Uncovering Gaps in Deductive Geometry Thinking: Rasch-Based Evidence from Students’ Work on Quadratic Functions

Abstract

The deductive structure is fundamental in mathematics, but students often struggle to derive logical consequences when constructing proofs or engaging in the bridging process. This study analyzed students’ ability to deduce logical relationships between properties in geometric thinking on quadratic functions. The participants were students (N=139) from the mathematics education program. The properties of quadratic functions and their interrelationships contained in the premises represented students’ responses to the instrument. The responses were dichotomously coded based on the criteria of the carried-out deduction process and then evaluated using Rasch analysis. The findings revealed that, in general, the distribution of students’ ability levels was below most levels of the carried-out deduction process. Although a group of students had already reached the high-ability category, the overall distribution was still dominated by low-ability levels. Many students continued to face serious challenges in reaching the final stage of the deduction process—advanced premise integration and deductive synthesis—since most of them established relationships among properties merely from the given information. There were indications that learning experiences during higher education contributed positively to the improvement of students’ ability at the deduction level. The study recommends four steps to habituate students to the process of deduction.