Teaching parametric equations of a line in space using Toulmin’s model integrated with analogical reasoning

Abstract

Reviewing relevant documents on reasoning abilities, teaching methods, and the requirements to teaching the topic "Coordinate method in space" under the current general education program, this study proposes a pedagogical solution to organize teaching activities on the topic "Parametric equations of a straight line" (Math 12) towards developing ability. On a clear lesson plan and a set of detailed assessment criteria, the study demonstrates the potential of this integration in fostering students' mathematical reasoning ability when transforming their perception of "Parametric equations of a straight line" from two dimensions to three dimensions. Although experiments have not been conducted, this approach provides teachers with a teaching process with a solid theoretical basis, contributing to supporting the process of fostering students' mathematical reasoning ability. However, it is necessary to conduct pedagogical experiments to verify the effectiveness of the model, and at the same time consider adjusting and expanding its application to other mathematical topics.