Investigate the effectiveness of single and multiple representational scaffolds on mathematics problem solving: evidence from eye movements

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.

KEYWORDS:

• Multiple representations
• single representation
• online scaffolds
• online mathematical problem solving
• scientific understanding

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Ministry of Science and Technology, Taiwan: [grant number 105-2511-S-009-011-MY3].

Notes on contributors

Chih-Ping Liang

Chi-Ping Liang is a middle school mathematics and technology teacher. He is also teaching mathematics method as a part-time Assistant Professor at the Institute of Education, National Yang Ming Chiao Tung University and National Chiao Tung University. His research interests include online mathematics learning, eye movement and educational technology.

Hsiao-Ching She

Hsiao-Ching She is a Chair Professor at the Institute of Education, National Yang Ming Chiao Tung University and National Chiao Tung University. Her research interests are focusing on scientific reasoning, argumentation, conceptual change, online science learning, scientific literacy, neuroscience, eye movement, EEG and fMRI.