Instructional guidelines for integrating Problem-based Learning with Desmos to Develop Mathematical Concepts of Pythagorean Theorem for Grade 8 Students

Abstract

This study investigates the development of instructional guidelines for integrating problem-based learning (PBL) with Desmos activities to enhance Grade 8 students' understanding of the Pythagorean Theorem. It further examines the effectiveness of this approach in promoting students' mathematical conceptualization. The research employed a single-group pretest-posttest design with 22 Grade 8 students from a school in Phetchabun Province, Thailand, derived from simple random sampling. Four instruments were used: (1) lesson plans integrating PBL and Desmos, (2) Desmos program lessons, (3) lessons with a post-instruction reflection sheet, and (4) a pre- and post-test assessing students' mathematical concept of the Pythagorean Theorem. Content analysis was conducted to identify instructional guidelines, while a dependent-samples t-test analyzed the change in students' conceptual understanding.

Results The findings revealed a six-step instructional framework: (1) problem scenario, (2) identify facts, (3) generate hypotheses, (4) address knowledge deficiencies, (5) apply new knowledge, and (6) abstraction. Key pedagogical considerations include (a) familiarizing students with Desmos, (b) applying Desmos to foster student analysis, discussion, and collaboration, (c) adapting lesson time based on student needs, (d) monitoring student progress using Desmos dashboards, and (e) providing ongoing encouragement. Furthermore, the study demonstrated significant improvement in students' concept of the Pythagorean Theorem following participation in the PBL-Desmos integrated learning approach. The pre- and post-test scores revealed a statistically significant increase (p < .05) in students' comprehension levels. This research contributes to the field of mathematics education by developing instructional guidelines for integrating PBL and Desmos for the Pythagorean Theorem and by demonstrating the effectiveness of this approach in promoting student learning.