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

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

by Dennis Lee Jarvis B. Ybañez
PhD Mathematics Education Candidate

Date: Thursday, 19 January 2023
Time: 10:30 am
Venue: Online

Advisers:
Catherine P. Vistro-Yu, EdD
Ateneo de Manila University

Panelists:
Maria Alva Q. Aberin, PhD (Critic Reader)
Ateneo de Manila University
Angela Fatima H. Guzon, PhD
Ateneo de Manila University
Ricardo G. Abad, PhD
Ateneo de Manila University
Flordeliza F. Francisco, PhD
Far Eastern University
Ferdinand Rivera, PhD
San Jose State University
 

Due to the advancement of technology and the sheer volume of visualization materials available for mathematics education, visualization has now become a major point of interest to many researchers with the goal to shift the focus away from a very restrictive and opposing viewpoint of a “visual–analytic” construct. Dubinsky‘s 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) through design science as a way to promote mathematical abstraction, 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) was used in Phase 2. All the participants were Grade 11 students enrolled in different academic strands at a Senior High School 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 the students who are able to do so. For students who could not visualize the mathematical object, everything seems arbitrary and do not have meaning. On the other hand, for students who are able to visualize the mathematical object, they are able to construct 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. The visual artifact (komiks) developed by the researcher helped provide meaning to the mathematical object making students establish the necessary intuitive knowledge needed, which later on was used (as a process) to bring them to 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 huge role in developing and retaining students’ conceptual understanding.

Key Words: Genetic Decomposition, Mathematical Abstraction, Structured Visual Thinking, Subjective Visual Imageries, Visual Artifact, Visualization