The Use of Three Learning Progressions in Formative Assessment in Middle School Mathematics

• In Event: Current Research on the Use of Learning Progressions in Mathematics Formative Assessment: Explorations and Synthesis

Abstract

This presentation reports on a project that uses three learning progressions as a basis for developing a computer-based locator assessment and in-class sets of assessment tasks to be used as part of formative assessment process in middle school mathematics. The three progressions cover the concepts of equality and variable, proportional reasoning, and linear functions. Progressions have either four or five levels. While the levels focus on conceptual change, they are multi-faceted in that they describe patterns of change in several dimensions of mathematics understanding including conceptual, procedural, representational, and contextual knowledge (cf. Kilpatrick, Swafford, and Findell (2001).
We have also developed network model that combines the progressions to express understandings that we predict will likely co-develop in students. The progressions were created starting with a literature review of mathematics cognition that included existing research-based progressions in each area. Sample assessment tasks were developed to collect evidence to distinguish between levels. Selected or developed progressions and tasks were then revised based upon feedback by an expert research panel and groups of teachers in three middle schools many of whom tried out tasks informally in their classrooms.
The paper focuses on the design of the in-class assessment tasks and analyses of data collected in piloting in three middle schools. In the cycle of formative assessment, there is evidence that after teachers have made inferences about students’ understanding, they particularly struggle when it comes to determining the next instructional steps (Heritage, Kim, Vendlinski & Herman, 2008). Therefore, the tasks were designed to provide a basis for teachers to 1) gather evidence of students’ understanding and 2) help students make key transitions in understanding characterized in the progressions. Pairs of starting and “landing” points were identified within and across levels in each of the progressions. We identified specific knowledge needed to build from a starting point to the associated landing point. Each incremental assessment task focuses on one transition and employs one or more approaches to build this knowledge in students and can be used in a variety of ways for formative assessment. Data from teachers and students early experiences with these tasks will be presented.
This work is significant in that it aims to show how instructional supports can be built directly into formative assessment tasks that teachers can use in a variety of ways in their classrooms. The role of the learning progression is critical in this process is critical, since it allows us to target those transitions from one level to the next, both in terms of the assessment and instruction.

Author

• Malcolm Bauer, ETS