Examining Potential Teachers' Capabilities for Creative Thinking in Geometry Problems Using Analytical Framework NEA

Abstract

In classroom practice, the use of problems that require students to engage both in higher-order thinking and creative reasoning has been recognized as among the most effective strategies for meaningful learning. Within this context, the present study was designed to investigate in depth the types of errors committed by mathematics education students, who are also prospective teachers, in demonstrating their creative thinking abilities when dealing with geometry-related tasks. The analytical framework employed was Newman Error Analysis (NEA), which provides a systematic way to examine mistakes in problem-solving processes. A qualitative approach with a descriptive case study design was selected in order to capture a detailed picture of the phenomena under investigation. The participants consisted of 22 mathematics education students from a university located in Surakarta. Several methods were used to gather data, including direct classroom observation, the administration of diagnostic tests specifically developed to measure mathematical creative thinking, and in-depth interviews. The data analysis followed the model proposed by Miles and Huberman, involving three interrelated steps: data reduction, data display, and the formulation of conclusions. The findings revealed that the most frequent and significant errors occurred during the transformation and encoding stages of problem solving. This study concludes that strengthening prospective teachers’ exposure to non-routine geometry problems and explicitly addressing common error patterns are essential for improving creative mathematical thinking.