Research on Teaching Method for Understanding in High School Mathematics (Ⅱ): Design of Mathematical Activity in Learning and Teaching Quadratic Function by the Emergent Modelling
2014 Volume 20 Issue 1 Pages 45-57
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2014 Volume 20 Issue 1 Pages 45-57
The purpose of this paper is to attain elaboration of the Koyama’s (2010)“two-axis process model” by designing mathematical activities that are understandable to students in lesson organization based on it, through an action research of“quadratic function” in high school subject Mathematics Ⅰ.
Entities of the mathematical thinking which are a vertical axis in the two-axis process model, were elaborated by quoting the“emergent modelling” by Gravemeijer (2007). In learning and teaching quadratic function, the author designed three learning stages based on the two-axis process model in each of the four activities by the emergent modelling and conducted lessons accordingly.
As a result of qualitative and quantitative analyses of the lesson based on these frameworks, the following two points were found out:
(1) By setting up a task from a scene which is familiar to students, they show active attitudes towards problem solving. They tend to try to understand the real phenomenon mathematically especially after they have had experiences in observing changes and correlations in a table that represents two relevant numerical figures.
(2) In the process of generalizing ways of solving problems given by a teacher, students are more able to understand the general formula y=ax2+bx+c by exploring and projecting relations between y=ax2 and y=ax2+bx+c, using function graphing software such as GRAPES.
