This research was designed to study Taiwanese junior high school students' understanding about the validity of conditional statements. Distinguishing between validity and truth is a crucial topic in mathematical reasoning and argumentation but has been always neglected in the mathematics curriculum at junior high school level of schooling. The…

In the present article, we argue that the conceptual change approach to learning can apply in the case of mathematics, taking into consideration the particular nature of mathematical knowledge and the neurobiological bases of mathematical cognition. In the empirical study that is reported in this article, we investigated ninth graders'…

The research on conceptual change has so far mainly dealt with cognitive outcomes, but especially during the last few years there has been a growing interest in and discussion about the processes of conceptual change. The purpose of the article is to contribute to this discussion and to present a theoretical model of the dynamics among the…

Children's accounts of their participation in sociocultural activity related to number are essential for their teachers in order that they can assist children in building their formal learning in number on informally acquired numerical understandings. Children's participation in sociocultural activity related to number will differ from child to…

This volume is a teacher's edition in a series of books that contain open-ended exploration activities and experiments. These activities allow and encourage students to set their own goals, use their own creativity and ideas, investigate the wonders of nature, learn about the workings of real businesses, and draw conclusions from their…

Team research is important in studying cognition as enactive. This paper contains four different pieces of research directed toward the evidences and artifacts of two students in Canada engaging in a sustained mathematical activity. These four portraits of mathematical cognition in action consider the conversation in which the activity occurs; the…

This book reinforces the outstanding work done by the National Council of Teachers of Mathematics (NCTM) in developing curriculum standards for students in kindergarten through fourth grade by discussing the 13 strands of mathematics and their implications for teachers and parents who work with students. It also provides some suggested resources…

Four preschool children with developmental delays were taught to name the numerical value of sets of geometric figures, the corresponding numeral, the corresponding number word, and the corresponding Roman numeral. Half of the stimuli were taught with instructive feedback and the other half without, as two conditions were established: the future…

The purpose of this document is to provide a framework around which systems and schools may build their mathematics curriculum. Important components of a mathematics education for the majority of students are identified. This document is presented in two parts. Part I, Principle for School Mathematics, addresses questions such as what is…

This paper describes a study that examined parents' beliefs about children's number skill development. Twenty-seven parents of 4- and 5-year-olds were interviewed about number tasks that could be solved by children between the ages of 4 and 7 years. In addition, parents were asked a series of open-ended questions about how they would answer a…

A mathematics curriculum for moderately and severely retarded and autistic students and adults should possess 10 necessary characteristics, including provision for instruction based on assessment results, stress on functional application, focus on generalization of skills, and specific criteria for mastery of each skill. The functional but…

This report, written in Finnish with a 10-page summary in English, concerns research on the interrelationship between Piagetian operations, various aspects of information processing capacity and mathematical thought processes and strategies related to number and measurement. In a theoretical discussion, Piaget's research on mathematico-logical…

Flowcharting of algorithmic procedures can be a useful tool for teachers of remedial arithmetic. (SD)

A problem solving approach to the teaching of the Pythagorean Theorem is described. (SD)

A unit on problems involving large numbers can begin with calculating the amounts of ingredients needed to produce several thousand hamburgers. Other sources of computational problems are described. (SD)