Developing Research-Based Learning Trajectories to Support Mathematical Reasoning in the Middle Years: An Australian Perspective

• In Event: Learning Trajectories as Boundary Objects for Psychometricians, Learning Scientists, and Practitioners in Mathematics Education

Abstract

Following on from earlier work that demonstrated the efficacy of using an evidenced-based learning trajectory for multiplicative thinking to address the significant range in students’ mathematical capabilities in the middle grades (Authors B, 2018), a project team was established to investigate the extent to which evidence-based learning trajectories could be developed to support the teaching and learning of algebraic, geometrical, and statistical reasoning in grades 7 to 10. The rationale for doing this was the perceived disconnect between multiplicative thinking and what teachers felt they had to teach, and the need to provide an empirical basis for adopting a more reasoning-centred, problem-oriented approach to teaching school mathematics at this level.
From our perspective a learning trajectory is an integrated, empirically-based learning and assessment framework focused on the development of big ideas and the links between them. The framework incorporates an evidence-based learning progression that serves as a model of how students’ thinking evolves over time, validated diagnostic assessment tools that identify where students are in relation to the learning progression, and targeted teaching advice to help teachers progress students’ learning from one level/zone of the progression to the next.
The decision to focus on big ideas (Baroody, Cibulskis, Lai, & Li, 2004) was shaped by our context. In Australia, curriculum refers to a set of nationally determined content descriptors and general proficiency statements organised by grade level. Teachers are responsible for planning and their day-to-day choice of learning experiences and how they are enacted. As a result, teachers were involved in the four-year project designed to address the following research questions:
To what extent can we develop rich tasks to accurately identify key points in the development of mathematical reasoning in the middle grades?
To what extent can we gather evidence about students’ achievement with respect to these key points to inform the development of a coherent learning and assessment framework?
Draft learning progressions in each domain were developed on the basis of an extensive review of the literature and tested using rich assessment tasks and Rasch analysis. Successive iterations improved task design and refined the draft learning progressions to yield validated assessment tools, empirically-based learning progressions in each domain, and targeted teaching advice. Feedback from the teachers involved in trialing the tasks, marking and moderating student responses, collating and reviewing results, and implementing and contributing to the teaching advice, indicated significant growth in their knowledge base for teaching and their capacity to recognise and build on students’ understanding. This has important implications for the design of professional development.

Authors B. (2018).

Baroody, A., Cibulskis, M., Lai, M., & Li, X. (2004). Comments on the issue of learning trajectories in curriculum development and research.Mathematics Teaching and Learning, 6(2), 227-260

Authors

• Dianne E. Siemon, Royal Melbourne Institute of Technology

• Lorraine F Day, University of Notre Dame Australia

• Marj H. Horne, The Australian Catholic University

• Rosemary Callingham, University of Tasmania