Form and Function of Learning Progressions in Mathematics: A Framework and Review

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

Abstract

At an abstract level, a learning progression is a characterization of student understanding in terms of a sequence of states or levels. Learning progressions vary along several dimensions relating to their form and function. To set the stage for subsequent talks in this symposium, this paper identifies several critical dimensions on which learning progressions differ, explores the role of each of these dimensions in classroom-based formative assessment, locates selected current and past research on learning progressions within these dimensions, and based upon this analysis, identifies additional areas of research that can advance the field. Dimensions include
1. The degree to which progressions are directly situated within a framework for formative assessment and instruction. The nature and flexibility of the supporting framework can greatly affect how and where progressions can be used by teachers. With respect to this dimension, Daro, Mosher, and Corcoran (2011) wonder:
“At this point we can only question whether the right label for the focus of that joint study is “learning trajectories,” or whether it should be something more compound and complex to encompass both learning and teaching, and whether there should be some separate label for the aspects of development that are significantly influenced by “internal” factors.” (P. 21)

2. The nature of student knowledge characterized by the progression. Examples of different types of knowledge include conceptual, procedural, contextual, and representational. Progressions can include some or all of these types of knowledge or others. The types of knowledge in a progression affect the activities teachers employ to collect evidence of student understanding, and the instructional steps that are likely to follow.
3. The grain size and scope of learning progressions. These characteristics can affect how progressions connect to curricula and to lesson plans, and can affect the nature of feedback progressions can help teachers provide to students
4. The structure and complexity of learning progressions. This dimension can affect how progressions characterize student development, and also the ease with which teachers and students can understand progressions.
5. The degree to which progressions have an underlying psychological basis and empirical support. This dimension impacts the validity of the use of progressions in formative assessment.
The primary purpose of this introductory presentation is to provide a context for the remaining talks. The larger significance is that by reflecting on prior research in a structured way, we can identify opportunities and directions for future work in the field.

Author

• Meirav Arieli-Attali, ETS