Science Technology Engineering Mathematics and Environmental Education Research Group

Re-imagining futures in STEME

Articulating a Learning Progression: Measuring and Visualising Space in K-5 Mathematics

Professor Richard Lehrer, Vanderbilt University

Friday 3 November 2023

Free event – in person and online

Learning progressions research has encouraged the consideration of learning from a long-term point of view, one that addresses how earlier forms of students’ knowledge can constitute resources for later forms of knowledge that may differ in kind after instruction. Yet, this principled expression of a learning progression tends to neglect its phenomenology, that is how to generate and instantiate a progression so that it is a living, working tool within an educational context.

A progression is valuable to the extent that it is articulated by its participants. An implication for design is to see the work of its development as being sustained by assembling elements to create dialogic spaces. Dialogic spaces refer to literal and figurative sites in which diverse perspectives are brought into contact and, as this is accomplished, aspects of a learning progression are progressively articulated by those who participate in its enactment. To illustrate how dialogic spaces can lead to increasing articulation of a learning progression, I describe a multi-year design study of children’s (K-5) changing conceptions of the measure of space, including length, area, volume, and angle.

The measurement progression also extended to rational number, and to science with its emphasis on related measured quantities, such as mass or rates of growth of animals or plants. Like other learning progressions, the measure progression focused on describing changes in student thinking, but with the broader goal of engaging teachers to both co-generate and put the emerging progression into productive use.

Accordingly, as a community, we sought to establish:

  1. a shared conceptual frame for describing instructional goals and valued forms of teaching and learning—a collective professional vision articulated most succinctly in constructs (Wilson, 2005), but realized in everyday practices (Goodwin, 2018);
  2. curriculum units designed to support teaching responsive to students’ emerging grasp of core concepts and procedures in measure;
  3. an assessment system that aligned in-the-moment teacher observations of student learning with formative and summative assessments that collectively contributed to responsive teaching and to potentially more robust estimates of student learning;
  4. a set of electronic tools to help teachers detect, share, analyze, and interpret evidence of student learning; and
  5. classroom and school-level professional activity structures to support and sustain the progression.

In this presentation, I will focus on change in what teachers noticed about student thinking, and on change in student thinking as a blend of formative evidence generated by teacher observations and summative evidence of learning generated by end-of-year tests.

Register here

Richard Lehrer is Professor Emeritus of Education at Vanderbilt University and a member of the US National Academy for Education.


Working in concert with teachers, he designs and analyses the impacts on learning of classroom learning ecologies that induct students in signature epistemic practices in sciences, such as modeling, and in mathematics, such as defining and explaining why (proving). In collaboration with Leona Schauble he has also investigated how children’s science education could be productively centred about the invention and revision of models of natural systems. Contemporary research investigates how to incorporate teacher’s judgments about students’ ways of thinking about mathematics, generated as students participate in carefully crafted classroom learning ecologies, into innovative psychometric models that meld formative and summative estimates of learning.

This effort, conducted with Mark Wilson, mines the potential of assessment for informing instruction and creates opportunities to transform the current climate of accountability assessment into one more responsive to teaching and learning.

Richard’s most recent book Measuring and Visualizing Space in Elementary Mathematics Learning is available now.

Posted Oct 31, 2023

3 November 2023, 3:30pm

Deakin Downtown and online