Asking Questions

What is your goal?

Before asking a question, make sure that you understand the goal of your question. What are you hoping to get as a result? Are you trying to:

  1. help the student engage in the work? (Student who doesn’t know where to start or is stuck.)
  2. understand the student’s thinking better?  (Student has partially completed or finished the question.)
  3. guide the student to a specific procedure or to the correct answer?
  4. extend the student’s thinking
  5. assign a value/score to the student’s work?

Knowing your goal will help you ask more purposeful questions.

Possible questions

Are you trying to help the student engage in the work?

A student who doesn’t know where to start or is stuck might be prompted with general questions such as:

  1. Can you explain the question in your own words?
  2. What might be mathematically important (in the question/information provided)?
  3. What might be the first thing you try?
  4. How might this question be similar to other questions you have seen? How might you use what you learned from those questions to help you?
  5. Is there an easier problem/set of numbers you could start with?

Are you trying to understand the student’s thinking better?

Regardless of whether a student answered incorrectly or correctly, the following questions might help them communicate/clarify their thinking:

  1. How did you come up with that answer?
  2. Where did <this number> come from? It’s not in the original question.
  3. Other than retracing your steps, how can you determine if your answer is correct?
  4. Does your strategy always work?
  5. How would you convince a skeptic you are correct?

Are you trying to extend the student’s thinking?

If a student correctly answers the question, the following questions might help them make connections to other questions and other strategies.

  1. How is your strategy similar to <another student’s> strategy?
  2. What if…? (Have the student make a conjecture and then explore it. ie. If this is true for a 2x2x2 cube, what might it look like for a 3x3x3 cube?)
  3. How could you help someone with this question without telling them the answer?