Thirty-eight sixth graders were trained in fraction calculation through progressive transformation dialectics (PT) whereas a control group of 38 was taught through a traditional mathematics education framework. The PT group, encouraged to form network-type knowledge representations, performed better on problems that required more than mere…

Describes computation of a continued radical to approximate the golden ratio and presents two well-known geometric interpretations of it. Uses guided-discovery to investigate different repeated radicals to see what values they approximate, the golden-rectangle interpretation of these continued radicals, and the golden-section interpretation. (KHR)

Two learning-disabled, three educable mentally retarded, and two trainable mentally retarded senior secondary students were trained to count money rapidly. All subjects significantly improved their counting rates, maintained a 90 percent level of accuracy, and maintained their skills across settings and over time. (Author/JDD)

This article describes techniques that utilize literature to help students develop a number sense and to enliven math classes. Books and activities are suggested that address concepts of pattern and order, counting, estimation, factorial analysis, and exponents. Techniques incorporate open-ended discussions that leave room for emotion, intuition,…

Presented are definitions and a grid to clarify relationships between terms. Discussed is an example of the application of Einstein coefficients and some suggestions for teaching this concept. (CW)

It is argued that number sense develops through meaningful, purposeful activities involving calculating, measuring, and estimating. Understandings that must be developed with each are discussed. More emphasis needs to be placed on thinking about the various procedures that can be used to solve problems and on interpreting the answers. (MNS)

The use of developmental algorithms to develop skills is described. Children make the transition from using concrete materials to using a standard algorithm. (MNS)

Shows how to model Newton's method for approximating roots on a spreadsheet. (MKR)

This study demonstrated the effectiveness and efficiency of a constant time delay procedure (four seconds) to teach five elementary students with learning disabilities multiplication facts. Learning generalized to a paper-and-pencil task, to a different presentation orientation, and to reverse facts. (DB)

Examples and solutions to these problems are presented. Figures for which different equations are necessary are presented. The use of the geoboard for this exploration is emphasized. (CW)

In the current study, a constant time delay (CTD) procedure was embedded in classroom activities and routines to teach counting to three preschool children with speech and language delays. CTD was effective in teaching numbers to all three children. One child out of two also was able to acquire non-target information. (Contains references.) (CR)

Web enjoyment has been regarded as a component of system experience. However, there has been little targeted research considering the role of web enjoyment alone in student learning using web-based systems. To address this gap, this study aims to examine the influence of web enjoyment on learning performance and perceptions by controlling system…

Following a pretest, 11 participants who were naive with regard to various algebraic and trigonometric transformations received an introductory lecture regarding the fundamentals of the rectangular coordinate system. Following the lecture, they took part in a computer-interactive matching-to-sample procedure in which they received training on…

This article presents a teaching experiment on the relationship between informal out-of-school and formal in-school mathematics, and the ways each can inform the other in the development of abstract mathematical knowledge. This study concerns the understanding of some aspects of the multiplicative structure of decimal numbers. It involved a series…

Hoping to develop in her students an understanding of mathematics as a way of thinking more than a way of doing, the author of this article describes how her students worked on a spatial reasoning problem stemming from an iteratively constructed sequence of cylinders. She presents an activity of making cylinders out of paper models, and for every…