Abstract:

Mathematical Proficiency can be defined by five interwoven and interdependent strands [1]: Conceptual Understanding (command over math concepts, functions, symbols & relationships), Procedural Fluency (ability to perform math procedures adaptably and appropriately), Strategic Competence (skill to frame and solve mathematical problems efficiently), Adaptive Reasoning (ability to reflect, reason, explain and justify decisions) and Productive Disposition (tendency to view mathematics as practical, valuable, beneficial).

Due to the complex and abstract nature of mathematics, especially calculus, conventional teaching practices are not sufficient to convey the information in a way that would make it easy for the student to understand and make sense of. Even static illustrations, diagrams and pictures cannot do justice to the dynamic relationships between various concepts.

The use of visualizations and animations can significantly increase the levels of learning as compared to teaching without visualization. Arcavi [2] claims that often while solving a mathematical question, there is a gap/mismatch between what the student was expecting and what the correct result is; visualization can help the student bridge this gap. Arcavi also states that visualization guides the analytical development of a solution as it meaningfully organizes the data. A pedagogically sound visualization can enable students to find intuitive and logical explanations to the solution of mathematical problems, which will improve mathematical proficiency.

In this study, a quasi-experimental research was conducted to compare the difference in the mathematical proficiency (conceptual understanding and adaptive reasoning) of high school students who are taught calculus with and without the use of visualization. The pretest posttest control and experimental group design was employed.

The resulting effect size was 1.59, therefore a strong effect was found and it was concluded that the use of visualization as a supplement to teaching considerably increases the conceptual understanding and adaptive reasoning of high school students.

References:
[1] Jeremy Kilpatrick, Jane Swafford, Bradford Findell. 2001. Adding It Up: Helping Children Learn Mathematics. Washington, DC: National Academy Press.
[2] Arcavi, Abraham. 2003. “The role of visual representations in the learning of mathematics.” Educational Studies in Mathematics 04-2003, Volume 52, Issue 3, pp 215-241

Keywords:

Visualization, Calculus, Mathematical Proficiency.