ABSTRACT

Representation is widely viewed as central to mathematical problem solving, while online scaffolding is considered helpful in supporting learners’ progress from actual to potential developmental levels of mathematics understanding. Therefore, this study investigated the effectiveness of employing online single vs. multiple representational scaffolds to facilitate students’ mathematics problem solving. Two classes (46 students) were assigned to the group with multiple representational scaffolds, while two other classes (45 students) were assigned to the group with a single representational scaffold. Results showed that using multiple representational scaffolds better-facilitated students’ mathematics conceptual understanding and problem solving than using a single representational scaffold. The progression of online problem-solving process further showed that the multiple representational scaffolds group displayed more sophisticated problem-solving performance than the single representational scaffold group as they moved from basic to advanced questions. Evidence of eye movement behaviors indicated that the multiple representational scaffolds group allocated significantly shorter mean fixation duration and mean re-reading time than the single representational scaffold group during the online problem-solving process. Relatedly, the eye movement behavior evidence demonstrated that the use of multiple representational scaffolds more efficiently and effectively facilitates students’ mathematics conceptual understanding and problem solving than the use of a single representational scaffold.

摘要

表征被广泛认为是数学问题解决的核心，而在线脚手架被认为有助于支持学习者从实际的数学理解水平发展到潜在的数学理解水平。因此，本研究调查了采用在线单一表征支架与多重表征支架促进学生解决数学问题的有效性。两个班级（46 名学生）被分配到具有多个代表性支架的组，而另外两个班级（45 名学生）被分配到具有单个代表性支架的组。结果表明，使用多个表征支架比使用单个表征支架更能促进学生的数学概念理解和问题解决。在线问题解决过程的进展进一步表明，当从基础问题转向高级问题时，多表征支架组比单一表征支架组表现出更复杂的问题解决性能。眼动行为的证据表明，在在线解决问题的过程中，多个表征支架组分配的平均注视持续时间和平均重读时间明显短于单个表征支架组。相关地，眼动行为证据表明，使用多个表征支架比使用单个表征支架更有效地促进学生的数学概念理解和问题解决。