Analyzing Student Thinking

bifocalsDo you use bifocals when teaching? No, not the kind that perch on your nose. The use of a "bifocal perspective," as termed by mathematics educator Deborah Ball (1993), is where the teacher is "perceiving the mathematics through the mind of the learner while perceiving the mind of the learner through the mathematics" (p. 159).

This thinking is important when designing and implementing collaborative tasks for our students. During these activities, the role of the teacher is to get the students to do most of the "heavy thinking." If you can "think like a student," you will be better able to guide them through the task through asking good questions and providing cues and prompts to move them forward, rather than simply telling them what you would do.

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In the clip below, you will have the opportunity to listen to a group of students as they work on the "Hikers Beware" task. Use your "bifocal perspective" and consider what the students' actions and statements tell you about their mathematical thinking.


What did you observe? Notice how each pair was conscious of what the other was doing, while working on their own. The girls calculated the rate of change, while the two boys discussed the method for doing so. Finally, the boys figured out the amount of water remaining at the end of each day.

Classroom Clip Reflection:

  • What did you notice about student thinking as they engaged in this problem?
  • What are the implications for your own work with students?