Anticipating students’ responses involves developing considered expectations about how students might mathematically interpret a problem, the array of strategies—both correct and incorrect— that they might use to tackle it, and how those strategies and interpretations might relate to the mathematical concepts, representations, procedures, and practices that the teacher would like his or her students to learn.
Smith & Stein 2018, p. 10
Anticipating student thinking is a vital part of planning effective instruction. Anticipating involves:
- envisioning likely student strategies.
- planning questions and responses to these strategies.
Before you teach
The best way to anticipate likely student thinking is in collaboration with colleagues. Working with others broadens the scope of likely solution strategies beyond those that a single teacher could come up with. Actually do the task with your colleagues and, as you do, consider the following:
- What are some common misconceptions which may arise during the task?
- How effective or ineffective are the different strategies that you anticipate students will use?
- How might students mathematically represent the strategies that they use?
- What questions or prompts should we pose in response to the different strategies so that students are moving closer to the mathematical goal of the lesson?
While you are teaching
Anticipating students’ strategies prepares you to actively observe and interact with students while they are working on the task. As you observe students, focus your attention on what mathematics you notice students actually using. Converse with students to assess what mathematics they do or don’t understand, and then use the prepared questions and prompts to advance students’ thinking towards the mathematical goal of the lesson. Having prepared questions and responses provides you with more time to think of purposeful responses when unanticipated student approaches arise.
Taking the time to anticipate student thinking before you teach gives you a clearer sense of the mathematics that you need to make visible to your students. Understanding what students are likely to do gives you greater capacity to help them to make connections between different solutions they might see as being disconnected, as well as enabling you to steer their mathematical thinking towards the learning goal of the lesson.
Have a go
If you can, complete this activity with at least one other colleague.
Select a task you will be using with your students. Work on the task individually and compare your solutions. Discuss with your colleagues:
- What strategies might students use to solve the task?
- How might they represent the strategies that they use?
- Are there possible misconceptions that may arise?
Plan questions and prompts in response to the different strategies that you have anticipated.
Then, teach the task!
Reflect: How did anticipating student thinking support you in your role as the teacher?
References
Smith, M. S. & Stein, M.K. (2018). 5 Practices for Orchestrating Productive Mathematics Discussions. National Council of Teachers of Mathematics.