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Developing Task Design Principles to Foster Students' Recognition of the Relativity of Truth in Mathematics Education

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A researcher from the University of Tsukuba and colleagues showed that designing and implementing mathematical tasks with ambiguous assumptions helps students understand that the truth of a conclusion depends on such assumptions and that explicitly stating these assumptions is crucial to achieving consensus on the conclusion.

Tsukuba, Japan—Although a typical mathematical task has a single correct answer, in some cases, the assumptions of a proposition determine its truth. Such relativity of truth plays a major role in the development of mathematics. Furthermore, in our daily lives, we must identify assumptions that underlie each other's discussions and clarify such assumptions for better communication. Hence, students' recognition of the relativity of truth involving assumptions must be developed; however, how to encourage such development in primary and secondary education remains unclear.

To address this issue, the researchers have developed principles that support the design of mathematics tasks. Contrary to typical mathematical tasks, they introduced an innovation in which the conditions of tasks are intentionally made ambiguous, directing students' attention to the task assumptions. The researchers collaborated with primary and secondary school teachers to implement research cycles, each of which composed of designing a mathematical task, implementing it in one or more classrooms, and evaluating such implementation. Based on these research cycles, they developed task design principles, which involved creating a task open to different legitimate assumptions and conclusions by intentionally leaving some of the task's assumptions implicit or unspecified, and demonstrated the effectiveness of these principles.

The task design principles developed in this study allow teachers to design relevant tasks independently and implement them in their classrooms, which would foster their students' recognition of the relativity of truth in different circumstances.

This work was supported by the Japan Society for the Promotion of Science, Grant Numbers 18K18636 and 19H01668.

Original Paper

Title of original paper:
Introducing students to the role of assumptions in mathematical activity
Cognition and Instruction


Associate Professor KOMATSU Kotaro
Institute of Human Sciences, University of Tsukuba

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