Towards Leveling Up in The Euclidean Algorithm: Evidence from Third Year Students

Abstract

The Euclidean algorithm is a fundamental mathematical procedure for finding the greatest common divisor of two integers. Yet research shows students often struggle to apply the algorithm accurately and efficiently. This research investigates the leveling-up plan in Number Theory, focusing on the Euclidean Algorithm. The study employs a descriptive research method and utilizes a purposive sampling technique. The researcher-designed instrument demonstrates high reliability, with a Cronbach's Alpha coefficient of 0.897. The key objective includes assessing and evaluating the extent of the students’ performance in the Euclidean Algorithm. Results indicate a statistically significant difference to a great extent in the students’ performance in Number Theory, focusing on the Euclidean Algorithm. This discovery is significant because the performance of the students will be improved in problem-solving using the Euclidean Algorithm.

In light of these findings, recommendations are proposed. It is suggested that students should be trained to solve problems independently to improve their ability to overcome difficulties and master the Euclidean algorithm. Moreover, teachers should intervene to educate students on using mental processes properly and recognize student errors and misconceptions in order to develop effective, modern, and inclusive math instruction on the Euclidean algorithm. Additionally, future research could further explore instructional techniques targeting specific student misconceptions, as well as factors impacting student performance with the Euclidean algorithm. Finally, full implementation of Project LEARN: Leveling up plan towards Euclidean Algorithm Recursive Numeric to help students gain conceptual understanding, procedural skills, and computational fluency with the Euclidean algorithm.