#18. Marking student ideas is a means of instantiating important mathematical ideas

Posted on January 30th, 2015

From the Institute for Learning, this is Laurie Speranzo.

In earlier podcasts, Victoria Bill talked about the need for Accountable Talk® discussions in all mathematics classrooms and about the effectiveness of revoicing as a means of inserting important mathematical ideas into classroom discussions. She also discussed how important listening is for teachers as well as students, if we want to develop academically productive talk in our math classrooms.

During the whole class discussion, many ideas will emerge. So, how do we ensure that the important mathematical ideas discussed are the ones with which our students walk away? In order to instantiate the math we want students to learn, we need to mark key student contributions.

"Marking" is a teacher move used to draw attention to and explicitly talk about an idea. So what can this sound like? In a 6th grade classroom, students have been working on a ratio task. There is a picture of 6 boys and 5 girls on the soccer team. The students have been arguing over the ratio that represents the picture. One group claims that the ratio is 6:5. One group states that the ratio is 6:11. One student says, "Wait, stop! Aren't both groups' responses correct because there are 6 boys and 5 girls which is 11 children altogether? We just have to say what the ratio means."

The teacher acknowledges the student's response by saying, "That is a really important point. Did everyone hear what she just said? When we write ratios, there are usually several ratios we can write. But we need to say what the numbers in the ratio represent. Here 6 to 5 represents 6 boys to 5 girls and 6 to 11 represents 6 boys to 11 team members." Acknowledging the comment and repeating the idea marks the importance of the mathematics.

It also clarifies what we want students to hear and understand about the math being investigated. It also validates student contributions.

Here's a note of caution though—marking should not be done too soon or too often. Why is that? What happens when we mark too soon? If we mark a mathematical idea early in the discussion, it may indicate that the discussion can stop, that the mathematical take-away has been stated so therefore learning is done for the day. We definitely don't want to shut down student thinking before kids have had enough time to delve into exploring the math. For example, it might be too soon to mark when the teacher hears students struggling with the big idea and she wants to let that go on a little longer to see if students can get there themselves. Or it might be too soon when only one group has shared and other voices have not been heard to cause students to think deeply about several ways to represent the math.

What happens when we start marking too often? Think about what it would sound like to children if a teacher says "that's important because x, y, or z" several times throughout the course of a discussion? How would students hold onto so many ideas? Also, it could transfer some of the intellectual heavy lifting from the students back to the teachers.

It's crucial that the key ideas marked in a discussion are the ones that are clear statements of the math content and practice objectives for the discussion. We want to be marking both the math content and the use of the Common Core Mathematical Practices students could make use of in the lesson. When planning, think ahead about the kinds of statements you want to hear from students. Those are the ones you want to mark so that marking can be done effectively!

Laurie Speranzo

Laurie Speranzo is a Fellow of the Institute for Learning's mathematics Disciplinary Literacy Team.

More information on Laurie Speranzo.