Although I loved the first day of school, September was always a difficult month for me as a teacher. It’s a month of establishing classroom norms–the rules and expectations of your classroom. What it means to have a conversation about math in your class may be different than what it means in another class.
As you begin to negotiate the norms in your class regarding classroom conversations, I wanted to share some insight from the research about how to make norms you may already be familiar with even stronger.
Two researchers (Kazemi and Stipek, 2001) observed four classrooms that encouraged classroom conversation about math. However, the quality of the math talk in the classes differed. Some classes had norms that encouraged a “high press” for conceptual thinking, while others did not.
Here are four things they observed about how to promote conceptual thinking:
- Explanations: While both types of classes asked students to explain their work, high-press classrooms set the norm that explanations needed to be mathematically based. Repeating a rule or citing a textbook or prior teacher did not count as an explanation.
- Multiple Strategies: While both types of classes, encouraged students sharing strategies for solving a problem, high-press classrooms focused on what was mathematically similar and different between the strategies.
- Student Mistakes: While both types of classes created a culture where it was ok to make mistakes, high-press classroom used mistakes as an opportunity for students to try out other strategies or explore contradictions. The teacher did not validate or invalidate the solutions, but presented both and then asked to students to determine which was correct and why.
- Collaboration: While both types of classes encouraged students working together, high-press classes focused on both individual accountability (every student must be able to explain the group’s solutions) and coming to agreement as a group through mathematical argument (as opposed to voting on which they liked best).
As I mentioned previously, change takes time. It will take a while for students to become comfortable talking about math in these ways.
What do you think? What norms do you set for classroom conversations?
Read more here: Kazemi, E., & Stipek, D. (2001). Promoting conceptual thinking in four upper-elementary mathematics classrooms. The Elementary School Journal, 59-80.
It takes time as well as appropriate tasks to effect that change. I’ve watched students begin a course asking conceptual questions, but … for instance, just when students are starting to grasp that adding two negative numbers gives a bigger (absolute-value-wise) negative number, we toss in subtracting integers and then while they’re still reeling over that we toss in times and division, due this Wednesday. Well, now they think there are 45 rules, none of which have anything to do with the other, and they’re trying to survive. Oh, and make sure that we toss in variables that they’ve only just been exposed to into the mix.
Well said. Students need to truly understand the underlying concept before moving on to something new. Tasks that help students in making the connections between different ideas helps so that math doesn’t become a long list of unrelated procedures a student needs to memorize.