Principal Curvature: Modeling With Mathematica and JavaScript

Abstract

This is participatory action research (PAR) explored master level students’ concept image and their understanding of principal curvature, in the course ‘Differential Geometry’. The steps used in PAR were P-plan, A-Action, O-Observation, and R-reflection (PAOR). This study focused on answering the question “How do students understand the concept of principal curvature while using Mathematica and JavaScript modeling?”. To answer this question, the study is based on University Campus, Central Department of Mathematics Education, Tribhuvan University during the 2024 academic year. The participants of this study were thirteen master’s level students (five girls and eight boys). The study followed the iterative cycles of PAR to understand how Mathematica and JavaScript visualization help students to build a concept image of mathematical understanding. In this study, observation checklist, students’ interactions and notes, and concept maps as artifacts were used as the data collection tools. The collected data were transcribed, and thematic coding was used to analyze the collected information. Based on the data analysis, the findings of this study showed that Mathematica and JavaScript-based interactive visualizations provided a bridge to connect ‘concept image and concept definition’ through engaged and interactive participation while learning Differential Geometry.