A course at the University of Georgia is described that helps students acquire problem-solving skills so that ultimately the entire remedial program would be improved, giving students with major deficiencies in basic skills a better chance to succeed in their regular university courses. (MLW)

Describes qualitative aspects of explicit and less explicit explanations of cognitive reasoning processes associated with mathematical problem solving strategies. Includes lesson excerpts to illustrate three major differences between explicit and less explicit explanations. (MG)

Middle school and college students were assessed on percentage. Better students in each group were given word problems involving percentage and asked to think aloud as they solved problems. College students made more use of strategies for control and monitoring of their own procedures. A three-stage model for problem solving is then hypothesized.…

Describes an action research project using Language for Understanding across the Curriculum to help year-seven students in a mathematics problem-solving unit. Strategies included unpacking the question, modeling the writing process, learning journals, glossaries, classroom charts, and the Newman Questioning Technique. Ability to explain…

Suggests ways in which mathematical models can be presented and developed in the classroom to promote discussion, analysis, and understanding of issues related to energy consumption. Five problems deal with past trends and future projections of availability of a nonrenewable resource, natural gas. (Contains 13 references.) (MDH)

Project questions are real-world problems with multiple solutions, no obvious solution sequence, requiring hands-on data collection, and investigation of topics within and outside mathematics. Discusses evaluation of solution processes, describes a detailed example involving the trajectory of a baseball, and suggests 19 other project questions.…

Presents three patterns found in math for elementary students. Spirolaterals are patterns made by repeatedly tracing a series of three numbers in four directions on dot paper. Tessellating can be a combination of teaching about patterns, geometry, and art. The King's Problem requires recognition of a problem to find a solution. (PR)

Presents criteria for designing craft activities that foster meaningful use of mathematical thinking and problem solving. (MKR)

Fifty children, ranging in age from 4 to 10, were individually administered a series of tasks involving different combinations of 2 items selected from a discrete set of items. Analyses of their performances revealed a series of six, increasingly sophisticated, solution strategies ranging from random number selection of items to a systematic…

Illustrates various methods to determine the perimeter and area of triangles and polygons formed on the geoboard. Methods utilize algebraic techniques, trigonometry, geometric theorems, and analytic geometry to solve problems and connect a variety of mathematical concepts. (MDH)

A number for which the number of digits categorizes the number is called a star number. A set of star numbers having a designated property is called a constellation. Discusses nature and cardinality of constellations made up of star square, star prime, star abundant, and star deficient numbers. Presents five related problems for exploration. (MDH)

Suggests structured investigations as a method of teaching mathematics to preservice elementary school teacher. Presents an example problem that asks students to determine the maximum number of regions that can be created by connecting any two points around the circumference of a circle. (MDH)

Presents three investigations that extend the problem of counting the number of squares on a grid in two dimensions to an analogous problem of counting the number of cubes in a three-dimensional cubic array. (MDH)

Describes alternative form of evaluation that enables the teacher to assign a grade to students problem-solving skills as they participate in a discussion to solve a problem. Discusses room arrangement, the role of the audience, grading, and secondary benefits of the method. (MDH)

Presented is the solution to the problem of calculating the probability of winning or losing a game played by moving a counter from the center of a hexagonal grid according to the number shown after the toss of a die. The exercise is an example of an interesting mathematical investigation. (MDH)