Penetration Strategies of the Number-Shape Combination Thought in Middle School Mathematics Teaching

Abstract

The number-shape combination is one of the most fundamental and important methods of thought in middle school mathematics. It organically combines quantitative relationships with spatial forms, serving as both a core method of mathematical research and a key competency in mathematical learning. This paper systematically explores the penetration strategies of the number-shape combination thought in middle school mathematics teaching. First, it expounds the connotation and educational value of the number-shape combination thought, pointing out its unique role in reducing cognitive difficulty, cultivating thinking ability, and promoting knowledge transfer. Second, it analyzes the prominent problems existing in the penetration of the number-shape combination thought in current middle school mathematics teaching, including teachers' cognitive deviations, single teaching methods, and students' difficulties in transformation. On this basis, five penetration strategies are proposed: the two-way construction of number-shape combination in concept teaching, the flexible application of number-shape combination in problem-solving teaching, the characteristic application of number-shape combination in different modules, the empowerment of number-shape combination teaching by information technology, and the systematic training and evaluation of the number-shape combination thought. This paper aims to provide theoretical guidance and practical reference for frontline middle school mathematics teachers to effectively penetrate the number-shape combination thought, promoting the comprehensive improvement of students' mathematical core competencies.