Can Big Idea-based Teaching Enhance Students’ Competencies？A Design Experiment Based on the “Optimization” Unit in Elementary Mathematics

doi:10.16382/j.cnki.1000-5560.2025.10.004

Abstract

Abstract:

Big idea-based teaching is an instructional paradigm that embodies the cultivation of competencies. The core of competencies is to solve real-world problems creatively, which better aligns with the mechanisms of high-road transfer. Guided by the methodology of the design experiment, the study took the “optimization” unit in elementary mathematics as an example. Firstly, the theoretical prototype of big idea-based teaching was refined through lesson study. A comparison was made between big idea-based teaching and conventional teaching from various dimensions of unit teaching, extracting elements and characteristics, and clarifying the model of big idea-based teaching, which was then exemplified. Subsequently, the effectiveness of the big idea-based teaching model was tested through comparative experimental research. The results of multiple regression analysis indicated that big idea-based teaching enhanced students' competencies, which was reflected in the enhancement of their ability for high-road transfer. Further analysis of students with varying levels of mathematical proficiency revealed that this instructional model could markedly improve the competencies of higher-achieving students in the short term and potentially benefit lower-achieving students over time.

Key words: big idea-based teaching, competencies, transfer, unit teaching, design experiment

Hui Liu, Xiaoying Cai, Yaxuan Xu, Xue Han, Dejiang Zhu, Peng Zhang. Can Big Idea-based Teaching Enhance Students’ Competencies？A Design Experiment Based on the “Optimization” Unit in Elementary Mathematics[J]. Journal of East China Normal University(Educationa, 2025, 43(10): 44-63.

Figures/Tables 6

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维度	要素	常规教学的特征	大概念教学的特征
单元结构	线索	主题	大概念
单元结构	序列	并行	进阶
单元目标	层次	低阶	高阶
单元目标	形态	分列	整合
单元评价	总结性评价	相似	多元
单元评价	形成性评价	封闭	开放
单元过程	组织	相加	相乘
单元过程	行为	验证	理解

	常数项$ {\beta }_{0} $	期末成绩$ {\beta }_{1} $	前测成绩$ {\beta }_{2} $	实验组别$ {\beta }_{3} $	迁移类型$ {\beta }_{4} $	前测成绩$ \times $ 实验组别$ {\beta }_{5} $	迁移类型$ \times $ 实验组别$ {\beta }_{6} $	F	df	$ {R}^{2} $
主效应模型	−12.81(3.97)**	0.26(0.05)***	0.22(0.13)	1.79(0.85)*	5.72(0.84)***	—	—	23.72	4,151	0.39
交互效应模型	−11.29(3.86)**	0.28(0.05)***	−0.18(0.17)	−4.77(2.82)	7.87(1.12)***	0.79(0.23)***	−4.31(1.59)***	20.69	6,149	0.45

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