Connecting and comparing across student strategies has been shown to be productive for students in elementary and secondary classrooms. We have recently been working on a project converting such practices from the K-12 level to the undergraduate classroom. In this paper, we share a particular instantiation of this practice in an abstract algebra…

Preparing students placing into developmental mathematics for success in undergraduate mathematics and preparing future teachers for the increasing demands of K-12 school settings are both persistent, yet seemingly divergent, problems facing higher education. In this paper, we shed light on a model that attempts to address aspects of each problem…

To promote and facilitate the teaching of math modeling throughout the K-16 setting, the Consortium for Mathematics and Its Applications and the Society for Industrial and Applied Mathematics recently published the GAIMME (Guidelines for Assessment and Instruction in Mathematical Modeling Education) Report. This paper provides insight into how the…

Research has highlighted that inquiry-based learning (IBL) instruction leads to many positive student outcomes in undergraduate mathematics. Although this research points to the value of IBL instruction, the practices of IBL instructors are not well-understood. Here, we offer a characterization of a particular form of IBL instruction:…

Large lecture halls are a common feature of many undergraduate mathematics programs. However, teaching effectively in a large lecture hall can be challenging. This paper discusses the use of personal whiteboards for students as a way to make large lecture halls a more productive learning environment. I discuss the logistics of using whiteboards,…

Constructivism is currently a hotly debated topic, with proponents and opponents equally adamant and emotional with respect to their viewpoints. Many misconceptions exist on both sides of the debate, and misuses of terminology and attribution are rampant. Constructivism is a theory of learning, not a particular approach to instruction and not a…

Teaching preparatory mathematics to first-time college students--who come from economically impoverished high schools that have not prepared their students to do college level mathematics--can be a daunting task for teaching assistants (TAs). The preparation of TAs to assist such students in the mastery of mathematical content is a complex…

This article reflects on the author's experience in teaching courses in mathematics content and methods in teacher preparation programs. It shows how technology-enhanced inquiry into a seemingly mundane task on situated addition found in a popular textbook for prospective elementary teachers, can reveal hidden properties of integers associated…

Describes student historical research and student classroom presentation of the results of that research. Feedback from the student surveys verifies that active-learning mathematics history can motivate students to learn mathematics. (Author/DDR)

Presents eight techniques for teaching undergraduate mathematics whose main aims are (1) learning how to pose problems in an easier and more attractive form; (2) fostering usage of mathematical symbolism; and (3) checking the level of comprehension of the principal ideas. Examples illustrate each technique. (Author/MDH)

Identifies and analyzes some recurrent problems with the implementation of cooperative and active learning strategies. Addresses the use of questions, management of instructor-centered activities, management of in-class group activities, and relinquishing forms of control in the classroom. (Author/ASK)

Discusses ways in which a mathematical pedagogy seminar can be an enlightening, engaging, and sometimes entertaining experience through which to bring together departmental colleagues and their students. Suggests logistics for such a seminar, 25 topics, and readings. Contains 64 references. (Author/ASK)

Discusses some of the differences between the ways mathematicians and physicists view vector calculus and the gap between the way this material is traditionally taught by mathematicians and the way physicists use it. Suggests some ways to narrow the gap. (Author/ASK)

Considers the extent that first-year teachers (FYTs) were able to implement the National Council of Teachers of Mathematics Standards in their teaching, the barriers to the FYTs implementation of the standards, factors contributing to their success, instructional practices used by the FYTs, and the implications for mathematics teacher-education…

Explains the cooperative learning technique of jigsaw. Details the use of a jigsaw lesson for explaining complex numbers to intermediate algebra students. Includes copies of the handouts given to the expert groups. (Author/ASK)