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Objective: We design and practice lessons to imagine and understand the shape dependence of electrical resistance in two dimensions. Methodology: A carbon nanotube paper resistor is the most suitable teaching material for these lessons because it can handle measured shapes and resistance values quantitatively, and experiments with reproducibility are possible. We designed a one-hundred-minute lesson based on the 5E instructional model, which strongly correlates with inquiry-based learning. These designed lessons were practiced in two junior high schools. The analysis of post-test average scores for experimental and control groups used the Mann-Whitney U test. Results: The students were engaged in hands-on experiments and elucidated the two-dimensional shape dependence of electrical resistance by experiments using resistors adjusted by themselves with creative thinking. Conclusion: The effects were confirmed in the degree of consent for combined resistance and the evolution problem of parallel circuits. We clarified that "Authentic learning", which has a deep understanding using knowledge, was realized. “Authentic learning” is one of the policies of the current Course of Study 2017 by the Ministry of Education Japan (Ministry of Education, Culture, Sports, Science and Technology Japan, 2019). It is an innovation for physics education to understand electrical resistance with an image of dependence on its two-dimensional shape.
Shintsuruta et al. (Sun,) studied this question.