Given is an alternative to individual divisibility rules by generating a general process that can be applied to establish divisibility by any number. The process relies on modular arithmetic and the concept of congruence. (MNS)

Plotting a polynomial over the range of real numbers when its derivative contains complex roots is discussed. The polynomials are graphed by calculating the minimums, maximums, and zeros of the function. (MNS)

Data on sex differences in rote-counting ability for 4722 first-grade children are presented. How different data-gathering methods and different statistical treatments of the data can yield differing results are indicated. (MNS)

Four worksheets are given to enhance the understanding of and facility with numerical concepts and relations for students in grades seven through nine. The focus is on enhancing deductive reasoning abilities with Venn diagrams and arrow diagrams. Teaching ideas are included. (MNS)

An addition "trick," an analysis of why it works, and steps in constructing other problems of the same type from the basis of a discovery learning activity for addition. (DT)

Suggestions are given concerning the use of the pocket calculator for computations that are too trivial to be processed by a computer but too time-consuming for manual calculation. Several examples from arithmetic, algebra, trigonometry, and calculus are included. (DT)

The proof of a number trick is given. (DT)

Activities are suggested which emphasize finding patterns in multiplication of fractions, decimals, and negative numbers, in division of fractions, and in conversions within the metric system. (DT)

Based on a survey of 3067 Finnish 5th and 7th graders and a task-based interview of 20 7th graders we examine student's understanding of fraction. Two tasks frame a specific fraction (3/4) in different contexts: as part of an eight-piece bar (area context) and as a location on a number line. The results suggest that students' understanding of…

This report describes a program for improving students' mathematical thinking skills through improved use of mathematics vocabulary and numerical operations. The targeted population includes sixth grade general education mathematics students and ninth grade special education mathematics students. The students' inabilities to effectively solve…

This document represents volumes 1 and 2 of the proceedings of the 24th annual conference of the Mathematics Education Research Group of Australasia (MERGA) held at the University of Sydney, June 30-July 4, 2001. In volume 1, papers include: (1) "Connecting Mathematics Education Research to Practice" (Judith Sowder); (2) "Understanding, Assessing,…

The view of the researcher is that students in the upper elementary to middle school range need to increase their problem-solving skills by making logical deductions and organizing and structuring their thoughts through the use of word problems. Giving children a daily word problem challenged and introduced them to the lesson. This activity…

This paper discusses the theories of conceptual change and how they explain the difficulties in mathematics learning, especially in enlarging the number concept. Two studies are presented, one of which examines the research questions: What is the role of prior knowledge in students' answers to questions about the density of rational and real…

The ability to use algebra in describing and analyzing real-world situations is becoming a basic skill for all students. The main focus of this book is on patterns, functions, and relationships. Information and ideas on how algebraic thinking can be developed in the years leading to a formal algebra course are included. K-8 teachers are offered a…

This book features a set of problems assembled to reflect the criteria of the mathematics portion of the North Carolina High School Comprehensive Test. The problems are not necessarily suited to timed situations but rather are intended for classroom use by teachers to review high school mathematics and build upon concepts and skills developed in…