The development of learning achievement in mathematics using Polya’s problem-solving process with Bar Models for grade 4 students

Abstract

        The objectives of this research were: 1) to compare the mathematics learning achievement of Grade 4 students against the 75% criterion, and 2) to examine the satisfaction of Grade 4 students learning through the mathematics problem–solving learning activities based on Polya’s problem–solving process combined with bar models. The instructional activities were systematically designed based on Polya's problem-solving process, which consisted of four key stages: 1) Understanding the Problem, 2) Devising a Plan, 3) Carrying Out the Plan, and 4) Looking Back. To improve students' cognitive processing, bar models were introduced as visual-representational aids to aid in the interpretation of numeric relationships buried inside word problems. This technique improved students' capacity to grasp issue structures and use systematic thinking throughout the problem-solving process. The samples in this study were 15 Grade 4 students from Ban Dong Daeng Nong Phia Khan School in the second semester of the 2024 academic year. The sample was selected using cluster random sampling. The research instruments included 1) 12 lesson plans for mathematics problem – solving learning activities using Polya’s problem – solving process combined with bar models 2) a mathematics achievement test containing 30 multiple – choice items with four options each and 3) a satisfaction questionnaire on learning through Polya’s problem – solving process combined with bar models, comprising 12 items on a 3 – point rating scale. The statistical methods used for data analysis included percentage, mean, standard deviation, and hypothesis testing using the nonparametric Wilcoxon Signed Rank Test.

        The research findings were as follows: 1) Grade 4 students who participated in learning activities using Polya’s problem–solving process combined with bar models demonstrated mathematics learning achievement significantly higher than the 75% criterion at the .05 level. 2) Grade 4 students who participated in learning activities using Polya’s problem–solving process combined with bar models reported an overall satisfaction level classified as high.