Does Anyone Really Know What Formative Assessment Is?

Assessment Icon

Karen Wootton, Assessment Coordinator

At NCSM’s 2015 national conference in Boston, I followed the assessment strand for three days. The majority of the sessions in this strand focused on formative assessment. I anticipated learning new and better things about formative assessment, and as I mapped out my three days I was tingly with excitement! (Yes, I am that much of a nerd.)

I gained some insights and some gems, but mostly I came to the realization that many people, even supposed experts, have a limited view of formative assessment. The only thing that was made clear to me was that there is no agreement on what FA is, what it looks like, or what it does. So where does that leave us?

After a particularly frustrating session, I took time to reflect on why I was disappointed, and what knowledge I could glean from this session. I decided that we can outline some general principles for FA, and we can certainly form some opinions, but there are too many variables involved in FA to formulate a clear definition. We cannot create a step-by-step guidebook to FA like we might be able to do with a manual for using a graphing calculator. The variables are just too complex. What variables? The first is the teacher who needs to know what to do with the information the FA provides and act accordingly. Another variable is the teacher’s ability to recognize pertinent information provided by the FA. The teacher must also have a goal before even planning the FA. And even if the teacher has a goal, and knows how to interpret the results, there are many different ways to “act accordingly.” There is no black and white. An even bigger variable is the student. Is the student putting in effort when being formatively assessed? Is the student being mindful during the process? Does the FA accurately represent the student’s knowledge? And, with the results of the FA, what will the student do with that knowledge? Will the student seek clarification? Further connections? Expand her view of the topic?

If no step-by-step manual can ever be made for FA, all we can do is provide a list of generalities to guide us and of which to be mindful. Here is the beginning of my list. I would love to hear thoughts on these, and hear what you would add or subtract from the list.

Formative assessments are understandable. If the directions are too complicated, or the wording unclear, you do not know if you are gathering information about the students’ understanding of the directions or of the math. Try to keep each item simple and clear.

Formative assessments are open enough that there are multiple strategies to completion. We can truly uncover student knowledge and thinking if we
let the student decide the path to a solution, and we do not suggest one. One FA piece can promote further learning if you have the ability to share the different student solutions with all students so they can see the varied approaches and discuss the processes.

Formative assessment does not just provide information to the teacher, but must provide information to the student. Calling a quiz a “formative assessment” is a very limited view of FA. While one can argue that the student will receive information when she receives her graded quiz back, the research on the effect of grades on student learning is clear, and the time between the quiz and the response does not promote learning. (See Ruth Butler’s research on the effect of grades vs. feedback.)

Formative assessment should be more work for the receiver than the giver. I think this is one of the most important characteristics that I picked up at NCSM thanks to assessment guru Dylan Wiliam. Think about a common FA, the Exit Slip. Who spends the most time, the most work, on an Exit Slip? It is the teacher. If we want FA to push student learning forward, how does the Exit Slip accomplish this? An Exit Slip will give the teacher some very limited information, but I believe the same information can be obtained through simpler, more immediate FA. For example, if you want to know if students can determine the x-intercepts of a linear equation, ask them during class as you circulate, in a quick Q&A format. You will know instantly which students know how to
do this, and which do not. More importantly, through your conversation and follow up questions, you will know WHY they might not know this. “What is an x-intercept?”, “What is special about the coordinates of an x-intercept?”, or “What do you think of when you hear the word ‘intercept’?” are all questions that give you more information about a student’s understanding that you will not discover with an Exit Slip.

I know there are more items that should be on this guiding list. What would you add? Do you disagree with any of these? And if so, why? Please share your thoughts with me at, and we will continue the discussion in future newsletters.

You are now leaving

Did you want to leave

I want to leave

No, I want to stay on

Algebra Tiles Blue Icon

Algebra Tiles Session

  • Used throughout CPM middle and high school courses
  • Concrete, geometric representation of algebraic concepts.
  • Two-hour virtual session,
  •  Learn how students build their conceptual understanding of simplifying algebraic expressions
  • Solving equations using these tools.  
  • Determining perimeter,
  • Combining like terms,
  • Comparing expressions,
  • Solving equations
  • Use an area model to multiply polynomials,
  • Factor quadratics and other polynomials, and
  • Complete the square.
  • Support the transition from a concrete (manipulative) representation to an abstract model of mathematics..

Foundations for Implementation

This professional learning is designed for teachers as they begin their implementation of CPM. This series contains multiple components and is grounded in multiple active experiences delivered over the first year. This learning experience will encourage teachers to adjust their instructional practices, expand their content knowledge, and challenge their beliefs about teaching and learning. Teachers and leaders will gain first-hand experience with CPM with emphasis on what they will be teaching. Throughout this series educators will experience the mathematics, consider instructional practices, and learn about the classroom environment necessary for a successful implementation of CPM curriculum resources.

Page 2 of the Professional Learning Progression (PDF) describes all of the components of this learning event and the additional support available. Teachers new to a course, but have previously attended Foundations for Implementation, can choose to engage in the course Content Modules in the Professional Learning Portal rather than attending the entire series of learning events again.

Edit Content

Building on Instructional Practice Series

The Building on Instructional Practice Series consists of three different events – Building on Discourse, Building on Assessment, Building on Equity – that are designed for teachers with a minimum of one year of experience teaching with CPM instructional materials and who have completed the Foundations for Implementation Series.

Building on Equity

In Building on Equity, participants will learn how to include equitable practices in their classroom and support traditionally underserved students in becoming leaders of their own learning. Essential questions include: How do I shift dependent learners into independent learners? How does my own math identity and cultural background impact my classroom? The focus of day one is equitable classroom culture. Participants will reflect on how their math identity and mindsets impact student learning. They will begin working on a plan for Chapter 1 that creates an equitable classroom culture. The focus of day two and three is implementing equitable tasks. Participants will develop their use of the 5 Practices for Orchestrating Meaningful Mathematical Discussions and curate strategies for supporting all students in becoming leaders of their own learning. Participants will use an equity lens to reflect on and revise their Chapter 1 lesson plans.

Building on Assessment

In Building on Assessment, participants will apply assessment research and develop methods to provide feedback to students and inform equitable assessment decisions. On day one, participants will align assessment practices with learning progressions and the principle of mastery over time as well as write assessment items. During day two, participants will develop rubrics, explore alternate types of assessment, and plan for implementation that supports student ownership. On the third day, participants will develop strategies to monitor progress and provide evidence of proficiency with identified mathematics content and practices. Participants will develop assessment action plans that will encourage continued collaboration within their learning community.

Building on Discourse

In Building on Discourse, participants will improve their ability to facilitate meaningful mathematical discourse. This learning experience will encourage participants to adjust their instructional practices in the areas of sharing math authority, developing independent learners, and the creation of equitable classroom environments. Participants will plan for student learning by using teaching practices such as posing purposeful questioning, supporting productive struggle, and facilitating meaningful mathematical discourse. In doing so, participants learn to support students collaboratively engaged with rich tasks with all elements of the Effective Mathematics Teaching Practices incorporated through intentional and reflective planning.