Mathematics Learning, Model-based Learning, Physically-Distributed Learning, Eye Tracking, Process Analysis
There are three broad strands in the project:
- Exploratory study
- Classroom based study
- Experimental study
This study was done to explore students’ conception of area measurement. This study was done mostly by interacting with students. Methodology was task based interviews.
Classroom based study
An instructional sequence was designed based on the insights drawn from exploratory study and from the research results from literature.
Manipulation of physical models such as tangrams and tiles is a popular teaching tool to make early mathematics concepts easier to learn. However, there is no clear account of the cognitive process by which such learning-by-doing leads to internalization of mathematics concepts. We report two observational studies that sought to characterize this process, by analysing the eye movement patterns as two groups solved area calculation problems. The study group manipulated a type of tangram, and a baseline group did a general knowledge test, before solving the area problem. Analysis of eye movement patterns showed a clear difference in the problem- solving process between the two groups. A second study showed that the geometrical structure of the tangram is needed to generate this change, just manipulation is not enough. Accounting for these results, we propose a theoretical model of how manipulatives change the problem-solving process, and discuss some implications of this account.
- Rahaman, J., Agrawal, H., Srivastava, N., Chandrasekharan, S. (2018). Recombinant enaction: manipulatives generate new procedures in the imagination, by extending and recombining action spaces. Cognitive Science, DOI: 10.1111/cogs.12518