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:
- help the student engage in the work? (Student who doesn’t know where to start or is stuck.)
- understand the student’s thinking better? (Student has partially completed or finished the question.)
- guide the student to a specific procedure or to the correct answer?
- extend the student’s thinking
- assign a value/score to the student’s work?
Knowing your goal will help you ask more purposeful 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:
- Can you explain the question in your own words?
- What might be mathematically important (in the question/information provided)?
- What might be the first thing you try?
- 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?
- 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:
- How did you come up with that answer?
- Where did <this number> come from? It’s not in the original question.
- Other than retracing your steps, how can you determine if your answer is correct?
- Does your strategy always work?
- 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.
- How is your strategy similar to <another student’s> strategy?
- 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?)
- How could you help someone with this question without telling them the answer?