Presents a project used to help students make connections between linear and exponential models and between arithmetic and geometric sequences. (KHR)

Presents an instructional forum in which students and teachers work with researchers to engage in coordinated cycles of planning and implementing instruction and studying forms of students' thinking that emerged in the classroom. Reports on an 8-week teaching and learning study of elementary students' thinking about distribution, including their…

Presents an activity for introducing probability by investigating the Chinese policy of having one child per family and a one-son policy of some rural Chinese. Discusses features of the problem, including counterintuitiveness, multiple options for analysis, and thought experiments. (MKR)

Describes the construction of an exponential decay graph that can be used in a science class to support discussions about the uses of radioactivity, its risks, limitations, and advantages. (WRM)

Some aspects of biology, for example the Hardy-Weinberg simulation of population genetics or modelling heat flow in lizards, have an undeniable mathematical basis. Students can find the level of mathematical skill required to deal with such concepts to be an insurmountable hurdle to understanding. If not used effectively, spreadsheet models…

We present a project for a differential equations class: an analysis of an H. G. Wells story in which is given a submersible's descent time, its ascent time, and its eruption from the surface before splashdown. (Contains 5 figures.)

Activities and teaching methods for developing an understanding of fractions are presented. The activities, which use mathematical models (visual representations of fractions), are divided into three sections: (1) equivalent fraction circles; (2) fraction bars; and (3) multiplication of fractional numbers using squares. Each section includes the…

Before implementing a course in the analysis of variance (ANOVA) taught through multiple linear regression, several concerns must be addressed. Adequate computer facilities that are available to students on a low-cost or cost-free basis are necessary; also students must be able to meaningfully communicate with their major advisor regarding their…

Argues that "appropriate practical work" in mathematics aids understanding. Presents ideas and activities for teaching mechanics. Discusses modelling, problem formulation, and interpretation. (PK)

Discussed are various models proposed for the Moebius strip. Included are a discussion of a smooth flat model and two smooth flat algebraic models, some results concerning the shortest Moebius strip, the Moebius strip of least elastic energy, and some observations on real-world Moebius strips. (KR)

Presents an approach to the concept of absolute value that alleviates students' problems with the traditional definition and the use of logical connectives in solving related problems. Uses a model that maps numbers from a horizontal number line to a vertical ray originating from the origin. Provides examples solving absolute value equations and…

Discusses the equation and proportion methods for teaching how to solve percent problems. Supplements the teaching of each method by introducing a representational model that enhances understanding when solving percent problems. (MDH)

Applies the Lesh Translation Model to develop conceptual understanding by showing relationships between five modes of representation proposed by Lesh to learn multiplication of fractions. Presents five teaching activities based on the translation model. (MDH)

Presents three teaching strategies requiring active student participation in which students (1) create and solve their own word problems; (2) generate trigonometric expressions to be solved by their classmates; and (3) act as points to model a basic locus of points. (MDH)

Presents a methodology of mathematical and technological principles as integrated components of the Design and Technology syllabus of the National Curriculum in the United Kingdom. The methodology is based on the syllabus area of product analysis and employs a structured problem-solving approach. (ASK)