Mathematical thinking processes based on decision-making types in Grade VIII numeracy: Foundations for differentiated instruction in Geometry

Abstract

Mathematical thinking ability in solving numeracy problems is a crucial 21st-century competency that students must possess to support critical, analytical, and problem-solving skills. However, in practice, students demonstrate diverse ways of making decisions when confronted with numeracy problems, leading to variations in mathematical thinking processes and often resulting in disparities in learning outcomes. This study aims to analyze students’ mathematical thinking processes based on decision-making types: namely intuitive, empirical, heuristic, and rational and to design differentiated instruction aligned with the characteristics of each type. A qualitative approach was employed, with data collected through numeracy tests and observations. The findings reveal that intuitive students tend to rely on visualization and prior experiences without formal proof; empirical students emphasize concrete measurement and validation through discussion; heuristic students demonstrate flexibility in exploring solution strategies and evaluating alternatives, while rational students think systematically in a deductive and argumentative manner. Based on these findings, differentiated instruction was designed in terms of content, process, and product, allowing teachers to adapt materials, strategies, and forms of assessment to students’ decision-making types. The study concludes that differentiated instruction that takes decision-making types into account has the potential to optimize students’ mathematical thinking processes and enhance numeracy competence in the domain of geometry.