The Role of Visualization Towards Students' Mathematical Abstraction: The Case of Probability

Date of Award

5-1-2023

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics Education

First Advisor

Catherine P. Vistro-Yu, PhD

Abstract

Due to the advancement of technology and the huge amount of materials available to help learners develop their visualizing skills, visualization has now become a major point of interest to many researchers who aim to shift the focus away from a very restrictive and opposing viewpoint of a “visual–analytic” construct. Dubinsky’s (1991) Action, Process, Object, and Schema – APOS Theory is one of the models that can be used to determine how visualization can be harnessed, from personal to a more structured form, using design science as a way to promote mathematical abstraction, and considering students’ culture and experiences. This study was primarily concerned with the concepts that are relevant in determining the possible role of visualization towards students’ mathematical abstraction in probability. It consisted of two phases in which phenomenography was used in Phase 1, and Grounded Theory design (Corbin & Strauss, 1990) in Phase 2. The participants were Grade 11 students enrolled in different academic strands at senior high schools located in two cities. For Phase 1, the participants were 79 students from the city of Manila, while the participants for Phase 2 were 104 students from the city of Valenzuela. Results show that the role of visualization can now be explained by looking at the difference between students who are not able to visualize the concepts in probability and students who are able to do so. For students who could not visualize a given mathematical object, everything seems arbitrary and does not have meaning. On the other hand, for students who are able to visualize the mathematical object, they are able to construct some meaning. This enables them to make representations and reach a certain level of mathematical abstraction, not only in a specific context but in varying contexts. Komiks, visual artifact developed by the researcher, helped provide meaning to the mathematical object while helping students develop the intuitive knowledge needed, which later on was used as a process to help them reach the desired level of mathematical abstraction. Whenever a student feels helpless and fails to recall the procedure for computing the probability of an event, visualization becomes not just an optional strategy or tool but plays a significant role in developing and retaining students’ conceptual understanding.

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