Current knowledge about cognitive development in mathematics is reviewed, specific effective strategies for presenting materials in class are described, and effective strategies for mathematics program content and organization are outlined. Substantial information on recent research and on instructional materials is included. (MSE)

Gifted/talented secondary-school students used the Students Questioning Students method in their mathematics classes. The method stimulated higher-order thinking, made students more attentive listeners, and improved their public speaking self-confidence. The paper offers suggestions for implementing the method and includes three pages of letters…

This study compared the effectiveness of a diagrammatic and a keyword method of teaching mathematics problem solving to 70 learning-disabled junior high school students. Results indicated no significant difference between problem-solving performance by students taught with different methods. Potential factors explaining inconsistencies between…

Outlines differences between classical statistics and exploratory data analysis. Provides examples in the use of the exploratory techniques. (YP)

Investigated was the use of cognitive conflict to probe the misconceptions held by preservice elementary teachers that in a division problem the quotient must be less than the dividend. Explains how preservice teachers' reliance on information about the domain of whole numbers and their instrumental understanding support their misconceptions.…

Presents 3 examples for setting teacher's aims in Japanese and American mathematics classrooms. Provides 10 guidelines for teachers who would like to include more mathematical dialogue and encourage the expression of conceptual splatter in their classrooms. (YP)

Examines teachers' beliefs about, and practices regarding, small-group teaching of mathematics. Reports that only 5 percent of the teachers used two or more groups in which students were encouraged to work cooperatively. Discusses variables related to deciding whether to group students for instruction. (Author/YP)

Discusses using the computer to promote versatile learning of higher order concepts in algebra and calculus. Generic organizers, generic difficulties, and differences between mathematical and cognitive approaches are considered. (YP)

Discusses teaching geometric concepts, including various shapes, patterns, and areas based on the NCTM Standards. Presented are activities for the geometric concepts. (YP)

Describes two instructional activities to develop spatial imagery and the pupil's responses to these activities. Discusses how the classroom atmosphere contributed to the success of the activities. (YP)

Provides methods of teaching negative number operations, including addition, subtraction, and multiplication. Presents examples and activities for the operations. (YP)

This article reports on the effects of a training program on teacher behavior, student achievement, and student attitudes toward mathematics. Results suggest that the timing of the training affected student achievement. No effect on student attitude was determined. Participants were 32 eighth grade Dutch mathematics teachers. (IAH)

Discusses the use of small groups for instruction. Topics include the composition of groups, the role of the teacher, choice of topics, and evaluation of students. (PCB)

Describes several phenomena in which interesting properties of numbers are demonstrated. Includes discussions of amicable, perfect, and sociable numbers. Presents computer programs for conducting a number chain search. (RT)

Provided is a mathematical recreation to strengthen student mathematics skills. The object of the activity is to build up an expression using the four digits of the current year, without rearranging the digits and using combinations of operations, to equal a prescribed value. Descriptions and examples are included. (RT)