Characteristics of Polya’s problem-solving process among senior high students in centers of focus figural pattern generalization
DOI:
https://doi.org/10.30762/f_m.v9i2.8945Keywords:
Pattern Generalization, Polya’s Problem Solving, Centers of FocusAbstract
Problem-solving ability is a fundamental competency in 21st-century mathematics education. However, 2022 PISA results indicated low performance in Indonesia. This descriptive-qualitative study aimed to describe the characteristics of Polya’s problem-solving stages among senior high school students in centers of focus: figural pattern generalization. Out of 34 students, three were selected through purposive sampling using Lobato et al.’s three centers of focus: additive growth, relationship between step number and object number, and routine dominated by additive growth. Data were collected through a figural pattern generalization test and semi-structured interviews. Findings showed that students with an additive growth focus solved problems by redrawing patterns, devising a plan based on repeated addition, and carrying out the plan using manual addition without producing general formulas or reviewing answers. The student who focused on the relationship between the step number and the number of objects applied the formula for an arithmetic sequence and verified the resulting solutions. Meanwhile, the student whose focus was on a routine dominated by additive growth transformed the constant increment into a multiplication routine, consistently produced correct answers, and reviewed the solutions. These findings indicate that students' centers of focus in figural pattern generalization are systematically associated with distinct problem-solving strategies at each of Polya's stages, ranging from recursive, additive-based approaches to structural, formula-based reasoning, thereby providing empirical evidence linking Lobato et al.'s center-of-focus framework to Polya's problem-solving stages. In addition, this study offers implications for designing instructional strategies that can support students' transition from recursive to structural reasoning in figural pattern generalization.
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