Describes the development of the ability to identify a ratio as the appropriate measure of a given attribute by (n=26) prospective elementary teachers. It was concluded that traditional procedural approaches to teaching ratios do not challenge students to develop their own mathematical models of the world. (21 references) (MKR)

Presents an alternative method to teaching percent problems which uses a 10x10 grid to help students visualize percents. Offers a means of representing information and suggests different approaches for finding solutions. Includes reproducible student worksheet. (MKR)

Discusses the problem of finding the amount of fence it would require for the outfield fence of a baseball field of given dimensions. Presents different solution methods for each of the levels from grades 9-12. The different methods incorporate geometry, trigonometry, analytic geometry, and calculus. (MDH)

Following a brief historical review of the mechanism of mathematical modeling, examples are included that associate a mathematical model with given data (changes in sea level) and that model a real-life situation (process of parallel parking). Also provided is the rationale for the curricular implementation of mathematical modeling. (JJK)

Described are student/consultant reports, turned in as homework, that reflected their abilities to distinguish useful from irrelevant information, solve the underlying calculus extremum problem, and reconcile the individual mathematical solutions with the ethical considerations surrounding the moral dilemma of the hypothetical consulting client.…

Identified are three obstacles which students must overcome when examining and interpreting diagrams. The resources of the Geometric Supposer, a set of microcomputer tools designed to aid students, are outlined. The advantages of the use of this software are emphasized. (CW)

Statistical data can be represented in a number of qualitatively different ways, the choice depending on the following three conditions: the concepts to be investigated; the nature of the data; and the purpose for which they were collected. This paper begins by setting out frameworks that describe the nature of statistical thinking in schools, and…

Cabri3D is a potentially very useful software for learning and teaching 3D geometry. The dynamic nature of the digital diagrams produced with it provides a useful aid for helping students to better develop concept images of geometric concepts. However, since any Cabri3D diagram represents three-dimensional objects on the two dimensional screen of…

This paper focuses on the cognitive processes that occur while students are exploring motion graphs. In a classroom experiment, we examine how high-school students (aged 17), with backgrounds in calculus and physics, interpret the graphs they create through drawing the path of the movement of their hand with a computer mouse. Based on recent, and…

Whenever teachers of young children get together there will be differences of opinion about how far children should be taught to count. Some will argue that the focus should be on small numbers to 9, building up the notion of what, say, the name 5 means, what it looks like, and how it can be represented. Others argue that with ice blocks retailing…

This paper examines 6th grade children's local conceptual development and mathematization processes as they worked a comprehensive mathematical modeling problem (creating a consumer guide for deciding the best snack chip) over several class periods. The children and their teachers were participating in a 3-year longitudinal teaching experiment in…

Two educational computer simulations are described in this paper. One of the simulations is STATSIM, a series of exercises applicable to statistical instruction. The content of the other simulation is comprised of mathematical learning models. Student involvement, the interactive nature of the simulations, and terminal display of materials are…

The use of the digital computer for the presentation of the topics of empirical model building and regression analysis is discussed. The author concentrates upon a description of computing exercises which are employed to provide the students with experience in model building and evaluation in a controlled situation. The types of exercises given…

Three examples are given in which students create their own Logo software to explore the topics of number patterns and operations, fractions, and decimal parts in measurement. (MNS)

In this paper, we address mathematics education in rural contexts from a critical pedagogical perspective. We imagine our audience to be mathematics educators and rural educators who may not have background knowledge of critical pedagogy. We also confess that we are mathematics educators first, with interests in critical pedagogy and rural…