This book deals addresses how the development of the human capacity for mathematical cognition occurs through educational experience. Chapters include: (1) "The Development of Math Competence in the Preschool and Early School Years: Cognitive Foundations and Instructional Strategies " (Sharon Griffin); (2) "Perspectives on Mathematics Strategy…

I, a teacher-researcher, present my fifth graders with an interesting but incorrect student-constructed proposal first seen in 1996. The students used the patterns they had detected while solving the chessboard task to formulate counterarguments. The five types of counterarguments which emerged offer insights into the children's understanding of…

This paper studies the modes of thought that occur during the act of solving problems in mathematics. It examines the two main instantiations of mathematical knowledge, the conceptual and the structural, and their role in the act. It claims that awareness of mathematical structure is the lever that educes mathematical knowledge existing in the…

NASA CONNECT is an annual series of integrated mathematics, science, and technology instructional distance learning programs for students in grades 6-8. This program is designed for students to learn about the evolution of flight. The program has three components--television broadcast, Web activity, and lesson guide--which are designed as an…

This paper explores the phenomenon of mathematical understanding, and offers a response to the question raised by Martin (2001) at PME-NA about the possibility for and nature of collective mathematical understanding. In referring to collective mathematical understanding we point to the kinds of learning and understanding we may see occurring when…

The degree of and the cognitive basis for the generalizability of academic self-efficacy were examined among 588 high school students from the greater Los Angeles (California) area. Students' self-efficacy perceptions clearly generalized beyond boundaries of specific tasks and also of specific school subjects, albeit to a lesser degree. There was…

The number and range of instructional resources in mathematics and science education can be overwhelming to educators. The chief mission of The Eisenhower National Clearinghouse for Mathematics and Science Education (ENC) is to help educators sort through the confusion by identifying relevant resources such as print materials, software, kits, and…

This paper discusses methodological difficulties in studying metacognition and proposes a new multi-method technique for assessing student metacognitive behavior. The major aim of the study was to develop and apply a strategy for assessing metacognition within the context of mathematical problem solving. Data were collected from 30 year-6 students…

Mathematics is not only about learning problem-solving methods; it is also about gaining a deeper understanding of their purpose, advantages and disadvantages. Frequently, the same problem can be solved by applying several different methods. Mathematics education should also include clues to those best fitting to the person's aim. To achieve that…

MathView is a computer algebra system designed to foster interactive exploration of mathematics. MathView is designed so that mathematics, both symbolic and graphic, is highly interactive. Change to a proposition in a MathView notebook produces a cascade of changes to the conclusions that are tied to the proposition. This structure helps to create…

Although proof and reasoning are seen as fundamental components of learning mathematics, research shows that many students continue to struggle with geometric proofs. In order to relate pedagogical methods to students' understanding of geometric proof, this 3-year project focuses on 2 components of student understanding of proof, namely, students'…

This digest discusses the unique needs of mathematically gifted students and reasons why curriculum and instruction should be differentiated for these learners in mixed-ability classrooms. Recommendations for differentiation include: (1) give pre-assessments so that students who already know the material do not have to repeat it but may be…

This volume presents different issues and views on research in mathematics education in Australia. Chapters include: (1) "An Introduction to This Review" (Kay Owens); (2) "Recent Research Monographs" (Kay Owens and editors of the monographs); (3) "Language Factors in Mathematics Education" (Nerida Ellerton, Ken…

There is plenty of "math on the menu" in the series of activities featured in this book. Students help the Rosada family start a Mexican restaurant featuring a variety of tostadas. Over the course of the unit, students apply different problem-solving strategies as they plan and expand the menu, determine different combinations of ingredients,…

This paper reviews an approach for finding optimal solutions to the traveling salesman problem, a well-known problem in combinational optimization, and describes implementing the approach using the MAPLE computer algebra system. The method employed in this approach to the problem is similar to the way ant colonies manage to establish shortest…