## Abstract

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 language | English |
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Pages (from-to) | 149-161 |

Number of pages | 13 |

Journal | Journal of Mathematical Behavior |

Volume | 31 |

Issue number | 1 |

DOIs | |

State | Published - 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 .

## Keywords

- 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