Developing a Preliminary Genetic Decomposition for Graphing Rational Functions: An Exploratory Study

Final Defense
Developing a Preliminary Genetic Decomposition for Graphing Rational Functions: An Exploratory Study

by Christian S. Abasta
MS Mathematics Education Candidate

Date: Wednesday, 27 November 2024
Time: 2 pm
Venue: SECA 215

Advisers:
Lester C. Hao, PhD
Ateneo de Manila University

Panelists:
Angela Fatima H. Guzon, PhD (Critic Reader)
Ateneo de Manila University
Maria Alva Q. Aberin, PhD
Ateneo de Manila University
Timothy Robin Y. Teng, PhD
Ateneo de Manila University

The study aimed to construct a preliminary genetic decomposition (PGD) for graphing rational functions, which is a theoretical model used to describe and possibly predict students’ cognitive pathways in learning a mathematical concept. The study adopted both the Action, Process, Object, and Schema (APOS) theory and the Multimedia Learn- ing Theory (MMLT) in the theoretical framework.

Using an exploratory research design, the present qualitative study utilized systematic literature review, reflexivity, classroom observation, and qualitative content analysis as research methods. The development of the PGD was anchored on the analysis of exist- ing scholarly and teaching-learning materials that have been published in the past 10 years. Furthermore, the researcher’s teaching-learning experiences on graphing ratio- nal functions were also considered in the analysis. Additionally, based on the conducted content analysis, the study implemented the Activity-Classroom-Exercise (ACE) teach- ing cycle supported by multimedia learning principles to substantiate the construction of the PGD for graphing rational functions. The findings suggest that the PGD contains pre-existing knowledge (e.g., factoring polynomials) to scaffold the underlying concepts (e.g., domain, intercepts, asymptotes) in learning graphing rational functions.

Moreover, the PGD indicates that students perform certain actions on a rational function (e.g., finding the zeroes of the denominator) to be interiorized as processes (e.g., vertical asymptote). Afterwards, these processes are coordinated to form the process of character- istics of the rational function, which is then encapsulated as the object of the graph of the rational function.