Formative Assessment Tool Kit

Assessment Icon

Karen Wootton, Director of Assessment

Last May I wrote an article asking the question “Does Anyone Really Know What Formative Assessment Is?” My thoughts stemmed from my frustration at the NCSM National Conference, following the formative assessment thread of sessions, and hearing inconsistent messages. I concluded that, while I may not be able to define formative assessment, I could at the very least, describe it. I came up with four descriptors.

  • Formative assessments are understandable.
  • Formative assessments are are open enough that there are multiple strategies to completion.
  • Formative assessments does not just provide information to the teacher, but must provide information to the student.
  • Formative assessments should be more work for the receiver than the giver.

See the May 2015 newsletter for more details.

This July, 18 teachers met in Las Vegas to develop formative assessment lessons. During the morning of the first day, we discussed whether we could create a suitable definition or a better description of formative assessment. After a great deal of debate, someone had the clever idea of developing a Formative Assessment Tool Kit. This FATK could provide options for teachers on how to formatively assess students and the advantages of each type.

The FATK is still being developed, and we are hoping to share it some time this school year. Here is a sampling of what you will find in the FATK.

Rethink your formative assessment. Forget that the term “assessment” is in the title of this teaching practice. There is nothing to grade in a formative assessment, and students should not be receiving a score. Formative assessment is the practice of learning what your students know and acting upon it in the most immediate way possible. When thinking about formative assessment in this manner, you might realize that the best way to do this is to ask the student a question and respond. You will quickly know what your student knows, and you and the student can act upon it immediately. Did the student clearly answer your question? Ask the natural follow up “Why?” to allow the student an opportunity to clarify or extend his thinking. Did the student stutter and falter? After a suitable wait time, ask the student a similar, simpler question. With each question, the student is also learning what she knows and on what she is unclear. You are not just finding out what your students know but also to what depth they know it. Having a conversation with your students is the best, most efficient way to formatively assess them. Additionally, this promotes the mathematical discourse we expect students to be having daily.

Try using a formative assessment that does not involve you. As the teacher in the classroom, we all know you are the most knowledgeable person in the room on the subject of the course. (At least we hope so!) But that does not mean that you are the only person who can contribute to the formative assessment process. Before students submit a problem for grading, have them turn to a partner to do a peer edit. Students may or may not be successful at solving the problem, but when they are looking at another student’s solution critically, they will be thinking things like “Hey, I didn’t do that,” or “Oh, she forgot the negative sign. I hate it when I do that,” or other thoughts that are engaging the student’s brain. In the toolkit, we will provide other examples that use the student to provide the necessary feedback to his classmates.

Understand that formative assessment is a process, not a product. Step away from the idea that the test you give the students at the end of a chapter is formative because they “learn what they got wrong.” First, the information the student is gaining is probably not very immediate. Second, studies have shown that when students receive a score, they do not look at anything else. When a score is on the paper, students do not read feedback, they do not try to fix their mistakes, but learning stops. Also, the formative assessment process is on going. There is no end, and you should never be thinking “It has been awhile so I think I will do some formative assessment today.” If you are interacting with your students, questioning and encouraging rich mathematical discourse, this is all formative assessment. This process is far more important to learning and understanding than an Exit Slip.

If you would like to contribute your ideas for consideration for the FATK, please email them to With teachers contributions we can make this a great resource.

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.