To Foster Mathematical Proficiency: Innovating Proof Strategies Within Mathematics Education Discourse

Abstract

We examine and combine etymological verification to show information in a longitudinal retrospective analysis. The data include 1,000 concepts, compared across 150 students. The problems are from the Academic Information System. The participants are learners in the pre-service graduate program for teachers covering the period from 2018 to 2022. Two research questions surface from the experimental review and word trajectories. Question 1 focused on identifying and creating proof models, while Question 2 explored word trajectories in contextual measures. The data are gathered from 400 proofs, divided into etymological sense and their understanding in exploring proof. The construct validity is assessed using the Test of Cramer, leading to a C coefficient of 0.83. The Plot Diagram examined interaction effects between variables through the ANOVA test. An intersection is identified based on the process of doing proof, with ρ < α = 0.05, confirming model validity. The multiple determination value for all independent and dependent variables is 1, indicating a strong correlation. The results propose that the pattern leans towards a meta-pattern, with a non-linear description or variation in proof, and logical steps representing a form of thinking. In general, an increase in doing proof correlates with a decrease in mathematical representations.