Assessing Geometric Proof Skills: Instrument Validation Through Reliability and Factor Analysis

Abstract

From a mathematics teacher education perspective, identifying the component processes involved in geometric proof reasoning may help prospective teachers interpret learners’ proof attempts and plan instruction. This study examined the internal consistency and empirical structure of a 25-item multiple-choice instrument for assessing proof-related reasoning in geometry. Responses from 275 Indonesian preservice mathematics teachers were analysed using item–total correlations, Cronbach’s alpha, and an exploratory analysis of the instrument’s component structure. The overall internal consistency was high (Cronbach’s α = 0.892), although four items had corrected item–total correlations below 0.30. The reported component analysis yielded a six-component solution accounting for 56.63% of the total variance. The components concern deductive relationships, linking premises, identifying relevant statements, recognising circular arguments, and reasoning with particular and universal propositions. These findings provide preliminary evidence of the instrument’s usefulness for investigating proof-related reasoning. However, weak items, cross-loadings, and the need for further psychometric confirmation mean that its subscale interpretations should be considered provisional. In mathematics teacher education, responses to the instrument may help teacher educators design activities in which prospective teachers analyse reasoning errors and consider appropriate instructional responses.