignment Initiative, which Lucy would direct: “Find a friendly mathematician.”  The goal was to align mathematics in grades K-16, through regular meetings of a working group of a few dozen local teachers of all grade levels.  Phil had many contacts, including national authorities in K-12 mathematics, but, for a project like this, he stressed the need for local mathematics experts.  A “friendly mathematician” would be respected for mathematics, but would also understand the importance of working with both pre-service and in-service teachers.  I became one of those friendly mathematicians.  What did I do to live up to this billing? Continue reading

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Teaching practices between and beyond all lecture and all student discovery

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

This post is inspired by an article by Karen Marrongelle and Chris Rasmussen [1], in which they discuss the false dichotomy between all lecture and all student discovery as the two exclusive teaching strategies available for mathematics teachers.  I’ve noticed that many discussions among postsecondary mathematics teachers lead to a debate of the merits of these two classroom teaching strategies, with the result that interesting teaching practices are left undiscussed.  Below I describe three key teaching practices that I’ve learned about and used over the past several years that fit between and beyond these extremes.  I’ve observed that when I use these practices, students are generally more engaged in the course, e.g. attending office hours, asking questions in class, forming study groups, etc.  Though they appear simple, using these practices successfully has required perseverance and effort on my part, and a willingness to regularly revise their implementation. Continue reading

Posted in Assessment Practices, Classroom Practices | 2 Comments

Striking the Balance between Examples and Proof

By Elise Lockwood, Contributing Editor, Oregon State University.

As an undergraduate, it was easy for me to assume that as my professors conducted mathematical research, beautiful, complete proofs came to them in moments of epiphany. Their work was mysterious to me, and I believed that somehow their superior intelligence and vast mathematical knowledge gave them immediate access to all things abstract. Had I been asked then, I likely would have said that mathematicians didn’t need to think about examples in their own research – surely they had outgrown the need for concrete examples. Continue reading

Posted in Classroom Practices | 2 Comments

Transformation of a Math Professor’s Teaching

By Jerry Dwyer, professor in the Department of Mathematics & Statistics and Director of the Science, Technology, Engineering and Mathematics Center for Outreach, Research & Education (STEM-CORE) at Texas Tech University.

This essay describes the changes that have taken place in my teaching philosophy and practice over the past 30 years or so. I have always loved teaching and the satisfaction of explaining concepts to others. However, my understanding and love of the profession has greatly increased over the years, with some pivotal moments emphasizing when those changes occurred. I present these reflections as a possible encouragement to others who may wonder about their teaching and how to make it more satisfying and enjoyable. Continue reading

Posted in Assessment Practices, Classroom Practices | 5 Comments

Welcome to “On Teaching and Learning Mathematics”

By The Editorial Board.

There are major changes afoot in both K-12 and postsecondary mathematics education.  For example, the widespread adoption of the Common Core State Mathematics Standards [5] has been a focal point for everyone involved in K-12 education in the United States.  The 2012 report Engage to Excel [4] from the President’s Council of Advisors on Science and Technology (PCAST) included substantial recommendations for experimentation and change in mathematics education, including at the undergraduate level for preservice teacher training.  A large and growing body of research [6] in STEM disciplines (Science, Technology, Engineering, Mathematics) is demonstrating that undergraduate learning and achievement can be increased by implementing evidence-based teaching practices.  Funding agencies such as the National Science Foundation are responding to this seriously, for example through the Widening Implementation and Demonstration of Evidence Based Reforms (WIDER) program [7]. Continue reading

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