Tesseract: International Journal of Geometry and Applied Mathematics

ANALYSIS OF STUDENTS' MATHEMATICAL PROBLEM-SOLVING ABILITY ON MATRIX TOPICS: A CASE STUDY AT SMK AL MUHTADIN

2026-07-22T08:07:39+00:00

Mathematical problem-solving ability is a fundamental competency that enables students to apply mathematical concepts to solve contextual problems. However, many vocational high school students continue to experience difficulties in solving non-routine mathematical problems, particularly in matrix topics. This study aimed to analyze students' mathematical problem-solving processes based on Polya's four-stage problem-solving framework. A qualitative case study approach was employed involving six eleventh-grade students from the Office Management and Business Services Program at a vocational high school in Indonesia. Participants were purposively selected to represent high, moderate, and low mathematical ability levels. Data were collected through written problem-solving tests, semi-structured interviews, and documentation and analyzed using the interactive model of Miles et al., while credibility was established through source and method triangulation. The findings revealed that students with high mathematical ability successfully completed all four stages of Polya's framework, whereas students with moderate ability generally experienced difficulties in evaluating their solutions. Students with low mathematical ability encountered difficulties from the initial stage of understanding the problem, resulting in inappropriate solution strategies and inaccurate conclusions. Overall, students' mathematical problem-solving performance was closely associated with their conceptual understanding, strategic reasoning, and reflective thinking. Therefore, mathematics instruction should emphasize systematic problem-solving strategies, conceptual understanding, and reflective learning practices to improve students' mathematical competencies. This study contributes to the literature by providing qualitative evidence of vocational students' mathematical thinking across different ability levels and offers practical implications for designing mathematics instruction that strengthens problem-solving and reflective thinking.

EXPLORING ORAL AND WRITTEN MATHEMATICAL COMMUNICATION SKILLS IN GEOMETRY PROBLEMS

2026-07-26T02:57:36+00:00

Problems in mathematics learning aspects of students' mathematical communication skills are still low, both in oral and written mathematical communication in geometry problems. Mathematical communication skills in geometry problems require students' ability to explore geometry problems in the mathematics learning process. The difficulty of students in learning geometry problems is still low in terms of expressing mathematical ideas correctly, and students have difficulty communicating their mathematical thoughts to their friends and teachers. Students' mathematical communication skills in the oral and written aspects are part of mathematics skills in the 21st century.Mathematics learning in the classroom needs to be designed related to flat building materials so that mathematics learning is more directed to learning objectives. It is necessary to explore students' ability to solve oral and written mathematical communication problems through discussion, argumentation, explaining answers and writing mathematical ideas both symbols, graphs, and tables. The purpose of this research is to explore the ability of oral and written mathematical communication in geometry problems in junior high schools in Riau Province. This research method is a qualitative research that is descriptive and exploratory. The subjects of the study were 25 students. This research was conducted in grade VII of SMP Negeri 3 Pangkalan Kuras, Pelalawan Regency, Riau Province, Indonesia. The result of this study is a mathematical exploration related to oral and written mathematical communication skills in geometry problems in grade VII in the good category.

INTRODUCING ‘REGION GEOMETRY’ IN MATHEMATICS

2026-05-15T07:35:53+00:00

In this work, a generalization of the existing classical subject Geometry is done by, introducing a new geometry called by “Region Geometry”. It is observed that the classical subject Geometry is R-Geometry, a special case of the subject “Region Geometry” corresponding to the trivial region R. Every region A generates its own region geometry called by ‘A-Region Geometry’ subject to fulfilment of few conditions. Although this is a purely theoretical work, but this theory is expected to cater to Mathematics and all branches of STEM including AI, Data Science, modern Statistics etc in a new direction.