How multiplication is usually taught in school and how it could be taught are discussed. Development of understanding is illustrated through children's words and work. (MNS)

The discussions of the theme group on Technology and Cognitive Development at the Fifth International Congress on Mathematical Education are summarized. How computers can be used to engage students actively, to promote problem-solving skills, and to achieve better understanding is discussed. (MNS)

Reviews recent research in the area of mathematical understanding and compares and contrasts it with a model formulated for the growth of understanding. Uses the analysis of a transcript from an interview with an eight-year-old boy to illustrate the power of the model to describe and map the growth of his mathematical understanding. (18…

The second in a series of three articles, some themes of an undercurrent of educational objectives that move beyond the evident content goals are outlined. The themes relate the computer software materials analyzed in Part I to the cognitive experiences that students should have in learning about subject matter. (MDH)

A year-long study in 40 eighth grade mathematics classrooms compared the effect on student achievement of teaching with meaning with algorithmic-practice teaching. In general, teaching with meaning was found to increase student achievement. However, differences in response to the methods was seen in the top, middle, and lower thirds of the…

Using case studies that are functionalist in orientation and computational in technique, the role of control knowledge in developing constructive thinking is illustrated. Further, the integration of related knowledge structures, emanating from diverse sensory modes and pertaining to both place value in addition and angle relationships in geometry,…

Responses of students in grades K-10 (42 interviewed; 98 written) to 4 common fractions problems were analyzed for iconic mode processes in relationship to concrete symbolic mode development. Concludes that progress in the latter, without development of complementary iconic support, limits both understanding and flexibility in solving problems.…

This study explored how one eighth grade girl learned about the structure of recursive programs in BOXER programing language. The method of impasse resolution was presented in detail and used both to understand how she constructed her understanding and as an empirical method to analyze her learning. (MDH)

Examines the issue of how calculators and computers can best be used in mathematics education. Contends that practicing a procedure is noncognitive and does not produce learning. Suggests utilizing customized computerized tools in schools for getting answers to algorithmic problems instantly, thus allowing teachers to explain and students to…

Discusses the use of writing to enhance learning in mathematics from a conceptual development perspective. Shuell's phases of learning are described as a general model for conceptual development and subsequently matched with Britton's categories for transactional-informative writing. Sample mathematics assignments for each writing category are…

Examines the potential role for Computer Algebra Systems (CAS) when teaching courses as functions, calculus, and linear algebra to students with low prerequisite algebra skills. A study reports the rationale, planning, and implementation of a functions course integrating Maple CAS into instruction. (MDH)

A longitudinal study followed Brian from grade five through grade seven to examine his representation and development of mathematical knowledge. Some observations over the four years were that Brian liked to figure things out, responded poorly to suggestions not fitting the representation he constructed, and changed attitudes from purposeful and…