An Empirical Study on the Integrated Mathematics Teaching in Junior and Senior High Schools under the 1+3 Training Model — From the Dual Perspectives of Curriculum Reconstruction and Students’ Cognitive Development

Abstract

In the traditional segmented structure of junior and senior secondary mathematics education, issues such as discontinuity in knowledge systems, cognitive leaps in learning progression, and misalignment of instructional objectives are commonly observed, which hinder the continuous development of students’ mathematical core competencies. Against this background, this study explores an integrated instructional approach based on the “1+3 Talent Development Model” from both curriculum reconstruction and students’ cognitive development perspectives. Focusing on key domains including functions, geometry, and probability and statistics, a vertically integrated framework of mathematics curriculum is constructed, characterized by hierarchical knowledge progression, gradual cognitive development, and continuous competency cultivation. Empirical evidence from teaching practice spanning Grade 9 to Grade 10 demonstrates that the proposed model effectively alleviates knowledge fragmentation and cognitive discontinuity, while significantly enhancing students’ abilities in function understanding, geometric transfer, mathematical modeling, and logical reasoning. The findings suggest that integrated mathematics instruction across junior and senior secondary levels contributes to the systematic optimization of curriculum design and the restructuring of learning pathways, providing both theoretical support and practical implications for curriculum reform in basic education.