This book is intended to provide practical guidance to elementary grade teachers in inclusive classrooms with students having difficulties in learning mathematics. Following an introductory chapter, chapter 1 provides an overview through the use of case studies of three students that note research on learning difficulties in mathematics, and on…

The following ideas are presented: (1) an approach to exploring some of the patterns of prime numbers as a junior high activity; and (2) an informal introduction to continuity functions that uses pictures to represent simple physical situations, with suggestions for follow-up exercises. (MP)

An investigation of patterns in magic triangles leads to a number of discoveries concerning the sums of sides and corners. (MP)

This article describes how two young children with moderate/severe mental retardation were taught functional counting skills by helping with a snack delivery activity. Instruction involved a task analysis, use of pictures to represent objects and numbers, self-monitoring to increase student independence, and ongoing evaluation. The importance of…

Performance of 5 students (ages 8 and 10) with moderate intellectual disability was compared as they received the DISTAR Arithmetic instructional intervention and a Discrimination Learning Theory (DLT) intervention not requiring a fast-paced verbal student response. Academic engagement and skill mastery were greater during the DLT intervention.…

Reviewed is an integrated approach to teaching place-value concepts. A semi-integrated approach is proposed which may provide a more effective implementation of the technique. (CW)

This experimental study compared the use of Belcastro rods with the use of traditional methods in teaching addition and subtraction of whole numbers to five blind students. Results showed a significant difference favoring the use of Belcastro rods. (Contains 30 references.) (MKR)

This article describes a series of mathematics activities based on the book "A Grain of Rice," which are designed to help students understand powers of 2. Ideas for activities in other disciplines are also provided. (Contains 3 tables.)

A sequence of number pairs can be used to generate many interesting examples in teaching mathematics subjects at various levels. It is often used in elementary or middle school mathematics classes to illustrate the concept of "patterns." In this paper the authors present a few interesting ways of using this sequence to form examples for high…

In this article, the authors would like to look at a range of solutions submitted by Year 4-5 teams in the 2003 "Naturally Mathematical Challenge" to a question that involves no more than the numbers 1 to 6 and possible arrangements of them. In the context of other competition questions and in their elaboration of mathematical process,…

We present a summary of a study carried out with students of the first year of Bachillerato (the first of two pre-university non-obligatory secondary education courses in Spain) to determine and analyse some of their errors and difficulties in learning inequalities with the aim of improving the teaching-learning process of this topic. The study…

The Proceedings of PME-XI has been published in three separate volumes because of the large total of 161 individual conference papers reported. Volume I contains four plenary papers, all on the subject of "constructivism," and 44 commented papers arranged under 4 themes. Volume II contains 56 papers (39 commented; 17 uncommented)…

The development of the place value system and its universal use demonstrate the elegance and efficiency of mathematics. This paper examines the concept of place value by: (1) presenting the historical development of the concept of place value in the Hindu-Arabic system; (2) considering the evolution of the number zero and its role in place value;…

This book contains a classroom-tested approach to the teaching of problem solving to all students in Grades 6-8, regardless of ability. Information on problem solving in general is provided, then mathematical problems on logic, exponents, fractions, pre-algebra, algebra, geometry, number theory, set theory, ratio, proportion, percent, probability,…

Activities and teaching methods for developing an understanding of fractions are presented. The activities, which use mathematical models (visual representations of fractions), are divided into three sections: (1) equivalent fraction circles; (2) fraction bars; and (3) multiplication of fractional numbers using squares. Each section includes the…