Duncan Symons and Derek Holton discuss the different types of mathematical reasoning and what each of these might look like in the classroom. By suggesting language that can be used to describe the different methods of reasoning, they hope to provide teachers with the tools they need to better recognise and assess student reasoning.

The present study is a part of design research in local instructional theory in a pre-algebraic lesson using the Realistic Mathematics Education (RME) approach. The article will focus on recommendations for the type of pre-algebra class that supports elementary school students' algebraic thinking. As design research study, it followed the three…

Turkish primary mathematics curriculum emphasizes the role of problem solving for teaching mathematics and pays particular attention to problem solving strategies. Patterns as a subject and the use of patterns as a non-routine problem solving strategy are also emphasized in the curriculum. The primary purpose of this study was to determine how…

What is the role of patterns in developing algebraic reasoning? This important question deserves thoughtful attention. In response, this article examines some differing views of algebraic reasoning, discusses a controversy regarding patterns, and describes how three types of patterns--in contextual problems, in growing geometric figures, and in…

The authors document their experience of working with 6-year-olds over several weeks. They share some observations that arise from weekly sessions they conducted which have been under way for several years and which have been widely reported. These observations show the payoff of a problem-solving approach to learning.

A set of geometric pieces is used to solve problems involving geometry, combinations, division, and money. (JT)

The focus is on the problem-solving strategy of find a pattern, with a problem explored to illustrate how to use the strategy. Other tips concern classroom climate, checking skills, research, and type of problems. (MNS)

Presents responses to the pattern problem that appeared in the November 1998 "Problem Solvers" section of this journal. (ASK)

This article reports on the use of a unique number system to facilitate teachers' understanding of the concepts of place value. Teachers' mastery of base-ten may hinder their recognition of the difficulties students have with place value, so the authors created a number system that used five symbols to represent values. Using this system, teachers…

These student worksheets include activities in counting, place value, estimation, the four operations with whole numbers, number patterns, volume, inequalities, decimal equivalents of fractions, and percents, all to be worked with a calculator. (MP)

Five different ways are outlined in which calculators can be used to develop a student's ability: (1) to solve problems which use real-world data; (2) for solving a greater number of standard word problems; (3) for using different approaches to solve problems; (4) for extending problem situations; and (5) for using the calculator in an…

When a simple game was presented as a challenge to a primary-school girl, she solved the problem, and went on to generalize her solution. (SD)