学习进阶理论嵌入线性方程组课程的教学探究——以昌吉学院为例

Teaching Exploration of Embedding Advanced Theory into Linear Equation Systems Course—A Case Study of Changji College

摘要: 学习进阶是学生的认知发展从低级到高级的发展过程。某一主题的学习进阶模型对有效开展该主题的教、学、评具有重要的指导价值。学习进阶是对学生在各学段学习同一主题的概念时所遵循的连贯的、典型的学习路径的描述，一般呈现为围绕核心概念展开的一系列由简单到复杂、相互关联的概念序列。本文要研究的主要问题为构建线性方程组内容的学习进阶模型，由模型可得出学生在线性方程组的每一个成就水平中，具体的学习表现。本研究构建了解线性方程组的三维度，每个维度又分为3个不同的层级，揭示了数学抽象、逻辑推理、数学建模三个维度的递进式认知路径。九个能力层级呈现“具体–抽象–应用”的循环递进，既体现知识掌握的纵向深入，又实现核心素养的横向贯通。本研究结果为解线性方程组内容的课程设计提供了理论框架，为教师评价学生的核心素养提供了层级化标准，为学生提供层次化的学习模型，具有一定的实际意义。

Abstract: Advanced learning is the process of cognitive development of students from lower to higher levels. The advanced learning model of a certain topic has important guiding value for effectively carrying out teaching, learning, and evaluation of that topic. Advanced learning is a description of the coherent and typical learning path that students follow when learning concepts related to the same theme at different stages of their studies. It generally presents as a series of interrelated concept sequences, starting from simple to complex, centered around core concepts. The main problem to be studied in this article is to construct an advanced learning model for the content of linear equation systems. The model can be used to obtain the specific learning performance of students at each achievement level of linear equation systems. This study constructs a three-dimensional understanding of linear equation systems, with each dimension divided into three different levels, revealing a progressive cognitive path of mathematical abstraction, logical reasoning, and mathematical modeling. The nine levels of abilities present a cyclic progression of “concrete abstract application”, reflecting both the vertical depth of knowledge mastery and the horizontal integration of core competencies. The results of this study provide a theoretical framework for curriculum design of solving linear equation systems, hierarchical standards for teachers to evaluate students’ core competencies, and hierarchical learning models for students, which have certain practical significance.