Exploring Mathematical Epistemology of Grade 6 Students in Validating the Sum of Two Odd, Two Even, and Combination of Even and Odd Numbers
Ainah S. Panoroganan-Tantao *
Madaya Elementary School, Maguing, Lanao del Sur, Philippines.
Bartolome L. Cagas
Institute of Science Education, Mindanao State University, Marawi City, Philippines.
*Author to whom correspondence should be addressed.
Abstract
To achieve a better understanding and performance from the elementary students in Mathematics, this study investigates on their epistemic reasoning patterns when dealing with the parity of the sum of odd and even numbers. Thus, this research study aims to present how elementary students think and reason out when they are learning basic concepts in mathematics which makes it important to the scientific community. It also provides proof on how Grade 6 learners explore the patterns and test ideas which leads them in drawing conclusions on even and odd numbers. This adds to new knowledge about the mathematical thinking ability of learners most especially at the elementary level where there are still few studies conducted. Respondents are from one of the public schools in a certain rural area in the Philippines which entails that students’ knowledge is limited only on what their teacher taught in class and majority of them in terms of academic performance belongs to average level. Data were collected from 30 students through a five-item open-ended questionnaire designed to prompt practical and formal reasoning about parity of the sum of odd and even numbers. This study employs a qualitative research design. Written responses of the participants were analyzed using thematic analysis and classified according to mathematical epistemic reasoning. Practical epistemic reasoning highlights the process of inquiry and validation of mathematical concepts such as establishing mathematical idea through testing, observing, and verifying results while formal epistemic reasoning highlights on constructing valid arguments and generalization following certain rules and established mathematical ideas. The result of this study generally implies that elementary school students’ reasoning regarding the parity of the sum of even and odd numbers highlights on how learners shift from simple pattern recognition to operational understanding and formal justification. Finally, the findings of the manuscript may provide help among individuals in improving teaching strategies in understanding, reasoning, and active learning in mathematical concepts.
Keywords: Mathematical epistemology, parity of the sum of even and odd numbers, mathematical reasoning, mathematics education