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• Darstellungen und Vorstellungen und ihre Bedeutung für eine wirksame Metakognition beim Problemlösen und Begründen

  195-220

  Johann Sjuts

  Views:

  26

  Metacognition has one of the highest effect sizes concerning successful learning. However metacognitive activities during task solving and problem solving are not directly obvious. But they can appear by writing someone's thoughts down. The following analysis, which focusses on the level of argumentation as well as on the way of derivation, shows that the quality of representation is an essential condition for the possibility of metacognition.

• Is it possible to develop some elements of metacognition in a Mathematics classroom environment?

  123-132

  Márton Kiss

  Eszter Kónya

  Views:

  89

  In an earlier exploratory survey, we investigated the metacognitive activities of 9th grade students, and found that they have only limited experience in the “looking back” phase of the problem solving process. This paper presents the results of a teaching experiment focusing on ninth-grade students’ metacognitive activities in the process of solving several open-ended geometry problems. We conclude that promoting students’ metacognitive abilities makes their problem solving process more effective.

  Subject Classification: 97D50, 97G40

• A constructive and metacognitive teaching path at university level on the Principle of Mathematical Induction: focus on the students' behaviours, productions and awareness

  133-161

  Agnese Ilaria Telloni

  Nicolina Antonia Malara

  Views:

  123

  We present the main results about a teaching/learning path for engineering university students devoted to the Principle of Mathematical Induction (PMI). The path, of constructive and metacognitive type, is aimed at fostering an aware and meaningful learning of PMI and it is based on providing students with a range of explorations and conjecturing activities, after which the formulation of the statement of the PMI is devolved to the students themselves, organized in working groups. A specific focus is put on the quantification in the statement of PMI to bring students to a deep understanding and a mature view of PMI as a convincing method of proof. The results show the effectiveness of the metacognitive reflections on each phase of the path for what concerns a) students' handling of structural complexity of the PMI, b) students' conceptualization of quantification as a key element for the reification of the proving process by PMI; c) students' perception of the PMI as a convincing method of proof.

  Subject Classification: 97B40, 97C70