In an accompanying study, Alibali et al. [Alibali, M. W., Ockuly, K. M., Fischer, A. D. (2009) "Learning new problem-solving strategies leads to changes in problem representation." "Cognitive Development, 24," 89-101.] present an important experimental result: introducing a new strategy can affect conceptual aspects of children's problem…

This paper suggests a route to deep, long-term algebra reform that begins not with more new approaches but with elementary school teachers and the reform efforts that currently exist. This route involves generalization and expression of that generality using increasingly formal languages, beginning with arithmetic, modeling situations, geometry,…

Are certain basic (manipulating and other) skills still necessary in math teaching? This paper provides examples to demonstrate that modern computers and hand-held technologies can be used to encourage students of all levels to practice those skills. The examples have proven to be successful in classrooms, and there are many other possibilities to…

Lists 19 arguments as to why mathematics history should be introduced into the mathematics curriculum, including: (1) history helps increase motivation for learning; (2) history makes mathematics less frightening; and (3) history helps students better understand concepts. Gives 10 specific examples of how this history could be provided to a…

This article proposes a taxonomy of strategies for single-digit multiplication, then uses it to elucidate the nature of the learning tasks involved in multiplication. In preceding work, it has generally been assumed that much of children's strategy development is driven by changes in their general conceptual capabilities relating to number. In…

Students should be encouraged to focus on a big mathematical idea and to look for connections between problems and solution strategies. This unified view suggests that the students are developing computational fluency with fractions.

Points out difficulties experienced by developmental students in dealing with abstractions in language and mathematics. Shows how students can be taught mathematical concepts by using concrete examples and their own colloquial language to better grasp abstractions. (DMM)

Mathematical thinking as a style of thinking that is a function of particular operations, processes, and dynamics is explored. A descriptive model of mathematical thinking is presented and used to provide answers to whether mathematical thinking can be taught and how. (MNS)

Raises issues and questions concerning the judicious choice of a textbook to teach the history of mathematics. (Author/KHR)

Investigates the effects of computers and Internet technology on teaching and learning. Presents electronic examples that integrate well with high-quality mathematics instructional programs. (KHR)

This paper describes one approach to implementing cooperative learning in mathematics classes virtually 100% of the time. By describing this maximum approach, it is hoped that teachers will be encouraged to try cooperative learning at least part of the time in their classrooms. Cooperative learning activities help identify widespread student…

Discusses diagrams and problem solvers' constructions of a problem situation, how the way of drawing changes during the problem-solving process, and the meaning and sense of diagrams. (Contains 15 references.) (MKR)

Proposes looking at the percent symbol (%) as an operator, which means to divide any number in front of it by 100. Stresses the importance of using correct words to describe the numbers generated in percent calculations. Explains how to (1) calculate percent using equivalent fractions; (2) divide fraction numerators by denominators, retaining the…

Based on the premise that meaningful learning in mathematics occurs when children link their understandings with the symbols and procedures they are taught, three places are identified where children can link symbols and their referents, procedural rules and conceptual knowledge, and answers to problems with other knowledge about what is…

This paper defines ethnomathematics and reviews the methods used to incorporate this philosophy into the current teaching of mathematics. Ethnomathematics rejects inequity, arrogance, and bigotry while challenging the Eurocentric bias that denies the mathematical contributions and rigor of other cultures. A review of the literature shows that the…