How Do Prospective Teachers Find Number Patterns Based on the Laws of Proximity, Closure, and Similarity in a Problem-Solving Activity?

Resumo

Background: Number pattern is a relevant topic in mathematics. Generally, the problems related to the theme can be solved by applying three principles: proximity, closure, and similarity. Besides, solving number pattern problems is closely related to students’ ability to present the problem mathematically. Objectives: To examine prospective teachers’ mathematical problem-solving processes based on the laws of proximity, closure, and similarity. Design: This qualitative research uses a case-study approach to achieve research objectives. Setting and participants: The researcher gave ten math questions to 67 prospective teachers (university students), choosing three to participate. The three focal participants were selected based on the categorisation results using indicators of proximity, similarity, and closure approaches from Gestalt theory. Data collection and analysis: Besides the test questions, the researcher conducted cognitive interviews with the three focal participants to confirm and explore the thought processes. Researchers used focus group discussion (FGD), cross-section data, and reviews with relevant references to validate the research outcomes. Results: The data show that the students could use the law of proximity, closure, and similarity in solving the number pattern problem, which can be seen from their ability to divide the pattern into two parts, complete it into specific geometrical shapes, and to divide it into similar shapes. In this study, prospective teachers’ thinking process schemes were also found when solving patterned number problems using the law of proximity, the law of closure, and the law of similarity. Conclusions: The students who apply proximity could divide each pattern into two parts: fixed and growth. The pattern of growth difference will become the key in generating the general form of the pattern. The students who applied closure could complete the pattern into a particular shape by adding the pattern element. Furthermore, the students who applied similarity divided the pattern into similar shapes. Every student showed a good process in making representation.