Background: This paper reports on a professional development workshop in University level mathematics. The workshop was grounded in Schoenfeld's (How we think. A theory of goal-oriented decision-making and its educational applications, 2010) theoretical approach, emphasizing the roles of "R"esources (primarily, knowledge),…

In this Research Commentary, the author explores what is meant by "teaching for understanding" and delves into these questions: How does teaching for understanding interact with the backgrounds of the students who experience it or the attributes of the contexts in which they learn? Which empirical findings are context dependent, and…

Two questions are dealt with: (1) Can those strategies or behaviors which enable experts to solve problems well be characterized, and (2) Can students be trained to use such strategies? A problem-solving course for college students is described and the model on which the course is based is outlined in an attempt to answer these questions. The…

Reflects on the history of the calculus reform movement and the development of course implementation projects, including use of technology in instruction. Highlights several themes permeating reform courses: reform calculus is more hands-on, students are expected to understand complex mathematical concepts in more connected ways, and new…

Eight suggestions for surmounting barriers between the student and the class teacher are given and briefly discussed: class evaluations, alternate class structure, student-written notes, in-class "experiments," quizzes without trauma, the class dummy, "programmed" spontaneity, and "treats." (DT)

The problem-solving processes of seven upper-division college students working a series of problems that could be solved by the application of one or more heuristics are described in detail. (MP)

A general method is given for determining an efficient problem-solving process for a given type problem. An application of the method is then described in an experiment involving teaching indefinite integration. (MP)

Some easily graded measures of problem-solving processes are introduced, and the impact of a month-long intensive problem-solving course on a selected group of college freshmen and sophomores is demonstrated. The measures are thought to have shown themselves to be both reliable and informative. (MP)

This paper considers the nature of "understanding" in mathematics, and of instruction designed to foster it. The first part is theoretical, presenting an argument that there are (at least) three qualitatively different components to competent mathematical performance: (1) possession of the appropriate set of cognitive "resources," (2) the ability…

Provides a brief summary of current research in mathematics education at the college level. Explores the current needs of college-level faculty. Suggests ways of coping with the apparent perception that some of the best contemporary research is useless or irrelevant from the practitioner's point of view. (22 references) (JJK)

Although it is commonly assumed that increases in mathematical knowledge and problem-solving skill alter one's understanding of mathematical problems, little research exists to support this assumption. The present study investigated the relationship between mathematical background and problem perception in two experiments. Experiment 1 employed…

The possibility of teaching students to recognize and apply problem-solving strategies used by experts is explored. (MP)

The project consisted of three related series of studies, designed to (a) determine some of the underlying competencies that contribute to experts' successful problem solving performance in college level mathematics, (b) to determine what productive behaviors students lack, or what counterproductive behaviors they have, that keep them from being…

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.…

Solves the problem of defining a smooth piecewise linear approximation to a given function. Discusses some alternative approaches to the problem. (YP)