Assessing conceptual learning in mathematics classrooms : a thesis completed in partial fulfilment of the requirements for the degree of Master of Education at Massey University, New Zealand
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This study explores how building a collective understanding of the big mathematical ideas and learning trajectory within an area of the mathematics curriculum, positions teachers to make consistent, accurate and effective judgements of student’s learning. Teachers and schools are shifting their focus from teaching and learning regimes that prioritize procedural mastery towards those that prioritise building conceptual understandings. This is resulting in a growing mismatch between what is taught and what is tested, since existing testing regimes primarily seek to assess procedural skill over conceptual learning. Schools must therefore rely heavily on teachers to judge students developing conceptualisations, until such time that assessment procedures better align with the outcomes sought by the education system (Jones & Inglis, 2015). Additionally, it looks at what factors support teachers to make judgments of student’s conceptual understandings. The paradigm of interpretivism and social constructivism underpins the focus of this research. Relevant literature is drawn on to support the claims made in relation to hypothetical learning trajectories and their positive impacts on teacher knowledge, practice and judgement. The research evidence that supports using free-response tasks is presented and justifies their use for assessing the breadth and depth of student conceptions. Comparative judgement as a tool for assessing free-response tasks is utilised with consistent and reliable results. The interventions utilised by this design study involved carefully planned, collaborative professional development around the Curriculum Elaborations. Teachers collectively mapped hypothetical learning trajectories, planned appropriate, levelled tasks, assessed student learning through free-response tasks and participated in a comparative judging session for each curriculum area covered. Significant growth was seen in teacher knowledge about the curriculum content and learning progressions. Teachers knew what content to cover, in what order to present it so that it made sense and, how learning outcomes planned into the HLT subsequently related to the mathematics curriculum levels. This understanding positioned teachers to made consistent and accurate judgements about their students learning for both teaching and assessment purposes. The research findings provide insight into the ways teachers can be supported to notice and judge student’s conceptual learning through engaging with collaborative professional development aimed at building their collective knowledge of the curriculum content and progression of learning.