Discusses mathematical tasks, classroom environments, and means of assessment that might encourage mathematical growth for middle grades students. Proposes a curriculum emphasizing mathematical connections, reasoning, and problem solving. Describes shifts in the culture of the mathematics classroom that support students' development of…

Kindergarten students' (n=7) thought processes were investigated during a problem-solving task to gain insight into students' problem-solving strategies and to guide students toward a closer awareness of their own mathematical thinking. Outlines some of the processes and problems of implementing a constructivist approach by an experienced teacher.…

A mapping procedure based on the SOLO Taxonomy developmental model was used to classify the problem-solving strategies of students (n=34) in grades K-2. Only one multiplication problem was used to isolate three components of the problem-solving procedure. (MDH)

Beginning physics students (n=42) were constrained to analyze mechanics problems according to a hierarchical scheme that integrated concepts, principles, and procedures. After five one-hour sessions, students increased their reliance on the use of principles in categorizing problems according to similarity of solution and in writing qualitative…

Examined the quality of responses of six classes of grade six students to four questions requiring multiple and generalized solutions posed under varying conditions. Results indicated that this type of question can be useful in classrooms because students can respond at a variety of levels. (13 references) (MDH)

Discusses the process of mathematical iteration, its benefits as a problem-solving technique, and how to teach it. Presents a selection of mathematical ideas and problems that can be solved and explored using iteration, along with related BASIC computer programs. (MDH)

When preparing middle-level students for the information Age, educators must consider staff-development needs in the areas of computer technology and portfolio design; classroom restructuring for project-based curriculum; integrated subject disciplines; and alignment of the portfolio approach to school, district, state, and parental expectations…

Twenty-four gifted girls in grades 4-7 in 3 rural school districts received a mathematics intervention program including problem-solving activities, math-related career options, and self-esteem issues. Pretest and posttest scores indicated that the program effectively changed the girls' attitudes toward mathematics. (Author/JDD)

Twenty-four sixth-grade children participated in clinical interviews on ratio and proportion before receiving instruction in the domain. Student thinking was analyzed in terms of mathematical components critical to proportional reasoning. Two components, relative thinking and unitizing, were consistently related to higher levels of sophistication…

Short essay questions are introduced into the calculus course as a technique to involve students with their own learning. Provides (1) instructions to the student for writing the report; (2) results of using the technique; and (3) reasons for using writing in mathematics classes. (MDH)

Thirty-one students (ages 8-14) with learning disabilities or behavior disorders solved arithmetic word problems while a narrative protocol was developed. Eight types of cognitive processing difficulties were identified (such as lack of self-correction and inclusion of extraneous information), and the utility of protocol analysis as an assessment…

Presents three teaching strategies requiring active student participation in which students (1) create and solve their own word problems; (2) generate trigonometric expressions to be solved by their classmates; and (3) act as points to model a basic locus of points. (MDH)

This study examined the effectiveness of peer collaboration in assisting 48 special education and 43 regular classroom teachers in developing and implementing alternative interventions for students with mild learning and behavior problems. Teachers using peer collaboration were found to have increased tolerance for the range of students' cognitive…

A model, dating its foundation to the Milford conferences in the 1920s, is presented that clarifies and advances concepts of both initial and advanced generalist social work. The model focuses on the interface between systems, uses a client-centered and problem-focused philosophy, and involves multiple theories and approaches for improving…

A study investigated reasoning processes of medical students in schools with different curricular formats, a conventional curriculum with basic science taught before clinical training and a problem-based curriculum with basic science taught in the context of clinical problems. Strengths and weaknesses of each curriculum type emerged. (Author/MSE)