Pre-Algebraic Concepts and Relational Thinking in Solving Number Sentence: A Textbooks Analysis

Final Defense
Pre-Algebraic Concepts and Relational Thinking in Solving Number Sentence: A Textbooks Analysis

by Reisid May B. Sumbilon
MS Mathematics Education Candidate

Date: Saturday, 27 January 2024
Time: 10 am
Venue: Online

Advisers:
Maria Alva Q. Aberin, PhD
Ateneo de Manila University

Panelists:
Maria Theresa T. Fernando (Reader)
Ateneo de Manila University
Angela Fatima H. Guzon, PhD
Ateneo de Manila University
Lester C. Hao, PhD
Ateneo de Manila University

The transition from arithmetic to algebra is often considered a challenging cognitive shift known as the "di- dactic cut". Pillay, Wilss, and Boulton-Lewis (1998) introduced a sequential developmental model bridging arithmetic skills and algebraic understanding, emphasizing a pre-algebraic stage. This study analyzed the presence and prevalence of pre-algebraic concepts in the solutions of number sentences within selected el- ementary Mathematics textbooks. The investigation also identified prevalent types of number sentences based on Singh and Kosko’s (2017) equivalence model.

Content analysis was conducted on Textbook A (634 discussions) and Textbook B (669 discussions), high- lighting equivalence as the most recurrent pre-algebraic concept across both series, while the use of inverses was notably infrequent. Examining 332 exercise sets in Textbook A and 307 in Textbook B revealed a pre- dominant reliance on the basic operational level, showing no progression across grade levels. Additionally, inadequacies were noted in discussing these concepts within the solutions of number sentences, leading to potential misconceptions and mathematical inaccuracies in exercises.

Given these findings, there is a need to review the curriculum in terms of the usage of pre algebraic concepts and relational thinking, this involves a progressive difficulty in the level of exercises, diverse problem-solving scenarios and a visual and narrative support in the solution. Moreover, it is important to conduct teachers’ training in bridging the gap left by the textbook.