The construction and validation of a geometric reasoning test item to support the development of learning progression
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The construction and validation of a geometric reasoning test item to support the development of learning progression Rebecca Seah 1
& Marj
Horne 1
Received: 21 September 2018 / Revised: 22 April 2019 / Accepted: 12 June 2019 # Mathematics Education Research Group of Australasia, Inc. 2019
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. Keywords Geometric knowledge . Visuospatial reasoning . Student knowledge . Learning progression
Researchers into improving student outcomes have long recognised that quality teaching is the most important determinant in student achievement, after all other source of variations, such as gender, social backgrounds of students, disabilities and differences between schools are taken into account (Alton-Lee 2003; Darling-Hammond 2000; Malmgren et al. 2005). Teaching that is informed by effective assessment data has a * Rebecca Seah [email protected] Marj Horne [email protected]
1
RMIT University, Melbourne, VIC, Australia
R. Seah, M. Horne
significant, proven effect on learning (Goss et al. 2015; Hattie 2009). This need to design targeted teaching advice, often referred to as differentiated or evidence-based teaching, has fanned much of the research into the development of learning progressions or learning trajectories as they are more commonly named. Learning progressions/trajectories are a set of empirically grounded and testable hypotheses about students’ understanding of, and ability to use, specific discipline knowledge within a subject domain in increasingly sophisticated ways through appropriate instruction (Seah and Horne 2019; Simon 1995). They are built on the premise that learning takes place over time and that teaching involves recognising where learners are in their learning journey and providing challenging but achievable learning experiences to support learners to progress to the next step in their particular journey (Seah and Horne 2019). As such, evidence-based learning progressions/trajectories can provide a guide for teachers to impro
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