By Renee’ Yates

“The available research evidence suggests that considerable enhancements in student achievement are possible when teachers use assessment, minute-by-minute and day-by-day, to adjust their instructional to meet their students’ learning needs.”

 – Dylan Wiliam, “Five ‘Key Strategies’ for Effective Formative Assessment,” National Council of Teachers of Mathematics, 2007

Renee’ Yates

Renee’ Yates

The Mathematics Design Collaborative (MDC) provides teachers with an instructional framework and processes to facilitate true formative assessment within and between units of study. It is a collaboration between the University of California, Berkeley, and the Shell Center team at the University of Nottingham.

The instructional processes are developed around the five key strategies for effective formative assessment. These strategies are from a 2007 research brief written by Dylan
Wiliam and published by the National Council of Teachers of Mathematics.

Wiliam lists the five key strategies as:

  • Clarifying and sharing learning intentions and criteria for success
  • Engineering effective discussion, questions, activities and tasks that elicit evidence of learning
  • Providing feedback that moves student learning forward
  • Activating students as owners of their own learning
  • Activating students as instructional resources for one another

One of the tools used with the Mathematics Design Collaborative are formative assessment lessons (FALs) – also known as classroom challenges. These lessons are well-engineered to provide teachers with opportunities to formatively assess students’ understandings of key mathematical ideas and applications. The concept development and problem-solving lessons are congruent with the Kentucky Academic Standards for Mathematics.

The FALs are designed to engage students in a productive struggle that builds fluency and procedural skills, while deepening mathematical reasoning and understanding. The lessons challenge students to put concepts into practice in meaningful ways.

The concept-focused lessons are intended to be implemented two-thirds through a unit of study to formatively assess how well students are able to apply the skills being taught to unique situations and then to make decisions for further instruction.


The structure of the lesson design calls for teachers to administer a pre-assessment task a day or so before implementing the lesson. Then teachers analyze the student work in a professional learning community (PLC) and create feedback questions for students based on misconceptions found within the student work.

After the pre-assessment task, students are grouped homogeneously with partners based on common misconceptions and understandings. When intentionally grouped with partners based on similar misconceptions, students take more responsibility for their own work, focus on understanding math concepts and are more likely to engage equally in a productive struggle with rich, challenging tasks.

In the lesson portion, the teacher facilitates a whole class introduction. Students participate in a collaborative activity and the teacher then concludes the lesson with a whole class debrief. Finally, the teacher administers the post-assessment task and again works with a professional learning community to compare pre- and post-assessment student work.

Through this collaborative experience with the PLC, teachers notice student growth and areas of misconception to inform teaching the rest of the unit before a summative assessment. The conversation also may influence teaching strategies when instructing the entire unit next year.

The teacher’s role is to prompt students to reflect and to reason through their ideas. Student questioning is central to support student thinking, depth of knowledge and student growth. The teacher’s role is not to provide answers and solutions, but to provide high-quality questions that encourage students to think through problems themselves.

Teachers across Kentucky have been implementing the Math Design Collaborative processes. Here’s what some Kentucky teachers say about the process.

“When students are intentionally grouped based on pre-assessment data, I am able to anticipate common misconceptions and tailor specific feedback for each group. Students are able to work through a productive struggle process that lends itself to success at their time and with their strategies.

“Through the MDC process, I have watched struggling students approach challenging tasks with reluctance and still achieve success. All students may not complete the assignment, but the way MDC works, quality of work and conversation is valued over quantity completed.” 

Jessica Willis, grade 6, Madison County

“Math Design Collaborative has had a profound impact on my students. It has made me, as the teacher, take a step back from doing all the talking and giving the students more of an opportunity to communicate/interact with each other.  

“The students are much more proficient at asking each other meaningful questions without the teacher being the leader. When students are appropriately grouped in small groups of twos or threes, I am hearing many more brilliant mathematical conversations and vocabulary. The students are now able to explain their thinking to each other as why they came up with an answer, whereas before MDC they were reluctant to do so. “

– Keith Gabbard, grade 1, Owsley County

In classrooms that implement the MDC process with fidelity, students are more likely to:

  • Engage in more critical thinking
  • Understand mathematics conceptually
  • Collaborate actively and problem solve
  • Engage in productive struggle with mathematics
  • Apply flexible application of mathematics knowledge

For more information about Mathematics Design Collaborative, email Renee’ Yates.

Renee’ Yates, a National Board certified teacher, provides MDC statewide support for the Kentucky Department of Education.


Resources …

Elementary Formative Assessment Lessons 

A Brief Guide for Teachers and Administrators 

Shell Center for Mathematical Education