Examines teachers' judgments of the difficulties of algebra problems. Offers classroom-tested instructional approaches that build directly on students' mathematical intuitions and inventions. (KHR)

Describes a mathematics trail created on the campus of Exeter Academy and in the town of Exeter, New Hampshire. A series of problems and puzzles enabled teachers to teach mathematics outdoors. Novel questions were created to permit students to look at things from a different perspective. Participants were often inspired to create questions of…

Presents solutions at several different levels of sophistication for a problem involving 10 stools arranged in a row at a diner: how many different ways can the ten stools be occupied, discounting which of three persons sit on any stool, so that at least one stool is between two people? (AIM)

Proposes a word problem concerning placing students around triangular tables. Students must determine how to place the touching tables so that everyone can be seated. (KHR)

Curriculum for teaching multiplication and division story problems was delivered via either computer-assisted tutorial or teacher-assisted instruction to two groups of mildly handicapped middle school students (n=19). No significant differences were found, indicating that computer-assisted instruction is effective when sound instructional design…

Describes how Suzuki's methods of teaching young pupils to play the violin can be combined with Polya's ideas on problem solving to teach mathematics to elementary school pupils. Six references are listed. (YP)

Investigated whether children who reflected the structure of word problems with their concrete models were successful in learning to symbolically represent problems with structure-based open number sentences. Forty-five first graders were taught to write canonical and noncanonical open number sentences. (Author/YP)

Creative activities can enliven math classes and enhance student learning. Several suggestions are given for creating amusing word problems and lively drills. Included is a reproducible word problem sheet. (IAH)

Determines which chessboards contain a chromatic rectangle having all four corners the same color for any black-white coloring. Expands the problem to a three color problem. (YP)

Analyzes fifth graders' approaches for solving the problem of the distance to the horizon. Describes determining the area bounded by the horizon. (YP)

Community college students with learning disabilities (n=38) and math-competent peers (n=22) were taught representation-related strategies for solving compare word problems. Results generally supported the hypothesis that students receiving schema training would improve more than students assigned to linguistic training. (JDD)

Third- and fourth-grade students (n=401) were taught problem solving through structure-plus-writing, heuristics, or no explicit instruction. The structure-plus-writing group outperformed the heuristics group, and the gap widened 10 weeks after the treatment. Includes sample student-authored problems. (MKR)

Describes an experimental test conducted with high school students to determine the effect of posting explicit goal structures on problem-solving performance in an intelligent tutoring system for calculus. Related rates word problems are discussed, and student performance in terms of speed and accuracy is analyzed. (Contains 29 references.) (LRW)

Discusses the use of activities demonstrating connections between algebra and geometry, which helps students gain a conceptual understanding of important calculus ideas and gives a historical appreciation of how mathematics evolves. Uses distance, speed, and time problems as an example. (MKR)

Contends that, though much attention is given in mathematics to the problem of sensitizing people to the need for identifying elements of a situation and representing them symbolically, little or no effort is devoted to the problem of helping them express the relationships among these elements. (11 references) (MKR)