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 focuses on some cognitive and didactical phenomena that feature processes and products of pupils in grades 7-12 who learned mathematical proof within technological environments. The main issues in the analysis of students' performances consist of metaphors, deictics, mental times, narratives, functions of dragging, abductions, and…

Presents a study designed to explore whether a student's use of the graphing calculator during instruction will affect their concept of function, how students' participation in a conceptual change assignment affects their concept of function, and how the graphing calculator and the conceptual change assignment interact with one another to…

In two parallel one-year studies, solution strategies for subtraction number facts and achievement patterns of matched groups of first graders in two different instructional programs were examined. Significant differences between groups were found favoring the strategy approach. (Author/CW)

This response to EC 607 382 stresses the value of dialog between mathematics educators and special educators and raises three concerns about the standards of the National Council of Teachers of Mathematics (NCTM). Cognitive strategy instruction is recommended as an effective approach for teaching problem solving to students with disabilities. (DB)

There has long been dispute in mathematics between the drill and practice orientation that focuses primarily on memorizing mathematics as meaningless rote algorithms and the approach based on understanding and making creative use of mathematics. This 25-chapter book, based on a 7-year study at the University of Illinois, seeks to explain and…

Student comments about having time in class to think and solve problems are presented. Stressed are teaching methods which allow students to familiarize themselves with the problem, think about solution processes, work through the solution process, and reflect while solving a problem. (CW)

An understanding of fraction addition can be thought to involve two quantitative ideas: (1) the understanding that adding to an original quantity increases its size, and (2) a sense of how much increase occurs. Both of these ideas should underlie or inform a child's approach to problems involving fraction addition and thereby constrain the class…

Reported is a naturalistic study of the role of mathematical paradoxes in the preservice education of high school mathematics teachers. Findings indicate that the model of resolving paradoxes as applied in this study has relevance to such aspects of mathematics education as cognitive conflicts, motivation, misconceptions, and constructive…

This article discusses ways to improve mathematics performance of students with learning disabilities through cognitive strategies instruction. Principles of a strategic classroom environment are explained, such as involving students in goalsetting and providing advance organizers. Three specific strategies for math instruction are described:…

This book explores what makes mathematics possible as well as what makes mathematics difficult. Included is a discussion of the definition of mathematics, mathematics in language, the meaning of numbers, calculating and measuring, notation, numbers in space, and the best ways to learn mathematics. Historical information and practical examples are…

Presents two teaching ideas for mathematics instruction. The first employs "mind maps" as a method to help students learn, record, and recall mathematical information. Provides examples for solving quadratic equations and complex numbers. The second discusses two ways to find the average speed during a trip employing differing constant…

Children's responses to an alternative model over three lessons were described and their learning assessed in a posttest. Their responses and performances were compared to that of a similar group of children learning through a conventional number line model. The two models were compared from practical and theoretical viewpoints. (Author/CW)

Used are test and interview data to extract evidence as to what level tenth graders have coordinated the worlds of arithmetic and algebra and can move freely between them. More dissociation is shown than was expected. (Author/MVL)

The contrast between the teaching of reading and mathematics is drawn. A new set of learning conditions for mathematics is presented based on a model of reading instruction. Immersion, demonstration, engagement, expectations, responsibility, use approximation, response, refinement, and outcomes are discussed. (CW)