Research on Students’ Development of Functional Concepts during the Transitional Period from Elementary to Secondary School Mathematics

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  • 小中接続期における関数概念の発達の様相に関する研究
  • ショウ チュウ セツゾクキ ニ オケル カンスウ ガイネン ノ ハッタツ ノ ヨウソウ ニ カンスル ケンキュウ

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Abstract

<p>　　The purpose of this research is to clarify the aspects of students’ development of functional concepts during the transitional period from elementary to secondary mathematics based on the findings from the qualitative research on the observations of the elementary fourth and fifth grade classrooms and the teaching experiment research on proportion in the seventh grade.</p><p>　　The findings and the points as a result of our analysis and discussion are as follows.</p><p>（1） The viewpoints of symbolization and signalization in the van Hiele theory can work for examining the development of students’ functional concepts during the transitional period from elementary to secondary school mathematics.</p><p>（2） It is important as the foundations in the learning of function that students have their images of motion of the event, switch them from the analog viewpoint to the digital one, and conceive the dependency relations in which they control the dependent variable based on the independent variable.</p><p>（3） Symbolization may be caused when students explain their activities on table, graph and expression using the languages for telling the event. Also, mediating the plural representations with each other through situating the event as a core may enhance their symbolization of each representation, and moreover it can lead to the signalization among the representations.</p><p>（4） When students explore an aspect of change in the event （e.g. speed） in the representations and connect them with each other based on the interpretations of the event, they can conceive the mutual relationships among table, graph and expression, and in particular enhance the meanings of rate of change in the functional concepts.</p>

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