We examined geometric calculation with number tasks used within a unit of geometry instruction in a Taiwanese classroom, identifying the source of each task used in classroom instruction and analyzing the cognitive complexity of each task with respect to 2 distinct features: diagram complexity and problem-solving complexity. We found that…

Discusses varieties of open-ended problems in mathematics, including problems that are unsolved in the field of mathematics, are open with respect to solution method, are open to interpretation of the problem or solutions, or that invite other problems as follow-up. (Author/MKR)

Middle school teachers (n=53) and prospective secondary teachers (n=28) posed problems related to billiards before and after solving a sample problem. Found systematic problem generation and more problems posed before solving a sample problem. Posed problems were not always solvable. (MTE)

Only 25% of fifth- and sixth-grade Chinese students (n=186) correctly solved a division-with-remainder computation task, about the same success rate as with American students, and only one-sixth of the students could interpret the result. (MKR)

This paper reports the latest in a series of studies investigating children's performance in solving division story problems involving remainders. One aspect of the work involved examining the way in which "sense-making" is involved in the interpretation of the numerical solution obtained. Subjects were 195 sixth, seventh, and eighth…

This paper discusses the central thesis that new research on estimation and mental computation will benefit from more focused attention on the situations in which they are used. In the first section of the paper, a brief discussion of cognitive theory, with special attention to the emerging notion of situated cognition is presented. Three sources…

This study examined the hypothesis that prior experience with augmented-quotient problems would positively influence performance on remainder-only problems and quotient-only problems. Analysis of sixth through eighth grade students' (n=545) responses to test forms that systematically varied the order of appearance of these three division problems,…

Middle school students' (n=200) solutions to division-with-remainder story problems and their attempts to make sense of their answers were analyzed for evidence that supported or refuted hypothesized semantic-processing models. The models helped explain students' failure to solve these problems in school settings. (Contains 17 references.)…

This study, presented at the 1979 meeting of the American Educational Research Association (AERA) in San Francisco, examines the relationship between a student's mathematical problem-solving ability and the nature of the student's recall of information from previously-solved problems. Seventy-seven seventh-grade students completed tasks measuring…