Examining Genetic Decompositions Through a Textbook Analysis of Contexts and Mental Constructions in Fraction Sum and Difference

Final Defense
Examining Genetic Decompositions Through a Textbook Analysis of Contexts and Mental Constructions in Fraction Sum and Difference

by Angel Mae O. Ombid
MS Mathematics Education Candidate

Date: Saturday, 15 June 2024
Time: 2 pm
Venue: SEC A 321 - MJR Room

Advisers:
Angela Fatima H. Guzon, PhD
Ateneo de Manila University
Maria Theresa T. Fernando
Ateneo de Manila University

Panelists:
Romina Ann S. Yap, PhD (Critic Reader)
Ateneo de Manila University
Ian June L. Garces, PhD
Ateneo de Manila University
Chara Deanna F. Punzal
Ateneo de Manila University

Cultivating a mathematically empowered citizenry is one of the main goals of Philippine mathematics education. This places emphasis on developing critical and analytical thinking skills among all Filipino students. Essential to achieving this goal is a solid grasp of fundamental concepts in mathematics, such as understanding fractions. However, students often struggle with this concept, specifically in connecting their understanding of natural numbers with the concept of rational numbers. While existing research has largely examined students’ explicit construction of rational number concepts and their misconceptions, only a few studies have delved into the implicit conceptualizations embedded in educational mate- rials. This shift in focus has led to the introduction of the concept of implicit genetic decom- position, which evaluates how textbooks suggest students could mentally approach specific mathematical concepts through APOS Theory. Through textbook analysis, this study investi- gated three Grade 4 mathematics textbooks to identify their proposed mental constructions that students could do in understanding sum and difference of fractions, as well as the dif- ferent contexts used to present these conceptualizations in textbooks. Eleven conceptualiza- tions of fraction sum and difference were determined and defined. Among all the conceptual- izations identified, only two conceptualizations have implied stages of understanding higher than the Action stage. Moreover, it was found that contexts were only used to present concep- tualizations with implied Action stage of understanding, mostly through personal and societal contexts. This suggests that the three textbooks seem to emphasize a strong relationship be- tween context and external representations in addition and subtraction of fractions.