Formative Assessment


Formative Assessment is the Essence of Teaching

There are many different definitions of formative assessment currently in the field of education. Research has shown that student learning improves significantly when students are provided frequent feedback on their progress and that student learning improves when teachers use assessment to inform their instruction. Throughout a lesson, teachers are questioning, observing, and listening to students and adjusting teaching as needed to accommodate and enhance student learning. Our work is grounded in the research done by Black and Wiliam around the five strategies:

  • Clarifying, sharing, and understanding learning intentions;
  • Engineering effective discussions, tasks, and activities that elicit evidence of learning;
  • Providing feedback that moves learners forward;
  • Activating students as learning resources for one another; and
  • Activating students as owners of their own learning.

Formative Assessment is Integral for Planning, Teaching, and Reflecting in CMP

This framework highlights how formative assessment is ongoing in Connected Mathematics during planning, teaching, and reflecting. This view of formative assessment extends beyond traditional paper and pencil formative tasks, such as check-ins, warm-ups, or exit cards, in that it also includes on-going assessment as part of the enactment of a lesson. Since planning, teaching, and reflecting in CMP classrooms attend to the CMP instructional model of teaching, the framework is centered on the Launch – Explore – Summarize phases.

From this perspective, teachers engage in three components of formative assessment: (a) anticipate student strategies and difficulties, (b) gather and analyze evidence of student learning, and (c) adapt their teaching to meet students’ needs and to help students develop their own reflective habits of mind. As indicated in the figure below, these three components of formative assessment are an integral part of the each phase of the instructional model of Launch – Explore – Summarize.

Launch, Explore, Summarize table


The following resources for formative assessment were developed to help mathematics teachers and instructional leaders make sense of formative assessment as an ongoing process occurring throughout CMP lessons.

For more information about current research on formative assessment carried out by the CMP staff, visit the Formative Assessment Research Project.

A Detailed Framework for Formative Assessment identifies and elaborates on the embedded practice of formative assessment that occurs daily in CMP classrooms. It is organized around two dimensions. The first dimension captures the three components of formative assessment: anticipating student strategies and difficulties, gathering and analyzing evidence, and adapting instruction. The second dimension focuses on the three instructional phases of teaching: Launch – Explore – Summarize.

Example Analyses of Classroom Videos are resource sheets that utilize the framework to unpack instances of formative assessment from CMP classroom videos.

A Template for Formative Assessment is a framework template for use in professional development or planning settings. In these settings, mathematics teachers or instructional leaders can use this resource to identify instances of formative assessment in the classroom videos or to plan for using formative assessment in classrooms.


The formative assessment resources are valuable for individual teachers and for creating and fostering conversations around assessment during planning, teaching and reflecting. The following questions provide teachers with prompts for using these resources. The first set of questions can be used prior to exploring the CMP Formative Assessment Framework. The second set of questions can be used during planning time, in a collaborative meeting, or in professional development activities to consider how, when, and for what purpose formative assessment is used.

Gathering Information on Formative Assessment Practices

  • How do I currently utilize formative assessment practices and strategies in the Launch? In the Explore? And in the Summarize?
  • What kinds of information do I use to anticipate students’ strategies and difficulties for each mathematical problem?

Relating Formative Assessment to Effective Classroom Environments

  • What do my students know? What are my students able to do? What is the evidence? How does this shape what I do in the moment or my plans for tomorrow?
  • How do I help students to engage in the mathematical problems, and how are the tasks effective in helping them learn mathematics?
  • How do I use the problems to stimulate the richness of discussion that helps students to develop mathematical power?
  • Are all my students participating in class discussions?
  • How does the classroom discourse promote learner independence? Curiosity? Mathematical thinking? Confidence? Disposition to do mathematics?
  • What can I do to ensure that the learning environment suits every student and supports his or her mathematical development?

[1] Black, P., & Wiliam, D. (1998a). Assessment and classroom learning. Assessment in Education: Principles, Policy & Practice, 5(1), 7–74.

Black, P., & Wiliam, D. (1998b). Inside the black box: Raising standards through classroom assessment. The Phi Delta Kappan, 80(2), 139–148.

Creighton, S. J., Tobey, C.R., Karnowski, E., & Fagan, E.R. (2015). Bringing math students into the formative assessment equation: Tools and strategies for the middle grades. Corwin Press.

Hattie, J. (2012) Visible learning for teachers: Maximizing impact on learning. Routledge.

Hattie, J., (2013). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Routledge.

Leahy, S., Lyon, C., Thompson, M., & Wiliam, D. (2005). Classroom assessment: Minute by minute, day by day. Educational Leadership, 63(3), 19–24.

National Council of Supervisors of Mathematics & Association of Mathematics Teacher Educators (2014). Position: Improving Student Achievement in Mathematics Through Formative Assessment in Instruction. Retrieved from

Ritchhart, R., Church, M., & Morrison, K. (2011). Making thinking visible: How to promote engagement, understanding, and independence for all learners. John Wiley & Sons.

[2] Wiliam, D. (2011). Embedded formative assessment. Solution Tree Press.