Abstract
The aim of the present study is to investigate pre-service secondary mathematics teachers' cognitive-metacognitive behaviours during the mathematical problem-solving process considering class level. The study, in which the case study methodology was employed, was carried out with eight pre-service mathematics teachers, enrolled at a university in Erzincan, Turkey. We collected data via think aloud protocols in which metacognitive supports are provided and not provided and with unstructured metacognitive protocols related to the process. The metacognitive support provided to the pre-service teachers and this case caused an increase in the numbers of cognitive-metacognitive behaviours in class level in general. Any pattern was not encountered for the sequences of cognitive-metacognitive behaviours in the process of mathematical modelling during the stages in which metacognitive support was given and was not given but some little patterns were detected. It was noticed that there was no relationship with respect to the metacognitive support and without metacognitive support between and frequencies of cognitive-metacognitive behaviour mathematical modelling progress. The 1st and 2nd grade-pre-service teachers claimed that the metacognitive support contributed to them such factors as understanding and detailing, the 3rd and 4th graders expressed that it enabled them to follow, reach alternative ways of solution. The participants, during the stage in which the metacognitive support was provided, demonstrated more success during the process of mathematical modelling compared with the first stage.
Highlights
Metacognition, which is one of the most talked about and mentioned concepts [54], its being noticed and using it dates back to 557 B.C. [31]
Do the numbers of cognitive –metacognitive behaviours demonstrated by pre-service teachers within the stages of mathematical modelling vary in terms of the class variable in the occasions with and without metacognitive support?
Related to the Research Question of ‘Do the numbers of cognitive –metacognitive behaviours demonstrated by pre-service teachers within the stages of mathematical modelling vary in terms of the class variable in an occasion with and without metacognitive support?’
Summary
Metacognition, which is one of the most talked about and mentioned concepts [54], its being noticed and using it dates back to 557 B.C. [31]. One of the two main parts of metacognition, which seems to be different but highly interrelated, is cognitive knowledge, and the knowledge of cognition consisting of beliefs [36]. The knowledge of cognition, which is called as metacognitive knowledge, is knowledge that individuals have about their weaknesses as a problem solver or learner, or their own cognitive skills of knowing where, how and why they are to apply a strategy [25]. The second main part of metacognition is regulation of cognition depending on checking and arranging cognitive events [36]. The regulation of cognition is related to the metacognitive skills, which consist of observing and arranging activities to which individuals apply during problem solving and learning process [25]. While the metacognitive knowledge are mostly declarative knowledge depending on the interaction between three features of
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