An exploratory framework for handling the complexity of mathematical problem posing in small groups

Igor Kontorovich, Boris Koichu, Roza Leikin, Avi Berman

Research output: Contribution to journalArticlepeer-review


The paper introduces an exploratory framework for handling the complexity of students' mathematical problem posing in small groups. The framework integrates four facets known from past research: task organization, students' knowledge base, problem-posing heuristics and schemes, and group dynamics and interactions. In addition, it contains a new facet, individual considerations of aptness, which accounts for the posers' comprehensions of implicit requirements of a problem-posing task and reflects their assumptions about the relative importance of these requirements. The framework is first argued theoretically. The framework at work is illustrated by its application to a situation, in which two groups of high-school students with similar background were given the same problem-posing task, but acted very differently. The novelty and usefulness of the framework is attributed to its three main features: it supports fine-grained analysis of directly observed problem-posing processes, it has a confluence nature, it attempts to account for hidden mechanisms involved in students' decision making while posing problems.

Original languageEnglish
Pages (from-to)149-161
Number of pages13
JournalJournal of Mathematical Behavior
Issue number1
StatePublished - Mar 2012

Bibliographical note

Funding Information:
The presented research was supported, in part, by Bernstein Research Fund , Israel Science Foundation (grant 557/07 ) and the Technion Graduate School .


  • Considerations of aptness
  • Group dynamics
  • Mathematical problem posing
  • Problem posing strategies
  • Small group interactions
  • Task organization

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Education
  • Applied Mathematics


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