The Effect of Problem Based Learning Assisted by Digital Mathematics Tools on Students’ Mathematical Problem Solving and Reasoning

Abstract

Mathematical problem solving and reasoning are essential competencies for developing students’ mathematical literacy, yet students frequently experience difficulties in interpreting non-routine problems, developing appropriate strategies, providing mathematical justification, and evaluating solutions. This study examined the effect of Problem Based Learning (PBL) assisted by digital mathematics tools on students’ mathematical problem-solving and reasoning abilities and identified factors contributing to successful implementation. A quantitative quasi-experimental study with a pretest-posttest control group design was conducted with 64 eighth-grade students, consisting of 32 students in the experimental group and 32 students in the control group. The experimental group participated in eight 90-minute lessons using PBL integrated with GeoGebra, while the control group received conventional mathematics instruction. Data were collected through open-ended mathematical problem-solving and reasoning tests and classroom observations. Descriptive and inferential analyses were conducted using mean scores, normalized gain, and ANCOVA, accompanied by effect-size estimation. The experimental group increased its mean problem-solving score from 54.31 to 81.56 and its reasoning score from 51.75 to 79.84. The control group increased from 53.88 to 69.41 for problem solving and from 52.09 to 67.28 for reasoning. ANCOVA indicated significant differences in problem solving, F(1, 61) = 34.62, p < .001, partial η² = .363, and reasoning, F(1, 61) = 31.47, p < .001, partial η² = .342. Teacher facilitation, student engagement, problem quality, digital interaction, and learning independence contributed to implementation effectiveness. The findings indicate that integrating PBL with GeoGebra provides a productive environment for strengthening mathematical problem solving and reasoning through investigation, visualization, collaboration, and reflection.