Discusses and provides sample lessons of learning by discovery and weekly problem sets, which are presented as alternative methods for teaching college calculus. Both approaches stress conceptual understanding and guide the students to explore the ideas of calculus in small groups in a computer laboratory setting. (JJK)

Presents three features of "Good" questions: requires students to do more than simply remember a strategy to answer; promotes student learning while answering the question; and have several acceptable answers. Considers how questions can be used to cater to the range of student abilities. (MDH)

Presents and discusses assumptions for a general-mathematics problem-solving curriculum that incorporate the belief that all students can do algebra, geometry, and trigonometry, that mathematics must be presented in problem situations, and that students should work cooperatively. Worksheets provide exemplary problem-solving activities. (MDH)

Presents a gamelike context that provides general-mathematics students the opportunity to explore situations involving chance and develop reasoning about probability. Provides three worksheets for activities that promote components of the NCTM's Curriculum and Evaluation Standards for School Mathematics. (MDH)

Presents results of 46 randomly selected children's performance measurement and partitive division problems when remainders are zero, nonzero but not used in the solution, and nonzero and used in the solution. Results indicate that children demonstrate an understanding of division prior to formal instruction. (MDH)

Discusses the use of the LOGO programing language as a problem-solving tool for elementary school students. Papert's theory is explained; the integration of LOGO into the language arts and math curricula is discussed; LOGO research is reviewed; and recommendations for future work are offered. (18 references) (LRW)

Presented is an activity that explores the relationship between the size of a rectangle and the number of squares intersected by a diagonal. Students incorporate pattern recognition and the concept of the greatest common divisor in solving the problem. A sample worksheet is provided. (MDH)

Described is the Educational Leaders in Mathematics (ELM) Project, a four-stage inservice teacher program designed to stimulate teachers' development of a constructivist view of learning. The impact of the intervention was studied, and results indicated that teachers' beliefs were affected, producing changes in teaching strategies. (MDH)

Associations between performance-oriented and structure-oriented tasks in elementary school mathematics instruction and achievement were studied for 33 third grade classrooms. A mathematics pretest and posttest were administered, and classroom observations were conducted. Results suggest that performance-oriented tasks promote automatization of…

Reports on a study of the influence of problem-solving computer software on the attitudes of secondary school students toward mathematics while using computer-assisted instruction. Student performance on pretests and posttests are compared, gender differences are discussed, and implications for mathematics instruction are suggested. (10…

Children's (n=70) solution strategies to a variety of multiplication and division word problems were analyzed to determine performance levels and strategies used. Solution strategies were classified at three levels: direct modeling with counting; no direct modeling with counting, additive, or subtractive strategies; and use of known derived facts.…

Describes four activities to develop visualization skills and the concept of dimensionality in which students (1) visualize transforming figures between the second and third dimensions; (2) identify the three-dimensional objects from their two-dimensional projections; (3) conjecture about the vertices, edges, and faces of zero- to four-dimensional…

High school mathematics project in which students interviewed guest speakers about the mathematics used in their jobs. Students wrote five real world problems based on the mathematics used by the person interviewed. The class worked through the problems and found that estimation was often a helpful strategy. (PDD)

Examined cognitive processing and performance of 12 average seventh-grade students during cooperative problem solving. Factors that impeded performance included lack of an experiential framework, imposition of unrequired restrictions, lack of individual monitoring of cognitive activity, and unproductive beliefs. Factors that enhanced performance…

Reports a case study in which a first-grade teacher's instructional decisions were affected by the pedagogical content knowledge concerning problem solving received during a four-week summer workshop on teacher's beliefs about teaching in conjunction with the teacher's beliefs that students can solve any problem they are given. (MDH)