The Gauss-Jordan Method as a Representation Framework for HOTS in Rotational Dynamics

Developing higher-order thinking skills (HOTS) in physics requires learning experiences that encourage students to construct mathematical representations rather than rely solely on procedural problem solving. Although the Gauss–Jordan method has frequently been introduced as a computational technique for solving systems of linear equations, its potential as a mathematical representation framework has received little attention. This study investigated whether integrating the Gauss–Jordan elimination method into rotational dynamics instruction could support the development of students' higher-order thinking skills through mathematical representation. A quasi-experimental study involving 68 eleventh-grade students at MAN 1 Jember, Indonesia, used a nonequivalent control-class design. Students in the experimental class learned rotational dynamics through a representation-oriented Gauss–Jordan approach, whereas those in the control class received conventional instruction based on substitution and elimination methods. Students' mathematical thinking was assessed using five essay questions covering reasoning, generalizing, critical thinking, problem solving, and communicating. The results showed greater improvement in the experimental class (N-gain = 0.63) than in the control class (N-gain = 0.26). The difference between classes was statistically significant (Mann–Whitney, p < 0.001) with a large effect size (r = 0.78). The strongest gains were observed in generalizing, reasoning, and critical thinking. Analysis of students' written responses further indicated that learning through the Gauss–Jordan method helped students translate physical situations into mathematical models and recognize explicit relationships among variables. These findings suggest that the educational value of the Gauss–Jordan method extends beyond solving systems of linear equations, highlighting its role as a mathematical representation framework that supports higher-order thinking in physics learning. Keywords: mathematical representation, Gauss–Jordan Method, mathematical thinking, Higher-order thinking skills, Rotational dynamics.