Mathematical problem posing is essential for developing problem-solving skills and fostering creativity in mathematics education. Despite its importance, the field still lacks comprehensive phase models for problem-posing processes. Addressing this gap is essential for advancing our understanding and teaching of mathematical problem posing. This study aims to validate and adapt Baumanns and Rott’s (2022) phase model, initially developed for structured situations, to unstructured ones. Thirty-four preservice mathematics teachers participated in task-based interviews involving unstructured problem-posing situations. Key findings indicate that the phase model’s core components—situation analysis, variation, generation, problem solving, and evaluation—remain applicable but require nuanced adaptations to accurately capture the processes initiated by unstructured problem-posing situations. These results highlight the model’s robustness and adaptability, contributing to a deeper understanding of problem posing in various contexts.

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Unstructured Situations as Initiation for Problem-Posing Processes: Validation of a Descriptive Phase Model of Problem Posing

  • Lukas Baumanns,
  • Benjamin Rott

摘要

Mathematical problem posing is essential for developing problem-solving skills and fostering creativity in mathematics education. Despite its importance, the field still lacks comprehensive phase models for problem-posing processes. Addressing this gap is essential for advancing our understanding and teaching of mathematical problem posing. This study aims to validate and adapt Baumanns and Rott’s (2022) phase model, initially developed for structured situations, to unstructured ones. Thirty-four preservice mathematics teachers participated in task-based interviews involving unstructured problem-posing situations. Key findings indicate that the phase model’s core components—situation analysis, variation, generation, problem solving, and evaluation—remain applicable but require nuanced adaptations to accurately capture the processes initiated by unstructured problem-posing situations. These results highlight the model’s robustness and adaptability, contributing to a deeper understanding of problem posing in various contexts.