A Study of Points of Teaching Proactive Use of Mathematical Representation in Arithmetic: Focuses on the Difference Between Arithmetic and Mathematics and Characteristics of Writing and Drawing
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Abstract
Focusing on writing, Shimizu (2012) found two difficulties contributing to students’ inability to write mathematical representation. The author proposes ways to overcome these difficulties in the teaching of mathematics.
In this paper, the author also proposes ways to address these problems in the teaching of arithmetic.
As suggestions for ways to address these problems, the author cites the alleviation of rules and abstractions and the promotion of the enjoyment of writing.
The author proposes ways of guidance to encourage children to write positively.
(1) Children should be encouraged to write their own ideas, freely using various kinds of representation including Illustrative Representation, with the teacher gradually making specificity and directness a priority.
(2) Teachers should prepare contents which are interesting and understandable, thereby encouraging children’s motivation to study autonomously by feeling the enjoyment of writing. The teacher should be aware of the need to carefully progress from the emotional in mind earliest stages of studying.
(3) Both teachers and children should be personally and positively engaged with the object of studying.
(4) Both teacher and children should be felt to value the quality and importance of writing.
(5) By the children seeking of higher goodness (value) of arithmetic, and children’s higher enjoyment of studying, children should study to use new representation over time, and in as natural a way as possible.
In proposals (1) - (5), while the author emphasis is on the early stages of studying in arithmetic and mathematics, it was necessary to take into account the unique characteristics of arithmetic.
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References
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