The art of questioning is very helpful when working with your student in math- whether he or she is a top student, or one who tends to struggle. One of the most important questions that you can ask your student is "How do you know?". Get them thinking about, and talking about, their thinking! This is called Metacognition and it can be very beneficial, not only for state testing, but for real life skills! Being able to express your reasoning is a life skill that everyone should possess. The ability to think about our thinking, and express it clearly, takes practice and should begin as early as possible.
The questions below are a great way to get your student thinking and talking about their understanding of the math problem.
The Art of Questioning in Math (NCTM)
Help students to rely more on themselves to determine if something is mathematically correct:
• How did you reach that conclusion?
• Can you make a model to show that?
Help students learn to reason mathematically:
• Is that true for all cases?
• Can you think of an example that won’t work?
• How could you prove that?
• What assumptions are you making?
Help students learn to conjecture, invent, and solve problems:
• What are some possibilities here?
• Can you predict the next one? What about the last one?
• How did you think about the problem?
• What is alike / different about your method of solution and hers?
Help students to connect mathematics, its ideas and applications:
• How does this relate to…?
• What ideas we have learned before were useful in solving this problem?
• Have we ever solved a problem like this one before?
• What uses of mathematics did you find in the newspaper last night?
• Can you give me an example of…?