Plan Ahead for Effective Formative Feedback in Math Class

What if we used the Building Thinking Classrooms technique to encourage our students to keep thinking rather than stop thinking, as we prepare to provide feedback on class assignments?

In the book, 5 Practices for Orchestrating Productive Mathematics Discussions, the authors Margaret S. Smith and Mary Kay Stein emphasize the importance of planning ahead in order to anticipate student responses and prepare to provide specific, targeted questions as part of a feedback loop to guide the students toward understanding and successful problem solving.

Example Problem Task

Before you share this problem task with your students, you should anticipate the strategies they will choose and prepare feedback questions to encourage them to keep thinking:

You LOVE soda water! Your friend has offered to share one of her bottles with you. Which would you rather have?

60% of 600 mL OR 25% of 1 liter

Strategy: Strip Diagrams

A strip diagram showing 60% of 600 is 360 and a strip diagram showing 25% of 1,000 is 250.

Feedback Questions:

• If the student incorrectly set up the strip diagram: How can you use your strip diagram to represent 60% (part) of 600mL (whole)? How can you use your strip diagram to represent 25% (part) of 1 liter (whole)?
• If the student did not convert to common units - mL: How can you compare common units (mL) in this problem situation as you find 60% (part) of 600mL (whole) and 25% (part) of 1000mL (whole)?
• If the student incorrectly/inefficiently calculated parts of the whole on the strip diagram: How can you decide how to portion the strip diagram based on the problem situation (600mL broken into tenths and 1000mL broken into quarters)?

Strategy: Tables

A table showing 60% of 600 is 360 and a table showing 25% of 1,000 is 250.

Feedback Questions:

• If the student incorrectly set up the tables: How can you use your table to represent 60% (part) of 600mL (whole)? How can you use your table to represent 25% (part) of 1 liter (whole)?
• If the student did not convert to common units - mL: How can you compare common units (mL) in this problem situation as you find 60% (part) of 600mL (whole) and 25% (part) of 1000mL (whole)?
• If the student incorrectly/inefficiently calculated parts of the whole on the tables: How can you use halving as a strategy to find parts of the whole (1000mL)? How can you use what you know about decimal fractions (tenths) to find parts of the whole (600mL)?

Do you plan ahead and prepare feedback for your students? How might this strategy encourage your students to keep thinking? Share your ideas in the comments.