Cognitive development of eighth-grade students, as identified by Jean Piaget, occurs during a time when many of them are transitioning between concrete operations and formal operations where the ability to think in abstract concepts becomes possible. Because of this period of transition, many eighth-grade students find difficulty in demonstrating…

This paper discusses ways to use worked examples in teaching mathematics. It is argued that neither investigative teaching such as discovery learning nor lecturing and starting from the abstract are helpful as they are based on emotive associations with general labels rather than precise details of pedagogic strategies. (KHR)

Evaluates the thinking of third grade students in relation to an instructional program in probability which was informed by a research-based framework that included a description of students' probabilistic thinking. Reveals that overcoming misconceptions in sample space, applying both part-part and part-whole reasoning, and using invented language…

The study examined methods of mathematical problem solving with 34 gifted and 34 average Dutch 10 year olds. Typical questioning protocols are diagrammed and results tabulated. Preliminary findings suggest the potential value of explicit teaching of advanced mathematical problem-solving skills to pupils of average ability. (DB)

Discusses geometrical reasoning in the framework of the theory of Figural Concepts to highlight the interaction between the figural and conceptual components of geometrical concepts. Examples of students' difficulties and errors in geometrical reasoning are interpreted according to the internal tension that appears in figural concepts resulting…

This pamphlet reviews five reports that highlight an emerging consensus among researchers about the value of systematically incorporating cognitive instruction into the elementary school curriculum. First is a comprehensive framework by Robert J. Marzano and C. L. Hutchins for an integrated approach to thinking skills that has been developed and…

The papers contained in this document were originally presented at the May 1978 conference on Modeling Mathematical Cognitive Development sponsored by the Models of Learning Mathematics Working Group of the Georgia Center for the Study of Learning and Teaching Mathematics. Most have been revised to reflect comments and suggestions made at the…

Features five activities to nurture "number sense," promote practice in mental calculations, and promote student self-confidence in mathmatical operations. These are "hands-off" exercises that are preparatory to calculator and computer use for math. (ET)

Pragmatic and semantic problem solving are examined as processes that enhance acquisition of mathematical knowledge. It is suggested that development of mathematical cognition involves restructuring and that math teachers can help restructure children's knowledge systems by providing them with situations in which semantic and pragmatic problem…

This article describes a problem-solving strategy unit to be used as a supplement to the regular mathematics curriculum at the primary level. Specific teaching steps and examples are given for three developmental stages of thinking: (1) concrete, (2) representational, and (3) abstract. (DB)

Proposes analogy as the central mechanism of knowledge acquisition in formal domains. Discusses experimental data on preschoolers' knowledge of one-to-one correspondence and college students' understanding of force decomposition. Suggests that a knowledge base domain is a thematically organized knowledge structure and that thematic relations in a…

A teaching experiment with six third graders to analyze their ways of operating while solving fraction tasks. Children's quantitative reasoning with fractions was based on their quantitative reasoning with natural numbers. Presents the constructive itinerary of one of the most advanced children in the group. (Contains 44 references.) (Author/MDH)

Describes three activities that the teacher can employ to help students develop thinking skills through mathematics instruction: (1) memorization using the technique of chunking; (2) higher order thinking with magic squares; and (3) predicting games. Identifies eight facets of the teacher's role in promoting thinking skills. (MDH)

Examines operations of generalization, identification, discrimination, and synthesis in mathematical concept development from early childhood to late adolescence according to Vygotsky's theory of development. (MDH)

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…