This article describes how spatial instruction with preservice teachers can be implemented in a middle-grades mathematics methods class. A "Reflect and Discuss" section is included for professional development study. (Contains 4 figures.)

As well as being important for school mathematics, spatial thinking is a big component of advanced mathematical studies too. As Jones (2001:55) points out, "Much of the thinking that is required in higher mathematics is spatial in nature. Einstein's comments on thinking in images are well known. Numerous mathematicians report using spatial…

Most primary teachers struggle to convey the proper values of coins with ineffective instructional materials. This study aimed to create a more developmentally appropriate money model for students in grades K-3. Instruction included concrete and visual money models. The paper also presents a proportional model of money and creates a visual…

Takes the concept of using a geometrical or visual approach to teach algebraic concepts and extends it to connect with the section on binomial expansion by using three dimensional objects. (ASK)

This quantitative study of imagery in 96 undergraduates addresses the problem of individual differences in the characteristics of mental imagery workspaces. A 20-item questionnaire embodying nine characteristics of mental imagery workspaces was administered to 78 females and 18 males. Analysis of variance by gender disclosed significant higher…

A 90-minute computer-assisted instruction (CAI) unit course supplemented by a 1-hour lecture on the dynamic nature of three-dimensional rotations and Euler angles was given to 29 undergraduate engineering students. The area of Euler angles was selected because it is essential to problem-working in three-dimensional rotations of a rigid body, yet…

We propose a methodology for studying the processes of learning and teaching mathematics. We will argue that this methodology carries many of the advantages of qualitative approaches while still keeping the main advantage of quantitative research methodology, which is the potential to produce findings that could be generalized. At the heart of…

Describes a calculator exercise that can help students develop a better visual and numeric feel for Newton's method. (KHR)

Presents the Shape Search problem to develop student visualization. Focuses attention on the National Council of Teachers of Mathematics (NCTM) Geometry Standard. (Author/NB)

Describes how elementary school teachers demonstrated for themselves and their students how using simple drawings and visualization can improve problem-solving ability. (ASK)

The graphing calculator affords the student in analysis a powerful tool to extend visualization, which was previously limited to textbook illustrations and time-consuming constructions. Provides illustrative examples used in initial classroom presentations of several topics including convergence and in student explorations of these topics. (ASK)

Presents four activities in which students cut out and assemble pieces to create Celtic designs. (ASK)

A random sample of middle school special education teachers from various classroom settings completed a survey asking them about what instructional practices and materials they used to teach students with disabilities how to solve word problems, how much time they allocated to problem solving instruction, and what type of problems they gave their…

Illustrates the contrasting thinking processes of two beginning calculus students' geometric and analytic schemes for the derivative function. Suggests that teachers can enhance students' understanding by continuing to demonstrate how different representations of the same mathematical concept provide additional information. (KHR)

Presents problems designed to focus student attention on the visual representations that accompany the verbal statements of problem situations involving motion over a period of time. Shows that as a result of engaging in these activities, students gain a better understanding of a given problem situation before they apply procedures to answer…