A Practical Study for the Development of Group-Competition-Style Mathematics Classes:The Occurrence of the Characteristics of Deductive Explanations in the Classroom
2019 Volume 25 Issue 2 Pages 73-89
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2019 Volume 25 Issue 2 Pages 73-89
The purpose of this paper involves two points: One is to clarify more essential elements for realizing “Group-Competition-Style Mathematics Classes”. In addition, in light of such essential elements, to clarify the concrete method to realize “Group-Competition-Style Mathematics Classes” and important teachers’ moves in realizing it. The second one is to obtain suggestions on classes to encourage understanding of “deductive reasoning” at elementary school, especially to clarify the mechanism and function of “Group-Competition-Style Mathematics Classes” in particular what type of understanding about “deductive reasoning” are invited to the students.
For that purpose, teaching experiment was conducted in the “school support project”, which was conducted at public schools in Joetsu City for about 4 months from September 2018 to December 2018, including 4 lessons with a 5th grade class on December 3, 4, and 5 in 2018. We planned and conducted a competition style of group-based lessons in the 5th grade class. The mathematical topic of the class was to investigate whether a certain geometric relation was established. The students were required to form their own assertions and their mathematical explanations together in groups to discuss them with each other. The lessons were recorded with video cameras and IC recorders and detailed transcripts were prepared for the analysis.
The analysis results are summarized in the following two points:
1. The most essential element for realizing “Group-Competition-Style Mathematics Classes” is a “gap” in students’ ways of thinking occurring in the lesson process, rather than teachers’ preparing in advance what will be conflicting. Therefore, the important thing in realizing “Group-Competition-Style Mathematics Classes” is that the teacher will be able to assess a “gap” between students’ ideas or ways of thinking occurring in the course process. That “gap” in itself is what teachers can not predict in advance. Therefore, in addition, teachers must be prepared to change the lesson plan according to the “gap”. However, by rethinking “gap” as a more essential element in this way, we could expand the scope of application of “Group-Competition-Style Mathematics Classes”.
2. T he “Group-Competition-Style Mathematics Classes” in our lesson study, more precisely, the lesson that changed the plan with the “gap” that occurred between the two guesses as the core after the stage of inductive activities, encourages students to understand the effectiveness of “deductive reasoning”. More specifically, such classes encourage students to understand deductive reasoning as a way to overcome the limitations of inductive reasoning. In other words, such classes encourage students to understand the generality of deductive reasoning. The conflict of arguments between inductive reasoning and deductive inference that occurs under the situation of “group competition” has the function of making the students realize the theoretical character which is a feature of deductive reasoning.
