Interviewed 59 2nd- and 44 3rd-year elementary school students concerning their solutions to arithmetic problems commensurate with their age and ability. The results indicate that as children progress through school, they continue to use counting as an important part of their problem-solving repertoire, combining counting skills in idiosyncratic…

In this article, constructivism is examined as an epistemological basis for school science and mathematics instruction. The nature and process of constructing scientific and mathematical knowledge in school settings is also considered. A distinction is made between truth and feasibility, and the implications for science education are discussed.…

This article describes "Thinking Actively in a Social Context," a multiphase model to assist in the development of problem-solving courses based on student needs and experiences. An example of such an interdisciplinary course (simulating a new settlement on another planet) for high ability children in grades five, six, and seven is detailed. (DB)

Examined differences in cognitive and metacognitive processes of 40 high- and low-mathematics-ability students in grade 12 as they solved 5 everyday mathematics problems. Competence in problem solving was characterized by a rich knowledge base, metacognitive strategies, and confidence. Boys and girls exhibited different cognitive structures for…

Examined the development of proportional reasoning by means of a temperature mixture task. Results show the importance of distinguishing between intuitive knowledge and formal computational knowledge of proportional concepts. Provides a new perspective on the relation of intuitive and computational knowledge during development. (GLR)

Describes a study that was designed to investigate the relationship between certain features of interactive video design and the deployment and development of cognitive problem-solving skills. Middle school mathematics students used for the study are described, the use of videotapes and interviews is discussed, and group dynamics are examined. (26…

A study demonstrated that the problem-solving ability of 45 first grade, Hispanic, bilingual children was related to the semantic structures of word problems in a similar manner for both of the children's languages and in a manner similar to that of monolingual speakers. (Author/LB)

Discusses the use of a historical profile for illustrating the significance of the mathematical components of scientific laws. Addresses the need for the purposive use of scientific laws rather than the blind substitutionary procedures characteristic of most problem solvers. Claims the approach has the potential for increasing female participation…

Mismatch between gesture and speech was used to study cognitive processes that characterize the transition between incorrect, but rule-governed, problem understanding to correct rule-governed understanding among 90 fourth graders in Chicago (Illinois). Data support the idea that the transitional state is characterized by concurrent activation of…

Argues that the correct use of positive and negative signs in textbooks is often ignored and that this misuse might be because the authors are unaware of some basic rules. (DDR)

Technology offers tools and information that students need to explore real-world mathematical connections and investigate questions reflecting their own interests. This article illustrates how students can use technology to gather and interpret information, perform descriptive and graphical analysis, make statistical predictions, and create and…

Argues that reform in curriculum and instruction should be based on students resolving problems rather than mastering skills and applying them. An alternative is proposed that builds on John Dewey's "reflective inquiry," arguing that this approach would facilitate students' understanding. This proposal is compared with other views on the…

A study examined understanding of number line concepts by 4th grade culturally and linguistically diverse (CLD) students (n=30), students with learning disabilities (n=23), and 21 controls. CLD students with disabilities demonstrated difficulty due to several factors beyond lack of language competence, including failure to apply number lines to…

Discusses geometry and Dynamical Geometry Software (DGS). Analyses the way DGS-use influences traditional geometry. Highlights changes in the interactions between geometry, computers, and DGS and human users, focusing on changes in the teaching and learning of geometry. Concludes that DGS deeply changes geometry if it is taken as a human activity…

This article presents specific instructional approaches and examples to develop the algebraic reasoning skills of middle and secondary students with mild disabilities. Discussion of the National Council of Teachers of Mathematics standards identifies general principles, content standards, and process standards. Discussion of effective instruction…