Math Forum Director Steve Weimar recently ran a workshop focused on student work and effective feedback. Afterwards, a teacher asked him if he had a list of good questions that he kept in his “back pocket” for working with students.
Steve recommended starting out by stating some aspect of the student work that you find interesting, intriguing, reasonable, useful, etc.
Then raise questions like these:
- What did you notice that led you to this way of solving the problem?
- How would you check your answer?
- How did you decide whether your answer made sense?
- What parts of your solution are you most happy with, or comfortable with?
- Which parts are you concerned about, or least confident in?
- Can you say some more about what you mean when you write….?
- What would it look like if….?
- Will it always work that way? How do you know?
- Can you give me an example (or show me how it works) when you think about it this way?
Let’s use the Elementary level PoW, “Horsin’ Around” to illustrate.
Zachary travels on a journey of 50 miles. He spends half of his time riding his horse and half of his time walking. When he rides his horse, he covers 9 miles every hour. When he walks, he covers 3 1/2 miles every hour. How long does it take him to complete the journey?
- You can ask ‘what would your method look like if it was about the “riding the horse” half of the trip?’
- “Will it always work to divide by 2, no matter whether we’re talking about equal time or equal distance?” This sort of question often changes into a “what if” question
Often times a student fails to connect two or more parts of an explanation, so ask them to make that connection.
- I am struck by what you said here and then what you said here. How did you connect those or how would you connect them as you think about them now?
All of those can present the student with an interesting new task to think about. It can also reveal more to us about how they think and give them a chance to reflect on the thinking they did.