ArticleOpen Access http://dx.doi.org/10.26855/jamc.2025.12.002
Deep Integration of the “Integration of Numbers and Shapes” Concept: Teaching Design of the Power Function Unit Based on UBD
Chen Han, Xiuqin Shao, Xinli Zhang*
Liaocheng University, Liaocheng 252000, Shandong, China.
*Corresponding author:Xinli Zhang
Published: December 16,2025
Abstract
The ‘integration of numbers and shapes’ (INS) is a critical thinking approach for nurturing students’ mathematical literacy and problem-solving skills. However, in traditional high school math teaching, it is often not taken seriously. Taking the teaching of the unit of power functions, as they have an intuitive connection between their exponent’s algebraic property and the geometric properties of their graph, as an embodiment of INS in a high school mathematics course. This paper discusses ways to deeply integrate INS into the high school mathematics curriculum. This study puts forward a new type of teaching design based on the ‘understanding by design’ (UBD) framework: using the ‘understanding by design’ backward-design method, we shift teaching focus from ‘memorizing types of graphs’ to ‘enduring understanding (why the graph is like this)’. clarifies the understanding goals expected, devises performances that demand flexible application of INS, and designs a WHERETO-learning plan. This UBD design attempts to shift INS to an active, internalized thinking habit rather than a passive observation phenomenon, and helps develop real math reasoning and apply the thinking method to other new problems.
Keywords
Integration of Numbers and Shapes (INS); Power Function; Understanding by Design (UBD); Teaching Design; Mathematical Thinking; Enduring Understanding
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How to cite this paper
Deep Integration of the “Integration of Numbers and Shapes” Concept: Teaching Design of the Power Function Unit Based on UBD
How to cite this paper: Chen Han, Xiuqin Shao, Xinli Zhang. (2025) Deep Integration of the “Integration of Numbers and Shapes” Concept: Teaching Design of the Power Function Unit Based on UBD. Journal of Applied Mathematics and Computation, 9(4), 233-237.
DOI: http://dx.doi.org/10.26855/jamc.2025.12.002