ABSTRACT

It is well known that students benefit from opportunities to interpret and create different representations (e.g., diagrams, graphs, tables, symbols) of mathematical ideas. Employing Marton’s Variation theory as a lens, I argue for an expansion of the use of multiple representations in task design for graphs: Incorporate two different forms of the same type of graph to represent a relationship between variables in a situation. With this approach, designers, teachers, and researchers can engineer opportunities for students to discern, or separate, features of representation systems, such as the Cartesian coordinate system, and in turn, promote students’ mathematical reasoning.

摘要

众所周知，学生有机会解释和创建数学思想的不同表示（例如，图表、图形、表格、符号）。以 Marton 的变分理论为视角，我主张在图的任务设计中扩展使用多种表示：结合同一类型图的两种不同形式来表示某种情况下变量之间的关系。通过这种方法，设计师、教师和研究人员可以为学生设计机会来辨别或分离表示系统（如笛卡尔坐标系）的特征，进而促进学生的数学推理。