The construction and validation of a geometric reasoning test item to support the development of learning progression

Abstract

This article presents preliminary analysis of a test item in a large-scale study design to promote the development of geometric reasoning progression. Two sets of data were analysed to validate the item designed to assess secondary school students’ knowledge of a rectangle. The first data set involved 155 Year 4–10 students from seven trial schools across social strata. The second data set involved 585 Year 7–10 students from eleven project schools situated in lower socio-economic areas. The aim was to audit Australian students’ knowledge of hierarchy of shapes and document the process of validating a test item. The findings indicated that an iterative process of design, test and redesign, incorporating Sfard’s mathematical discourse framework and a multi-stage Rasch analysis, is vital in validating the results. A distinct change in students’ reasoning about rectangle is observed and this is not due to age. Moreover, Rasch analysis identified eight distinct thinking zones to assist in mapping out a learning progression for developing geometric reasoning.