Panyawat Haarsa
Department of mathematics, Srinakharinwirot university, Bangkok

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STRUCTURED MATHEMATICAL THINKING: EVALUATING POLYA’S PROBLEM-SOLVING APPROACH IN EXPONENT MULTIPLICATION AND DIVISION Janyaporn Pookhung; Ratchadaporn Phobubpa; Panyawat Haarsa
Jurnal Numeracy Vol 13 No 1 (2026)
Publisher : Program Studi Pendidikan Matematika, Universitas Bina Bangsa Getsempena

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46244/numeracy.v13i1.3507

Abstract

This study examines the effectiveness of Polya’s four-step problem-solving approach in strengthening students’ structured mathematical thinking when learning multiplication and division of exponents. Although exponent operations are fundamental in algebra, many Grade 7 students continue to experience difficulties in interpreting problem structures, applying exponent rules, and verifying their solutions. This research employed a quasi-experimental one-group pretest-posttest design involving 32 students at a junior secondary school. The instructional intervention applied Polya’s four phases: understanding the problem, devising a plan, carrying out the plan, and looking back. These phases were integrated into guided teaching activities and structured practice tasks. Data were collected through a ten-item test, an analytic scoring rubric, and an error analysis framework. The findings reveal a statistically significant improvement in students’ posttest performance when compared with the predetermined sixty percent competency benchmark. This indicates meaningful progress in both procedural fluency and structural reasoning. The error analysis also shows that students initially struggled with misinterpreting the structure of exponent expressions, inconsistent use of exponent laws, and limited monitoring of their own work. After the instructional intervention, most students demonstrated clearer reasoning patterns, more accurate translation of problem structures, and greater consistency in checking their answers. These results confirm that Polya’s four-step approach can support students in developing structured mathematical thinking by helping them express problem meaning, plan appropriate solution steps, and reflect on accuracy.
INTEGRATING SYMPY INTO COLLABORATIVE LEARNING FOR PARTIAL FRACTIONS AND INTEGRATION: A QUALITATIVE STUDY IN CALCULUS Panyawat Haarsa
Jurnal Numeracy Vol 12 No 2 (2025)
Publisher : Program Studi Pendidikan Matematika, Universitas Bina Bangsa Getsempena

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46244/numeracy.v12i2.3422

Abstract

This qualitative classroom study explores how collaborative learning (CL) supported by Python (SymPy) can strengthen university students’ understanding of partial fraction decomposition and its application to integration. Thirty‑two second‑year mathematics majors participated in four weekly sessions that blended manual problem solving with computational checking. Students worked in six small groups with defined roles (problem solver, coder, recorder, presenter), engaged in real‑world tasks (e.g., economic growth, fluid flow, and motion analysis), kept reflective journals, and delivered group presentations evaluated with an analytic rubric. Data sources comprised observations, journals, and presentation assessments. Thematic analysis indicates improved participation, clearer conceptual linking between algebraic manipulation and integral calculus, and more systematic error‑checking when Python was used to validate manual work. Groups demonstrating stronger within‑group communication tended to employ Python more effectively and reached higher rubric scores. The study discusses practical design choices for CL tasks that combine traditional and computational approaches, and reflects on limitations such as heterogeneous prior programming experience and the absence of pre–post achievement testing. Implications for practice include structuri