Formative Assessment Lessons in Mathematics, from the Mathematics Assessment Project

Learning to conduct formative assessment – to provide opportunities for students to express their understandings, and to react in the moment in ways that “meets the students where they are” – is a significant challenge. To support teachers in this endeavor, the Mathematics Assessment Project produced 100 2-3 hour Formative Assessment Lessons (FALs). The lessons were designed to have the following properties:

  • The lessons focus on key mathematical concepts and practices in grades 6 through 10, with 20 lessons at each grade level.
  • Each lesson can be “inserted” into the regular grade level curriculum, so that for particular topics they help teachers discover what their students have learned, and what challenges they face. They provide ways to address those challenges.
  • The lessons – with lesson plans that extend to 20 pages to support the use of a pre- assessment and 2-3 hours of instruction – are aimed at helping teachers to:
    • Uncover some misconceptions by using the pre-assessment, and have time to think through the ways in which the main content of the lesson addresses them;
    • Be prepared for the main lesson with a list of “common issues” that the lesson will likely uncover, and ways to respond to those issues without simply re-teaching the content (e.g., by using questions that cause the students to consider a particular example that challenges their statement, or to look at a specific simpler case to see how things work);
    • Launch the main lesson in ways that (often contradictory!) student ideas are made public, so it becomes apparent to all that there are issues to resolve;
    • Lead a number of activities in which students build on each other’s ideas (in making posters for presentation, etc.) as supported by the teacher; and
    • Bring the lesson to closure, with activities that expand on and solidify student learning.
  • Perhaps most ambitious, the FALs are designed to support teachers in changing their pedagogy – the goal being that, having been scaffolded in teaching this new way with very carefully guided lessons, the teachers might open up their practice so that their “regular” lessons are taught differently. The FALs scaffold teaching in a way that is entirely consistent with the five dimensions of TRU.

The FALs are available from the MAP website, here. To date, there have been about 8,000,000 FAL downloads. The Gates Foundation, which funded the project, also funded professional development projects, known as the Mathematics Design Collaborative (MDC) to support their implementation. An independent evaluation on the impact of MDC on 9 th grade algebra students in Kentucky (Herman, Epstein, Leon, La Torre Matrundola, Reber, & Choi, 2014) describes the results:

Participating teachers were expected to implement between four and six [FALs], meaning that students were engaged only 8-12 days of the school year. (p. 10)

We used recently developed methodology to convert the observed effect size for MDC into a gross indicator of the number of months of learning represented. Relative to typical growth in mathematics from ninth to tenth grade, the effect size for MDC represents 4.6 months of schooling. (p. 9)

That is, the average student learning gains resulting from 8-12 days of instruction using FALs was 4.6 months. A report by Research for Action (2015) indicates why: the vast majority of teachers who used the FALs learned new pedagogical strategies that they implemented in regular instruction. They did a lot less telling, and a lot more asking, listening, and adjusting instruction accordingly.

Next Page: Summative Assessment Tasks and Tests from the Mathematics Assessment Project