The need to provide understandable problems and ways to help children understand problems are explored. An interview with a sixth grader depicts his incorrect strategies and leads to suggestions for teaching problem solving using a range of mathematical models for each operation. (MNS)

Reports that microcomputer use will help six year-old children solve some types of problems better but will not improve their general learning and thinking abilities. Logo programing resulted in higher creativity scores and in children's ability to monitor their own thinking, but revolutionary changes in cognitive development were not found. (DH)

Beginning with a simple computer program to teach a fundamental concept and building in small increments is suggested. For the topic of repeated operations, three activities, an extension, and some problems are given. (MNS)

Solutions to addition and subtraction word problems were studied in a three-year longitudinal study that followed 88 children from grades one to three. They solved problems using a variety of strategies before formal instruction and used invented strategies several years after formal instruction. Four levels of problem-solving ability were found.…

The case study presented in this report was part of assessing a teaching proposal on ratio and proportion. A group of sixth-grade students of elementary education in Mexico participated in the implementation of the proposal. The girl of the case study was representative of those students in the group who had a lot of recourse to handling…

The Purposeful Algebraic Activity project aims to explore the potential of spreadsheets in the introduction to algebra and algebraic thinking. We discuss two sub-themes within the project: tracing the development of pupils' construction of meaning for variable from arithmetic-based activity, through use of spreadsheets, and into formal algebra,…

Teachers' concerns and efficacy beliefs (EB) are important for the success of any reform. Previous research has shown that teachers? concerns develop in three levels: self, task and impact, respectively. Thus, this study examines the concerns and EB of primary teachers with respect to a reform concerning the use of Schema Theory in teaching…

This report summarizes findings of current research supported by the Office of Special Education Programs on effective mathematics instruction for students with disabilities. The first brief article notes that most special education teachers do not have sufficient knowledge about the National Council of Teachers of Mathematics Standards and this…

This paper explores the role of open-ended realistic division problem in the development of algebraic reasoning. A written test was administered to 672 students. From the results of this test students were selected for semi-structured interviews. The students were interviewed in pairs and were asked to explain to each other how they would solve…

This paper will discuss some findings from a study investigating the development of the proving process in a dynamic geometry environment. Through a detailed analysis of students' processes when working with open geometry problems involving conjecturing and proving in Cabri, an analytical and explanatory framework has been developed. This paper…

In the study, a part of longitudinal research focused on the emergence of mathematical knowledge structures in a learner's mind is presented. It concentrates on the analysis of introspective data gained from the author's study of a non-standard arithmetic structure in terms of the model of abstraction in context (Hershkowitz, Schwarz and Dreyfus).…

This paper examines the change in young children's understanding of equals as equivalence over a three-year period and their ability to express this understanding in real world problems. Seventy-six children participated in the longitudinal study. The results indicate that approximately one third of the sample had an understanding of equals as…

The first in a three-volume set, this book focuses on young children between the ages of four and eight as they construct a deeper understanding of numbers and the operations of addition and subtraction. Rather than offer unrelated activities, this book provides a concerted, unified description of development with a focus on big ideas, progressive…

Children in primary education often encounter mathematics having picked up a general fear of mathematics from the society around them. This results in lack of confidence, avoidance of non-standard thought processes, weakness in problem solving strategies, and other negative consequences. This study offers an alternative approach: presenting…

This book is a compatible instructional component to any algebra textbook and was developed by University of Hawaii under the Dwight D. Eisenhower Mathematics and Science Education Improvement Act. The tasks align with the content and instructional approach used in daily classes that emphasize standards-based teaching and learning. The tasks…