In the world of mathematics, not only are there cases in which there is only one correct answer, but also cases in which the truth or falsity of a proposition changes depending on the premises. This ``relativity of truth'' is often seen in the society and world in which we live, and we may face misunderstandings and problems due to differences in assumptions.
Therefore, it is extremely important to foster an awareness of relative truths and assumptions, not only in mathematics but also in human development, but the methodology for how to foster this in elementary and secondary education is not clear. There wasn't.
This time, a research group at the University of Tsukuba designed and practiced a task in which the premises are intentionally vague in mathematics learning, and learned that the truth of a conclusion depends on the premises, and that in order to determine the truth or falsity, it is necessary to clarify the premises. The results showed that students were able to understand what they needed to do.
In the development of normal mathematics teaching materials, it is common to clarify the prerequisites of a problem so that there is only one answer, but in this research we purposely developed the idea of setting tasks with vague prerequisites. Introduced. With the intention of directing the students' awareness to the premise of the task, we repeated the review cycle in collaboration with elementary and junior high school teachers, and as a result, we found that ``by intentionally making the premise of the task vague, different correct answers will be generated.'' ``If different correct answers are theoretically possible but are expected to be difficult for students to come up with, suggest the possibility of such a correct answer.'' ``Revise the task so that there is only one correct answer to eliminate ambiguity.'' This led to the establishment of a mathematics task design principle that provides opportunities to eliminate problems.
Using the tasks designed based on the established principles, we conducted classes at elementary and junior high schools and analyzed the effects based on students' utterances and worksheet descriptions. This study was shown to be effective in fostering a strong sense of truth.
The principles developed in this study are general task design principles that support the design of individual specific tasks, so it is hoped that in the future each teacher will be able to design appropriate tasks on their own based on them. be done. In turn, it is thought that this will lead to children and students developing a relative view of truth in a variety of situations.
Paper information:【Cognition and Instruction】Introducing students to the role of assumptions in mathematical activity
