By Sybilla Beckmann, Josiah Meigs Distinguished Teaching Professor in the Department of Mathematics at the University of Georgia, and Andrew Izsák, Professor of Mathematics Education in the Department of Mathematics and Science Education at the University of Georgia.
One of the challenges of teaching mathematics is understanding and appreciating students’ struggles with material that to the instructor, after years of thinking about it, may seem straight forward. Once we understand an idea, it may seem almost impossible not to understand if it is presented clearly enough. Yet experienced math teachers know that presenting mathematical ideas clearly, as important as that is, is generally not enough for students to learn the ideas well, even for dedicated and determined students. At the same time, students who struggle can have insightful and productive ways of solving problems and reasoning about mathematical ideas. Research into how people think about and learn mathematics reveals why this surprising mix of struggle and competence can coexist: learners can use what they do understand to make sense of new things, yet ideas that are tightly interconnected and readily available for an expert may be fragmented or inchoate for a learner.
From The Editorial Board.
We thought our readers might be interested to know that nominations are now open for several American Mathematical Society awards related to teaching and learning. The deadline for nominations for the following awards is September 15, 2014.
- Award for Impact on the Teaching and Learning of Mathematics.
- Award for an Exemplary Program or Achievement in a Mathematics Department.
- Mathematics Programs that Make a Difference.
More information about these awards and the nomination process can be found here: http://www.ams.org/profession/prizes-awards/prizes
By Benjamin Braun, Editor-in-Chief, University of Kentucky.
Our understanding of the importance of processes and practices in student achievement has grown dramatically in recent years, both in mathematics education and education more broadly. As a result, at the K-12 level explicit practice standards are given in the Common Core Mathematics Standards  and the Next Generation Science Standards  alongside content standards. At the postsecondary level, studies regarding student learning and achievement have revealed the importance of many key practices, and accessible sources exist on this topic [3, 4, 5]. Further, we understand now that not all advanced postsecondary mathematics students are well-served by the same curriculum; for example, pre-service high school mathematics teachers need to develop unique ways of practicing mathematics compared to math majors with other emphases [6, 7]. As discussed by Elise Lockwood and Eric Weber in the previous post on this blog, mathematicians generally appreciate these issues; for readers unfamiliar with mathematical practice standards, their article is a nice introduction to this topic.
All of this leads us to the following question:
Given the breadth of both content and practices required for students to deeply learn and understand mathematics, what are effective techniques we can use at the postsecondary level to gauge student learning? Continue reading
By Elise Lockwood, Contributing Editor, Oregon State University and Eric Weber, assistant professor of mathematics education in the College of Education, Oregon State University.
As students’ mathematical thinking develops, and they encounter more advanced mathematical topics, they are often expected to “behave like mathematicians” and engage in a number of mathematical practices, ranging from modeling and conjecturing to justifying and generalizing. These mathematical practices are distinct from specific content students might learn because they are characteristics of broader behavior, rather than mastery of a single concept or idea. However, these practices represent indispensable components of what it takes to become a successful mathematician. Continue reading
By William Yslas Vélez, Professor in the Department of Mathematics at the University of Arizona.
The best recruiting tool I have to convince students that they should continue in the study of mathematics is the mathematics that I am teaching, no matter the level. It is all fascinating. In almost every lower division course that I have taught I have convinced at least one student to add the mathematics major. The last time I taught second semester calculus, three students added the math major and one the math minor (and the student selecting the math minor simply could not fit in the last three mathematics courses for the major). One of those students is now a graduate student in biostatistics at Harvard. Continue reading
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
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
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
By Benjamin Braun, Editor-in-Chief, University of Kentucky.
This post is inspired by an article by Karen Marrongelle and Chris Rasmussen , 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
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