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…

Thirty-one 8- and 9-year-old children selected for dyscalculia, reading difficulties or both, were compared to controls on a range of basic number processing tasks. Children with dyscalculia only had impaired performance on the tasks despite high-average performance on tests of IQ, vocabulary and working memory tasks. Children with reading…

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…

This paper presents a description of the different types of arguments that emerged as two students, working in a computerized environment, engaged in an investigation of several number theory concepts. The emerging arguments are seen as a result of the influence of the computerized environment together with collaborative learning. Using…

This article presents several activities (some involving graphing calculators) designed to guide students to discover several interesting properties of Fibonacci numbers. Then, we explore interesting connections between Fibonacci numbers and matrices; using this connection and induction we prove divisibility properties of Fibonacci numbers.

A conceptually sound, research-based method is presented to make sense of students' thinking about length. It is suggested that the levels of framework is an important tool for improving instruction and formative assessment as well as effectively diagnosing and remediating students' difficulties in learning about length. Some of the measurement…

The authors present an analysis of portfolio entries submitted by candidates seeking certification by the National Board for Professional Teaching Standards in the area of Early Adolescence/Mathematics. Analyses of mathematical features revealed that the tasks used in instruction included a range of mathematics topics but were not consistently…

This course guide is intended for classroom use by teachers of secondary level mathematics to Spanish-speaking students of English as a second language (ESL). Both mathematical instruction and acquisition of English mathematical terminology are emphasized. The book is divided into chapters that comprise a Spanish-English glossary of mathematical…

"How much popcorn will our classroom hold?" This intriguing question sparked a terrific integrated science and math exploration that the author conducted with fifth-and sixth-grade students. In the process of finding the classroom's volume, students developed science-process skills (e.g., developing a plan, measurement, collecting and interpreting…

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…

Counting books offer children the time and the tools to develop the understanding needed to solve problems. Stimulated by these books, children may use mathematic language and talk about mathematics as they get involved with materials to move and manipulate, as they use supportive aids found in illustrations, and as they interact with materials to…