Linear Algebra Kit
A low-cost, hands-on tool to learn about linear tranformations, my master's thesis project.
Description
This project focussed on creating hands-on tools for more complex and higher order concepts like Linear Transformations. While softwares are available for teaching-learning of advanced math concepts. Higher education often lacks access to hands-on tools and manipulatives. And that is what this project aimed to address by creating a low-cost tool for undergraduate students studying linear algebra. It was based on two main theoretical frameworks. First, the embodied cognition theory that suggests that cognitive processes are intertwined with the body's physical and sensory experiences, rather than being solely brain-based and second visualization in mathematics education which focuses on linking abstract mathematical concepts with their visual representations.
Students can use pins and strings to represent vectors and 2-D shapes, they can then how such objects are transformed when different matrices of linear transformations are applied on them.
The Study
An empirical study was conducted to evaluate the effects of using the tool on understanding of linear algebra 32 first year students participated in the study. I created the measures with experts and used a longer post-test to reduce practice effect. It was a within group experiment where participants first took the pre-test, then I delivered structured lessons using the tool followed by a post-test. Findings revealed significant improvement in understanding, even after a short intervention period, with largest gains in application-based items, probably because students could "apply" the abstract concepts associated vectors, matrices, and transformations they were learning about. They also scored lowest in application knowledge items at pre-test indicating a lack of focus on that aspect of mathematics. The students were excited about using the tool and we observed positive engagement and motivation to learn with such tools as well.
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Team Members
- Robin Sharma — Project Lead, University of Delhi and Jamia Millia Islamia
- Jyoti Sharma — Professor, University of Delhi
- Tarun Aggarwal — University of Delhi and Jamia Millia Islamia
Publications and Presentations
- Sharma, R. (2017). Using MATLAB as an effective resource in mathematics classroom. National Conference on ICT in Education, Regional Institute of Education, National Council of Educational Research and Training, Mysuru, India. https://www.researchgate.net/publication/384472853_Using_MATLAB_as_an_effective_resource_in_Math_Classroom
- Sharma, R. (2017). Visualizing math concepts through hands-on approach. National Conference on Quality Education in the Present Educational Scenario, Regional Institute of Education, National Council of Educational Research and Training, Shillong, India.
- Sharma, R., & Aggarwal, T. (2016). Visualizing linear transformations: A hands-on approach. National Conference on Mathematics Education, Regional Institute of Education, National Council of Educational Research and Training, Bhubaneswar, India. https://www.researchgate.net/publication/384472936_Visualizing_Linear_Transformations_-_A_Hands-on_Approach