Developing Students’ Mathematical Mindsets and Academic Conversations, by Stacy Dustman and Kim Meyer

We have been using CGI for the past 7 years in teaching third, fourth and fifth graders. Our school is a Title 1 school where 46% of the students are classified as English Language Learners. Even though we have been using CGI for 7 years, when we begin working with a new group of children, we still wonder, “How can we get our new students talking about math?” and “Will this group be able to have conversations as strong as last year’s group?” We’ve always been pleasantly surprised by how our new group comes together and grows in their ability to have academic conversations.  

During the first two weeks of school, we focus on team building activities, learning how to have academic conversations and developing the mindset that everybody has the ability to do math. The activities that we do in the first week of school help students build confidence when solving problems. Although we do these activities at the beginning of the school year, they could be used at any time of the year.

On the first day of school, we pose a team building challenge to the class: cup stacking.  Students must create the tower shown using string and a rubber band. The students are only allowed to touch the string.

The students have to figure out how to accomplish this task without direction from us, forcing them into conversation with each other. This cup stacking task supports students to feel comfortable talking with each other without the pressure of understanding all the content.  While the students engage in this conversation, we assess how well each student is able to discuss ideas with others and we can plan support for students who struggle. 

After the students complete the activity, we have a class discussion about what makes a great teammate and what attributes are needed for a great intellectual discussion. Here is a poster where we recorded what the students said.

We also discuss what a good listener looks and sounds like, and what a good speaker sounds like during a conversation. We explicitly discuss how to agree and disagree with someone, or what to say when you don’t understand something. Posted in our rooms are sentence stems for students to refer to for discussions (I agree with ___ because ____., I’m confused about _____.) To help us see when someone is engaged, we also have the students show the sign language sign for the same or different. 

We continue to teach about academic conversations in our next lesson, which is to develop the mindset that everyone has the ability to do math. We start with the prompt, “Some people are math people and some people are not,” and ask students whether or not they agree with this statement. Students throw a ball of yarn around the room as they share their responses. Only the person holding the ball of yarn can talk and the person holding the ball of yarn is responsible for throwing the ball to the next person. We don’t call on students during this activity. The students are responsible for including everyone in the conversation. After the discussion, we look at the trail of yarn to show how a conversation travels across the room and from person to person. We directly explore the fact that the conversation isn’t only between the teacher and one student. During this debrief we also talk about things we might need to add to our anchor chart for what makes an intellectual discussion great. 

After this discussion, we talk about how all people are math people and everyone has the ability to do math. We continue to work on supporting this mindset throughout the school year by:

• Having students generate their own strategies for solving math problems,

• Not demonstrating strategies for solving problems,

• Providing problems with multiple entry points that all of our students solve, 

• Accepting multiple strategies for solving problems, and 

• Engaging student discussions to explore their mathematical ideas.

 We pose our first math problem in the second week of school. For example, in third grade our first problem this year was a base 10 problem, 

Mrs. Meyer has __ bags of books with 10 books in each bag.  How many books does Mrs. Meyer have?  (5 bags, 8 bags, 10 bags of 12 bags)

In fourth grade, our first problem was a multiplicative comparison problem 

An iguana is ___ times as long as a lizard. A lizard is ___ inches long. How long is an iguana?  (5, 2)         (2, 10)  (4, 5)    (5, 6)).

We first ask students what they know about the topic. Then we read the problem out loud so that all students have access to it. When needed, we translate this problem into students’ preferred language. Before working the problem, students have think-tank time where they sit and make sense of the problem alone for a minute or two. Students then discuss with their table groups what they know and what they don’t know about the problem. We then ask our students to solve the problem in any way that makes sense to them. 

While the students work, we circulate around the room looking for strategies used, misconceptions students may have, or enrichment opportunities. There are always a few students who aren’t able to correctly solve this first problem.  We resist the urge to lead these students through a strategy for this problem because right now, it’s more important for them to learn that they can figure out how to solve problems themselves than it is for them to get the right answer. We tell these students that they will have a chance to see how some of their classmates solved the problem and we will do a similar second problem later.

After the students have had about 20-30 minutes to work the problem, we collect the papers and have the students come to the carpet for a discussion. Students are assigned a turn and talk partner for this discussion. Each student receives a 10 x 12 inch white board and marker for use during the whole class discussion.  These boards keep students engaged for communication during turn and talk time, since sometimes it easier to represent an idea than to state it. The small white boards also allow us to assess students’ understanding during the discussion. We can ask a question, ask students to provide an answer on their white boards and quickly see their answers to the question. Even though we work with third – fifth graders, we still need to provide some ground rules for the white boards such as the board and markers are to be used as math tools, and the lids stay on the markers unless it’s turn and talk time or we ask them to write something on their board.

The discussion begins with one student’s strategy posted on the board for students to analyze. We typically don’t name the author of the strategy. This encourages students to understand that the purpose of the whole group conversation is to discuss the strategy, rather than have the person who generated the strategy explain it to the group. After students have had a chance to analyze the posted strategy, students are asked to turn and talk with their partner and explain what they think this person did to solve the problem. Doing turn and talks throughout the discussion allows for students to both feel confident and to participate in a discussion without the pressure of the whole class looking at them. After turning and talking, we bring the whole class back together to discuss the strategy. 

Since we spent the first week of school focusing on team building activities, learning how to have academic conversations and developing the mindset that everybody has the ability to do math students have better conversations and feel more comfortable sharing their ideas without fear of being judged or made fun of by a classmate. Students understand that it is okay to make mistakes and that mistakes are valued throughout the lessons. Our students’ abilities continue to grow as they work on team building and have academic conversations through the school year.

Edited by Hallei Halter and Linda Levi