Improving student reasoning

Sometimes kids who are seemingly brilliant at maths have a great deal of trouble showing or explaining how they solved a problem.  Try these suggestions:

Try asking these questions instead of “How did you get your answer?”

  • What operations did you use? With which numbers?
  • What did you do first? Then what did you do after that?
  • How do you know that you’re right? How do you know that the answer wasn’t __ instead? Prove it to me.
  • What do you mean in this part? Explain it to me.


Tips for dealing with, “I just knew it”:

  • Change the numbers in the question and ask them the steps for solving the new question.
  • Ask the student to tell you how to work out the answer to the new question without telling you the answer. “As soon as you tell me the answer then I won’t be able to mark it. I want to try and follow your steps and see if I can get the answer without you telling it to me.” Scribe for the student as needed.
  • Ask the student to “help” someone who is stuck. Watch what they do and scribe their talking.
  • Deliberately make a mistake or give the wrong answer and have the student correct you. “So if I… does that work? What do you think? Prove it.”
  • Give the student other similar questions to solve and ask them to show you what is the same about each of them. “How is this question kind of the same as this other question? What is similar? What do you have to do to solve each of them?”

Tips for dealing with low literacy levels:

  • Remember that marking “reasoning” is not the same as marking literacy.  You are marking whether or not they have a mathematical process that makes sense, not their spelling or grammar.
  • Give the student sentence starters or equation starters with parts to complete. You might even provide words, phrases or numbers on sticky labels to stick into the spaces. Make sure that you provide lots of wrong ones as well so that they can’t just complete the sentences with the only words that fit!
  • Have the student write the “calculator buttons to press” onto boxes. Show a
    calculator at the side so that students can only select from the numbers, operations and signs on the calculator.
  • Give the student new numbers and go through their process, skipping all of the
    bits that they skip. Give him/her a chance to correct you when you make mistakes
    and then go back and add those parts into his/her own process.

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