Formative assessment data is one of those elusive educational terms we say a lot but can mean different things for different educators. We often think of formative assessment data to mean a paper pencil exit ticket or check for understanding at the end of a lesson. Yet, formative assessment data can be found everywhere in the classroom, we just need to know where to look.
What is formative assessment?
The formative assessment guru, Dylan Wiliam, has a few things to say in his recent blog that highlight the meaning of formative assessment in the classroom.
“To teach effectively, the teacher needs to find out what the learner knows and teach accordingly.”
“Assessment is the bridge between teaching and learning. It is only by assessing that we can find out what our students learned from our teaching.”
“There is no point in doing formative assessment if you are not going to use the information to improve your teaching.”
Often, I hear from teachers that they have so much content ‘to get through’. Yet, teaching is not about covering the standards; it is about students learning the standards. Formative assessment data can tell you exactly what students have learned and where they are in their journey towards mastery of the standards.
Formative Assessment Data in a Lesson
Let’s use an example of a recent 6th grade classroom I was teaching using a teacher table with a station rotation. The standard the students were learning was:
Solve real-world problems with positive fractions and decimals by using one or two operations. (E)
I began the lesson with a Thinking Task in vertical spaces (Lijedahl, 2020), in random group of 3 students.
As the students worked at their vertical spaces I walked around the room gathering formative assessment data in my Success Criteria Student Tracker. I noticed if students were working collaboratively in their groups and what type of strategies they were using. Several of the groups were multiplying 2 times 1 ½ by incorrectly using ‘keep, change, flip’. I noticed many students knew to multiply by 2 but were working to recall the wrong strategy.
I marked those students as ‘approaching’ on my tracker. I had 2 groups of students who drew a picture of 1 ½ cups of flour twice to determine there were 3 cups of flour needed. I asked one of the ‘drawing’ groups to share their thinking. I then asked one of the groups who was trying to multiply incorrectly to share their thinking. We then moved on to stations, but I had collected some data.
At the teacher table, the students were asked to engage in the following task on their whiteboards. I told the story of how my granddaughter and I were building a birdhouse in our garage, and we needed to cut the sides of the birdhouse to ⅙ yards from the piece of wood I had that was ¾ yards in length. The following conversation ensued:
Aman: “I think we should multiply because we have been doing multiplication in class a lot.”
T: “Claire, do you agree or disagree with Aman?”
Claire: “ I disagree. I think we should add ⅙ and ¾ together.”
T: “I would like all of you to sketch the piece of wood I have in my garage that is ¾ yards. Let’s see what that might look like.”
Students drew a variety of rectangular pieces of wood on their boards.
T: “Sean, can you hold up your board and show us your drawing?”
T: “Aman, what do you see in Sean’s drawing?”
Aman: “He drew a rectangle and labeled the bottom with ¾. Now he needs to draw 6 sections in his rectangle because that is how many pieces of wood you can cut.”
T: “Claire, what do you think about what Aman said? You have sectioned your piece of wood, but you don’t have six sections; you only drew one section.”
Claire: “I don’t know how many ⅙ are in ¾, so I only drew one to start.”
T: “Let’s use these fraction bars to show our piece of wood and measure how many ⅙ are in ¾.
The students used physical fraction bars while I used polypad to provide a visual model. Below is their representation.
T: “Sean, how many ⅙ do you think fits into ¾?”
Sean: “It looks like 4 ½, but I don’t know for sure.”
T: “Let’s check Sean’s guess by using an equation. Aman, what equation could I write for this problem?”
Aman: “I think you would divide ¾ by ⅙, and you could use keep, change, flip for that.”
T: “Sean and Claire, do you agree or disagree and why?”
Claire: “I multiplied ¾ times 6/1 and I got 18/4 which is the same as 4 ½. I agree with Aman.
T: “What would happen if my blueprints for the birdhouse asked for the sides to be ⅕ instead? How would I do that problem?”
The formative data I collected on the three students was valuable. Their conversation and reasoning led me to understand that they misunderstood when to use the short-cut for fraction division, additionally, they weren’t sure when to divide or multiply in a situation. However, by the end of the 12-minute teacher table, using fraction bars and a visual model, students better understood the operation and how to model the problem in 3 different ways. I placed each of these 3 students closer to proficient but not quite there.
The students rotated to teacher table throughout the lesson and most students used keep, change, flip for almost every problem I asked them to solve. The teacher had indicated this as a review lesson for the students, yet I found that most students were not at proficiency. Through using multiple representations, the students were better able to gain a conceptual understanding of the standard.
What do I do with the data?
The point of collecting formative assessment data is to use the data to make instructional decisions. My next steps would be to circle back to this standard several more times using a combination of fraction bars, pictures, and equations to ensure students understood the math. At the end of this lesson, despite the students having been taught the content, they did not have it YET. Formative assessment data is gathered by listening to student conversations, not jumping in to instruct, but asking questions and letting students guide the instruction through their responses. When we jump in with a few examples we are going to teach through, we can’t assess where students are in their journey toward mastery.
Key steps in formative assessment.
- Do less talking and more listening.
- Use the 5 Representations to ensure students have an understanding of the math.
- The ‘answer’ does not tell you all you need to know about a student’s level of mastery. Don’t be fooled into thinking a student ‘has it’ just because they can get the answer.
- Avoid mnemonic devices that teach students to mimic instead of think through a task.
- Keep digging into how a student is thinking about the math through quality questions and prompts to elicit their thinking.
Formative assessment begins the minute the bell rings and never ends. We want to find meaningful ways to collect that formative data to use the information for our next teacher move