The potential of dynamic mathematics systems to promote mathematical abstraction levels of secondary school students
摘要
Mathematical abstraction constitutes the foundational cornerstone for the establishment and evolution of mathematical disciplines, serving as the pathway through which mathematical concepts emerge. As one of the information technologies widely applied in mathematics education, the Dynamic Mathematics Systems (DMS) have been found to have a positive impact on mathematics learning. However, how DMS enhances students' mathematical abstraction skills remains a worthwhile area of exploration. In this research, with the aim of fostering secondary school students' mathematical abstraction skills, we have developed a visual, dynamic, and incremental Learning Progression- Dynamic Mathematical System (LP-DMS) teaching model. This model is grounded the dynamic mathematics systems and is guided by the theory of learning progression. It comprises five key stages: Delineating dimensions of the level of mathematical abstraction, Designing the content and activities of instruction, Formulating realistic representations of mathematical abstraction levels, Designing evaluation tasks, and Assessing the effectiveness of teaching. Students from a secondary school in Guangzhou were selected to participate in a quasi-experimental research under the guidance of the LP-DMS model. The changes in the mathematical abstraction levels of the students in the experimental class were evaluated by quantitative analysis and interviews. The results suggested that (1) the mathematical abstraction of students in the experimental class was significantly elevated, and (2) students' ultimate mathematical abstraction varied notably among different knowledge topics, especially in challenging domains. The findings of the study indicate that the LP-DMS teaching model is effective in enhancing the mathematical abstraction levels of secondary school students.