Independent study for gifted and talented middle-level students progresses through five stages, from the affective sensing of a problem to be solved through assessing both product and process. J. Renzulli's Enrichment Triad model can serve as a framework for independent study, which must be carefully structured and guided. (CL)

This document contains informal geometry explorations that provide students with opportunities to investigate the environment from a geometric perspective, construct connections between related mathematics and other content areas, and solve problems in a geometric context. The activities provide experiences that develop curiosity, understanding,…

The purposes of this study were: (1) to test several social decision schemes to obtain plausible explanations of different group processes in solving different disjunctive tasks; and (2) to study both dyads and tetrads solving a eureka and a non-eureka disjunctive task. Social decision schemes theory assumes that a group decision is a joint…

Develops a division algorithm in terms of familiar manipulations of concrete objects and presents it with a series of questions for diagnosis of students' understanding of the algorithm in terms of the concrete model utilized. Also offers general guidelines for using concrete illustrations to explain algorithms and other mathematical principles.…

This article describes a proposed model of self-directed critical thinking that comprises two interrelated and equal components: one cognitive and the other motivational. The model stresses the importance in critical thinking of the child's present store of general information. Examples illustrate the operation of the model. (IAH)

Outlines Piaget's late ideas on categories and morphisms and the impact of these ideas on the comprehension of the inclusion relationship and the solution of arithmetic problems. Reports a study in which fourth through sixth graders were given arithmetic problems involving two known quantities associated with changes rather than states. Identified…

Describes a paradigm for generating a variety of problem situations in middle school mathematics, ranging from combining a single mathematical concept or process with a single context, to combining multiple concepts or processes with multiple contexts. Offers several illustrative examples. (SR)

This paper discusses a cognitive model of how action agendas and goals emerge through the dynamics of self-organization in collaborative activities. While machines are designed to perform a function, or goal, humans are self-organizing systems that set their own goals and produce order without having external order imposed on them, or, more…

Demonstrates and compares three commercially available statistical software packages, Statistics Workshop, Data Insights, and Data Desk, using a five-component investigation model to analyze a problem about hat sizes. (MKR)

Student questioning within the Search, Solve, Create, and Share (SSCS) problem solving instructional model was investigated. The results suggest that the SSCS problem-solving instructional model increases student questioning in the presence of the teacher (n=22) when compared to a teacher-directed laboratory instructional model. The implications…

Describes the Six Through Eight Mathematics (STEM) middle school mathematics curriculum project. Emphasizes that the use of thematic modules promotes students' development and application of mathematical concepts in broad contextual situations. Presents an assessment criteria for teachers and focuses on the use of open questions and their role in…

Examines the impact of one unit of a curriculum module for sixth grade from the Model-based Analysis and Reasoning in Science (MARS) project. Provides an overview of this unit on mass and discusses three aspects of the evaluation of the unit. Contains 22 references. (DDR)

U.S. mathematics education has been criticized for being too broad. This article examines ways middle school students use simple problems and situations to foster a deeper understanding of underlying concepts. Presents a sample area and perimeter problem, describes extending the problem using tiles to determine minimum perimeter, and discusses…

A school district's program coordinator designed and implemented a practicum study intended to provide intermediate grade teachers and students with problem-solving techniques and skills needed for success in a course in contemporary Canadian issues. Teachers' and students' problem-solving skills were assessed through reports based on…

One hundred French children in grade five participated in an experiment to determine how the problem frame facilitates comprehension of a problem solution text. Results demonstrate the positive role of frames in macrostructure construction and support the model of T. A. van Dijk and W. Kintsch (1983). (SLD)