It is generally agreed that the ability to read mathematics is an important skill--one that few of our students possess. A number of people have published some suggestions for helping students learn to read their mathematics textbooks. What these have in common is suggestions for getting students more active while reading. Using these resources as…

In Fall 2004, Virginia Commonwealth University (VCU) piloted a modeling-based approach to college algebra. This paper describes the course and an assessment that was conducted to determine the effect of this approach on student achievement in comparison to a traditional approach to college algebra. The results show that compared with their…

This article describes a reading and writing project designed for an undergraduate survey course in mathematics. For the Math Book Club, students in groups of four read and discuss one of six books related to mathematics and the history of mathematics. As part of the assignment, students take turns developing discussion questions and summarizing…

We present a design for a junior level numerical methods course that focuses on a series of five open-ended projects in applied mathematics. These projects were deliberately designed to present many of the ambiguities and complexities that appear any time we use mathematics in the real world, and so they offered the students a variety of possible…

This article describes a learning community for early-career faculty in the sciences aimed at course redesign and active-learning. Through findings from surveys, interviews, and observations, program outcomes regarding faculty teaching skills and confidence, understanding of how students learn, and use of assessment are explored. Finally, the…

Japanese Lesson Study is a collaborative approach for teachers to plan, present, observe, and critique classroom lessons. Through the lesson study process, teachers systematically and thoughtfully examine both student learning and their own teaching practices. In addition, the process paves the way for a much broader approach to education…

Intended to improve mathematics education at two-year colleges and other institutions offering lower division courses as well as to encourage more students to study mathematics, this publication presents the American Mathematical Association of Two-Year Colleges' (AMATYC's) standards for revitalizing the pre-calculus mathematics curriculum and…

This report, prepared for and published by the Mathematical Association of America's Committee on the Teaching of Undergraduate Mathematics, includes a description of the state of the art on problem solving, lists available resources, and makes recommendations regarding the place of problem solving in the college curriculum and ways to teach it.…

This paper presents a laboratory exercise in which an integration problem is applied to cinematography, without the need for apparatus. The problem situation is about the oscillation control of a camera platform to attain the contrast angular rate of objects. Wave equations for describing the oscillations are presented and an expression for…

A laboratory experiment, based on a simple electric circuit that can be used to demonstrate the existence of real-world "related rates" problems, is outlined and an equation for voltage across the capacitor terminals during discharge is derived. The necessary materials, setup methods, and experimental problems are described. A student laboratory…

In most mathematics problem solving work, students' motivation comes from trying to please their teachers or to earn a good grade. The questions students must tackle are almost never generated by their own interest. Seven open-ended college algebra-level problems are presented in which the solution of one question suggests other related questions.…

In light of substantial declines in enrollments in liberal arts mathematics courses in two-year colleges, this paper looks at some of the reasons for these declines and suggests ways of revitalizing the traditional "great ideas" mathematics course. First, a brief outline is presented of the history of liberal arts mathematics, focusing on the…

This paper presents the thesis that pair problem-solving serves as an aid to students in developing their metacognitive skills. Metacognition has been defined as knowledge and cognition about cognitive objects and as any kind of monitoring. The ability to monitor one's thoughts and actions is greatly facilitated through the pair problem-solving…

Sophomore and junior students in the College of Engineering at Cornell University have been taught engineering mathematics using new computer software that performs exact symbolic algebraic and calculus operations. Describes this software, the computer-based mathematics laboratory, changes in the teaching/learning environment, and short- and…

In this theoretical essay the psychological aspects of genetic approach to teaching mathematics (mainly at universities) are discussed. Analysis of the history and modern state of genetic teaching shows that its psychological aspects may be explained using both Vygotskian and Piagetian frameworks. Experience of practice of mathematical education…