Improving student reasoning

Kids who have a strong intuitive understanding of maths can sometimes have trouble slowing down their thinking to explain how they got the answer. Here are a few simple tips for helping them to work out what process they used.

Great questions:

• How do you know that the answer isn’t ___? Prove it wrong.
• What pattern can you see? How are the questions all kind of the same?
• What answer would definitely be too big? How come? Too small?
• Which numbers did you use? Let’s write those down first. Now what did you do with the numbers?
• What operations did you use?
• How do you know that you’re right?
• 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 to think forward to explain what the steps would be for solving the new question. Scribe for the student as needed.
• Ask the student to “help” someone who has a wrong answer. Watch what they do and scribe their talking. NB – this won’t work if the student has no answer, as a wrong answer helps with the stimulation.
• 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.” NB – year 6s just love proving the teacher wrong.
• 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? Where is it different? How does that change what you would 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.

Some final thoughts:

Sometimes we forget to use the analytical and deductive parts of reasoning in favour of explaining. One of the best ways to stimulate reasoning is to ask students to make, test and prove conjectures. As a simple idea, try asking students to turn sevenths into decimal numbers using a calculator. What is the pattern? What is coming next? How do you know? How can you prove it? BTW – thirteenths are even more fun!