The Collaborative in Action

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K-5 Orchestrating Math Discussions Series (2 of 5)

3 Steps for ANTICIPATING Student Thinking

Post 2 of 5 in the Series ‘Orchestrating Math Discussions’

This blog series is inspired by the book 5 Practices for Orchestrating Productive Mathematics Discussions by Margaret S. Smith and Mary Kay Stein as well as our own classroom experiences.


In our previous post, we shared that an effective math lesson begins by intentionally selecting a task to meet the learning goal. Once a task is selected, our next step is to anticipate approaches our students might use to solve it. This happens during lesson planning, before using the task with students.

Anticipating student thinking prepares us to monitor students as they grapple with a task. Anticipating helps us predict possible strategies, mistakes, misconceptions, and solutions. As we anticipate how students might approach a task, we also anticipate questions to pose in response to their strategies. Some of these questions help us understand students’ current thinking and others elicit deeper thinking about the task and mathematics underlying the task. Anticipating strategies and questions prepares us to advance students’ thinking toward the learning goal rather than focusing only on a correct solution.

 

Steps We Can Take When Anticipating

  1. Solve the task using our own strategy. As adults, we recognize our strategies might be more sophisticated than our students’. However, taking the time to solve tasks ourselves helps us think through the mathematics.
  1. Anticipate strategies students might use to solve the task and mistakes they might make. We can use the problem solving strategies described in the book Children’s Mathematics Cognitively Guided Instruction to anticipate students strategies. The authors found that students typically solve problems using three types of strategies:
    • Direct Modeling: The physical act of joining, separating, grouping, or matching sets (coupled with counting from 1)
    • Counting Strategies: Includes counting on, counting down, and skip counting
    • Fact Strategies: Using known facts or deriving facts (using known facts to find unknown facts).

As we anticipate strategies students might use to solve a math task, we also anticipate possible mistakes and misconceptions. This prepares us to provide appropriate in-the-moment support as students approach the task. Common mistakes include misinterpreting the task, using the wrong operation, and making calculation errors. Misconceptions often involve incorrect assumptions about numbers (e.g., the bigger the denominator, the bigger the fraction) and overgeneralizing rules (e.g., multiplication always makes bigger).

  1. Generate questions to assess and advance student thinking. By anticipating possible strategies, mistakes, and misconceptions, we recognize students approach math tasks in a variety of ways depending on their unique perspectives and backgrounds. The questions we pose in response to students’ approaches are the tools we use to differentiate instruction, offer support, and advance students toward our learning goals. The questions we pose allow each and every student to engage with the task. There are two types of questions we anticipate before facilitating a task: assessing questions and advancing questions.

Let’s See These Steps In Action:

Think back to Ms. Reames’ jumping contest task from the first post in this series.

After writing this task for her second graders, Ms. Reames took a moment to solve it herself. Then, she anticipated her students’ strategies, possible mistakes/misconceptions, and the questions she might pose in response to these approaches. Ms. Reames compiled her ideas in this anticipating chart:

Now, Ms. Reames is ready for her students to solve the jumping task! In our next post, we will share ways Ms. Reames uses her anticipating chart to monitor students as they work.

In the meantime, here are some Tools4NCTeachers lessons that include anticipated strategies, possible misconceptions, and questions to pose.