Students’ Ways of Thinking on Geometry

Abstract

Ways of Thinking (WoT) is a fundamental ability that is part of the mental act that students must learn to solve geometry problems. The purpose of this research was to describe how WoT is used to solve geometry problems. This research used the descriptive qualitative methodology with a holistic case study design and data collection techniques such as tests, interviews, observation, documentation, and triangulation. The subjects in this research were 35 fourth-grade students from Sambas Regency Public Elementary Schools, Indonesia. The research focused on three students with varying levels of cognitive abilities: low, medium, and high. The results showed that students with high, medium, and low cognitive capabilities performed mental acts with the corresponding WoT. Students with high, medium and low cognitive capabilities were more likely to work on questions that required interpretation. Besides, it also revealed that errors committed students were learning errors, reading errors, careless errors, conceptual errors, and procedure errors. The implementation of WoT on the topic of geometry can be utilized as an alternate reference for mathematics teachers when developing teaching materials for mathematics learning to increase studentss' mathematical knowledge.

Student’s ways of thinking and ways of understanding analysis in solving mathematics problems in term of adversity quotient

“…Nurhasanah et al, (2021) examined the characteristics of WoT that are interconnected with students' WoU in vector material. Further, in her following research regarding the implementation of WoT, students who have high, medium, and low cognitive abilities in geometry material can be reference in developing mathematics teaching materials (Nirawati et al, 2022). As a result, the difference between this study and previous ones is the material used which are lines and angles, as well as the selection of subjects based on the adversity quotient.…”

Students’ Ways of Understanding and Ways of Thinking in Solving Trigonometric Problems

“…Thinking also allows someone to get ideas or thoughts about what they are thinking (Sunaryo, 2011). Every student is able to think because they generally have mathematical abilities in ways of thinking and understanding since their early stage of childhood (Nirawati et al, 2022). For example, critical thinking which is an important tool that students should use to solve the problems they face in their daily life because it involves logical reasoning, interpreting, analyzing, and evaluating information to enable them to make reliable and valid decision (Widana, 2018).…”

“…It is also called by a reciprocal process to develop students' ways of thinking because one can't be done without the development of students' way of understanding. This process happens when students are at the center of learning and building their knowledge that leads to the development of students' learning skill which focuses on the developing mindsets and ways of understanding the mental actions of the students (Nirawati et al, 2021). In other word, the two terms ways of understanding and ways of thinking not only influence each other but also the changes in ways of understanding will not occur without the changes in ways of thinking.…”