In this paper, I comment on the set of papers in this special issue on mathematical problem posing. I offer some observations about the papers in relation to several key issues, and I suggest some productive directions for continued research inquiry on mathematical problem posing.

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)

Specific examples are used to discuss assessment, an integral part of mathematics instruction, with problem posing and assessment of problem posing. General assessment criteria are suggested to evaluate student-generated problems in terms of their quantity, originality, and complexity.

Presents an overview of the 6-8 Standards and their rationale. Demonstrates the need for a cohesive mathematics curriculum. (YDS)

Examined are the problem similarity dimensions perceived by a student when classifying mathematical word problems as related and the relationship between a student's perception of problem similarity and performance on achievement tests. (MP)

Illustrates how engagement in worthwhile mathematical tasks can provide rich opportunities for professional development. Presents different solution strategies for the effective tax rate problem. Emphasizes that, to help students recognize differences among the preceding arguments, teachers need to recognize reasoning based on part-whole…

Discusses five research areas offering guidance to people concerned about teaching problem solving in elementary schools. Areas are (1) components of problem difficulty; (2) the contribution of reading difficulties to problem-solving deficiencies; (3) characteristics of successful problem solvers; (4) children's use of problem-solving techniques…

Expert mathematicians are contrasted with undergraduate students through a two-part analysis of the potential and actual use of visual representations in problem solving. In the first part, a classification task is used to indicate the extent to which visual representations are perceived as having potential utility for advanced mathematical…

Presents a problem included on the 1992 National Assessment of Educational Progress in mathematics at grade eight in the content area of algebra and functions. Collects and examines a set of responses to this problem and discusses some examples of strategies that students used to determine the answer to the problem. (ASK)

Discusses problem posing as a feature of creative activity or exceptional mathematical ability, inquiry-oriented instruction, mathematical activity, improving students' problem solving, a window into students' mathematical understanding, and improving students' disposition toward mathematics. (Contains 70 references.) (MKR)

Despite general agreement that students should consider more than one way to solve a complex mathematics problem, this practice is rarely observed in U.S. classrooms. In this paper, we examine data that trace the year-long professional development experience of 12 veteran teachers of middle grades mathematics--experienced users of a…

The harmonic mean is defined, and examples of problems viewed suitable for classroom exploration are presented. Such exercises provide many opportunities for students to engage in interesting nontrivial problem-solving activities and practice on many algebraic skills. Class discussion of the arithmetic, geometric, and harmonic means is suggested.…

Krutetskii's claim that good problem solvers differ from poor ones both with respect to solution performance and nature of their recall of problem information is supported by this study. The use of recalled information in the solution of related problems is also examined. (MP)

Describes an examination of arithmetic problem posing designed to examine the behaviors of 63 prospective elementary school teachers. Findings indicate that the test effectively evaluates arithmetic problem posing. Most subjects were able to pose solvable, complex problems. Performance improved when the task contained specific numerical…