Mathematics is used in the physical sciences to describe and model phenomena, resulting in a unique interface between mathematics and disciplines such as chemistry and physics. This paper focuses on themes emerging from a larger project that investigated how students understand and use mathematics in chemical kinetics, a field of study concerned…

Contributing to a growing body of research on undergraduate students' quantitative reasoning, the study reported in this article used task-based interviews to investigate business calculus students' quantitative reasoning when solving two optimization tasks situated in the context of revenue and profit maximization. Analysis of verbal responses…

The aim of this paper is to present and discuss some of the evidence regarding the resources that students use when they establish relationships between a contextual situation and an ordinary differential equation (ODE). We present research results obtained from work by seven students in a graduate level course in mathematics education, where they…

Women are underrepresented in science, technology, engineering and mathematics (STEM) areas in university settings; however this may be the result of attitude rather than aptitude. There is widespread agreement that quantitative problem-solving is essential for graduate competence and preparedness in science and other STEM subjects. The research…

Peer-Led Team Learning (PLTL) is a specific form of small group learning recognized by Project Kaleidoscope as best practice pedagogy (Varma-Nelson, 2004). PLTL was first developed by Woodward, Gosser, and Weiner (1993) as an integrated method that promoted discourse and creative problem solving in chemistry at the City College of New York. It is…

This article presents an instructional approach to constructing discovery-oriented activities. The cornerstone of the approach is a systematically asked question "If a mathematical statement under consideration is plausible, but wrong anyway, how can one fix it?" or, in brief, "If not, what yes?" The approach is illustrated with examples from…

In beginning chemistry classes, students are taught a variety of techniques for balancing chemical equations. The most common method is inspection. This paper addresses using a system of linear mathematical equations to solve for the stoichiometric coefficients. Many linear algebra books carry the standard balancing of chemical equations as an…

For over a decade it has been a common observation that a "fog" passes over the course in linear algebra once abstract vector spaces are presented. See [2, 3]. We show how this fog may be cleared by having the students translate "abstract" vector-space problems to isomorphic "concrete" settings, solve the "concrete" problem either by hand or with…

This paper describes a modification of a popular TV game show, "American Idol[R]," conducted in an undergraduate calculus course. The focal point of this game show is to get students to interact in competitive self-assessment. Student competition is an effective device to engage students in the learning process. Placing students in the role of…

Summarizes a simple design algorithm which identifies nested loops of equations which must be solved by trial-and-error methods. The algorithm is designed to minimize such loops, provides guidance to the selection of variables, and delineates the order in which systems of equations are to be solved. Examples are included. (TW)

Describes teaching strategies that help students improve problem solving skills. Lists three factors good problem solvers were found to possess. Gives step by step instructions for solving problems. (MVL)

Computer-assisted-instruction software was developed to supplement the conventional lecture-laboratory mode of instruction with another instructional aid for learning science in an individualized, nonthreatening environment. This development project was designed to teach physical concepts, mathematical techniques, and problem solving strategies.…

This monograph presents 13 papers dealing with various aspects of elementary problem solving. They are: (1) "Training for Effective Problem Solving" (Gary A. Davis); (2) "Patterns of Problem Solving--A Campus-Wide Course at UCLA" (Moshe F. Rubinstein, L. Robin Keller, Edward A. Kazmarek); (3) "A Taxonomy of Problem-Solving Activities and Its…

The increasing availability of the computer in the classroom has created a need for informed and creative instructional software. Two areas of cognitive research in mathematics and science learning have implications to instruction and, consequently, to educational software design. These are research on misconceptions and on differences between…

The emphasis on writing in the teaching of mathematics and science can empower teachers to reach all sectors of the pupil population. The use of ordinary language can help break the cultural barriers that have prevented minorities and women from achieving well in proportionate numbers in these fields. This volume focuses on pedagogical issues of…