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Formative Assessment in Math

About a decade ago I was a Math Teacher on Special Assignment at a large urban school district. The math subject area coordinator took me along with her to a full day PD about formative assessment. It wasn’t a PD I was particularly interested in, but I went. I was blown away by the presenter and his information. I immediately bought his book and it has been a resource I still use to this day when planning my own PD for schools and districts now.

What was this PD?

It was by Dylan William all about his book, Embedded Formative Assessment.

After digging into the reason for and definition of Formative Assessment, the book is divided into 5 types of formative assessment:

1) Clarifying, Sharing, and Understanding Learning Intentions and Success Criteria

2) Eliciting Evidence of Learners’ Achievement

3) Providing Feedback That Moves Learning Forward

4) Activating Students as Instructional Resources for One Another

5) Activating Students as Owners of Their Own Learning

Not only does he define what these categories are and what they look like in classrooms, he has a “practical tips” section in each of the chapters so you can easily implement them in your own classroom! If these categories sound interesting to you, I highly suggest you buy his book!

In this post I’m going to share three of his practical tips from Category 2: Eliciting Evidence of Learners’ Achievement, as it is most closely related to increasing student engagement, and student engagement is what I'm all about!

What is Formative Assessment

First I want to share the definition William gives of formative assessment,

“Encompassing all those activities undertaken by teachers, and/or by their students, which provide information to be used as feedback to modify the teaching and learning activities in which they are engaged.” (William, Embedded Formative Assessment, 2011, p. 37)

More than ever it’s vital that teachers are using feedback every day to inform and modify their teaching. The disrupted learning our students have experienced has made this abundantly clear.

But how?

How do we collect that kind of data from our students without being buried in grading?

Three Formative Assessment tips from Dylan William's Embedded Formative Assessment (2011)

1) Student Engagement

My takeaway here is that he’s really talking about cold calling. Yup, we’re talking popsicle sticks with student names. This is actually a practice I used in my own classroom after reading Doug Lemov’s, Teach Like a Champion, but William writes about it in his book too. If you’re unfamiliar with cold calling, it’s when you create a system that is visibly random to call on students to answer your questions. You can write students' names on popsicle sticks or you can do what I did and have students write their name on an index card during the first week of school, decorate it with drawings about them, then use them every single day to call on students to answer your questions. William has this to say about the importance of student engagement,

“When teachers allow students to choose whether to participate or not - for example, by allowing them to raise their hands to show they have an answer - they are actually making the achievement gap worse, because those who are participating are getting smarter, while those avoiding engagement are forging the opportunities to increase their abilities” (pg 81).

The amount of quick formative data you get from your students while doing cold call is incredible and SO helpful. If you’re calling on students randomly and getting a lot of wrong answers and “IDK”s, use that data to tell you that you need to reteach the concept. If you’re getting all correct answers, it’s time to move on!

2) Alternatives to Questions

In this practical tip William writes, “asking questions may not be the best way to generate good classroom discussions” (pg 84). And offers this math example,

“Asking, ‘Are all squares rectangles?’ is likely to yield a less thoughtful discussion than framing what is, in effect, exactly the same question as a statement: ‘All Squares Are Rectangles.’”

You could add a four corner activity here where you post signs in each classroom corner of: strongly agree, agree, disagree, and strongly disagree. Then when you post a statement like this students can get up and move to the corner that describes their choice! Engagement and movement… win win! This strategy provides such excellent formative data because not only do you know if students are getting finding the correct answer to the statement (if there even is one correct answer), but this will elicit so much amazing conversation and listening to your students thinking is the real formative data here to inform your instruction. Are students thinking deeply about the concept or is it still very surface level? Listening to your students thinking will help inform you if it's time to move on or if you need to hit this topic again.

#3) ABCD Cards

This one might be a little more familiar to us. Students each have cards with ABCD on them (William gives an additional tip that you could do this for far more than just four answer choices and you could also add a true and false card in there!). The teacher asks a question and presents answer choices labeled ABCD. Students then hold up the card (or cards if it’s a select all that apply) to show their answer. I love this a quick formative assessment check. You’re able to see the answers of your whole class quickly, easily, and visually. Something that is vital for teachers! BUT... Just make sure you then USE this data to inform your teaching, don't just move on because that's what in the lesson plan. If students are struggling, adjust your pacing and stay on this topic a bit longer. If students are crushing it, it's time to move on. That's the key to making this a true formative assessment.


William offers SO many more practical tips in his book about how to collect formative assessment data quickly and easily from your students. I hope this quick post has given you some actionable next steps!

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