This paper is the "Discussion Document" for a forthcoming ICMI Study on "Applications and Modelling in Mathematics Education." As will be well-known, from time to time ICMI (the International Commission on Mathematical Instruction) mounts specific studies in order to investigate, both in depth and in detail, particular fields of interest in…

In this research paper we discuss how some multiple-choice questions may be used to improve understanding, to develop and to assess modelling capabilities and as an aid to teaching.

The theme of the 38th meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the 36th meeting of the North American Chapter of the Psychology of Mathematics Education (PME-NA 36) was "Mathematics Education at the Edge." Academically, the theme provides opportunities to highlight and examine…

Proposes an enhanced approach to teaching topics in ecology--an approach that uses mathematical models and A Programming Language (APL) to produce short, quickly comprehensible computer "programs" that can be run to allow students to study the behavior of a particular model. (Author/IRT)

This paper describes three models of learning theories, derives optimal presentation strategies for the models, and compares the effectiveness of the strategies in two computer assisted instruction experiments. The three models described are: 1) the linear, or response-insensitive model, in which the error probability for a given item depends on…

Describes the instructional strategies and activities used to illustrate the essential features of mathematical modeling to a group of infant and junior high school teachers. The intent was to involve the group with some number work, elementary algebra, and some simple work on arrangements by way of tree-diagrams. (JN)

Learning processes have been investigated for regularities of the changes in the strength of a reflex that result from manipulations of several parameters of a stimulus. Most of this work has been carried out in the tradition of associative theory. One consequence of this emphasis was that for a long time several phenomena that can be…

Explains how the language of mathematics can be used in teaching boys who have negative attitudes toward learning the lnaguage arts. (SW)

Models for division are discussed: counting, repeated subtraction, inverse of multiplication, sets, number line, balance beam, arrays, and cross product of sets. Expressing the remainder using various models is then presented, followed by comments on why all the models should be taught. (MNS)

Typical difficulties involved in solving combinatorial problems are examined and seven common pitfalls are discussed. (MP)

Describes the Treisman model which involves supplemental workshops in which college students solve problems in collaborative learning groups. Reports on the effectiveness of Math Excel, an implementation of the Treisman model for introductory mathematics courses at Oregon State University over five academic terms. Reveals a significant effect on…

Topics such as linear and nonlinear equations and inequalities, compound inequalities, linear and nonlinear absolute value equations and inequalities, rational equations and inequality are commonly found in college algebra and precalculus textbooks. What is common about these topics is the fact that their solutions and graphs lie in the real line…

This article is a discussion of some geographical problems related to geographic and population centers of the U.S. The focus is on modeling, using concepts from calculus.

A inquiry-based approach called the "modelling discussion" is introduced for structuring beginning modelling activity, teaching new mathematics from examining its applications in contextual situations, and as a general classroom management technique when students are engaged in mathematical modelling. An example which illustrates the style and…