How do we combat the increasingly popular stereotype that maths is boring and a waste of time in an increasingly complicated world where this perspective can prove a real handicap? I’ll just use a calculator.”, or ‘I’ll just ask Google” are answers heard in a classroom when asked how we go about answering a question. These answers will of course give solutions in some cases, but it only gives a short quick fix; what happens if google or the person using the calculator doesn’t understand what question to ask or which buttons to press. Problems in maths shouldn’t be seen as an inconvenience; they should be seen as opportunities for personal and mental development. It is akin to saying “why bother learning to swim when I can use armbands?” The arm bands might not be there when you need them; when splashing around in a world full of maths how will a calculator help?
It is undoubtedly true that some children find maths boring and constrictive. Perhaps this can be true for the basic stuff that has to be taught, but the way in which those basics are taught can take maths from a boring motorway journey to a journey of discovery. The rigidity of the national curriculum and emphasis on exam results has been a major factor in squeezing the joy out of maths. The major advantage of one to one tutoring is that it allows the tutor to guide and encourage as the child develops their mathematical thinking. This means the tutor has to ensure that those rules and facts are learnt in meaningful ways and in meaningful situations. Intriguing contexts are more likely to hook children in to a task and ensure engagement, which also means they are likely to remember what they have been engaged in and why they were doing it. Using tasks that involve problem solving and reasoning offer children an opportunity to stamp their personal mark on the mathematics they do. In the best lesson children take the lead and steer the task in a direction of their choosing, just like an expedition where they have gone from follower to leader.
As a maths teacher the most rewarding thing to hear from a child is, ‘I think I’ve spotted something’, or a hand shooting up and a child making a strange squeaking noise in a desperate attempt to grab your attention. That moment for a teacher is incredible, the boost it gives the child in confidence and self-esteem is immeasurable. Children who think maths is all about the right answer suddenly realise it’s all about how you get to the right answer. Success is measured not by ticks on the page but by the process that a child has undertaken to get to the right answer; taking prior knowledge and applying it to a new situation, persevering through the difficult bits and arriving at a point where the problem is solved. Then this can be the beginning of a whole new adventure, developing that idea further in a direction the child wants to take, always under the guidance of a tutor.
Even what seems like the most basic of problems can see the child move through progressive stages of learning and understanding until before they suddenly realise they’re doing maths they never even realised they could do. For example, a simple investigation into the sum of two consecutive can start by looking at a 1-100 number square and asking the child to take any two numbers next to each other and add them together and see what they notice. For example, 10 + 11 = 21. They may say the answer is always odd, but is this always the case? They need to show that when you add two consecutive numbers you always get an odd answer, so we need more evidence. Did that happen because we started with an even number, 10. What happens if we start with an odd number?
Then we could look at the two numbers you started with, 10 and 11. They add to 21; is there a connection or link between the two numbers you started with and the total of those two numbers. How can 10 be linked to 21. Hopefully they’ll see that by doubling ten and adding one, you get 21. Once more is this true in all cases? Ask the child to prove it is. Then is there a relationship between 11 and 21? They might see by doubling 11 and taking away 1 they get 21.
There are key questions all the time:
Is what you’ve discovered true all the time?
How do we prove it?
Are there exceptions?
Can you explain why this is the case?
Then the child could take over the lead – what else could you investigate about consecutive numbers? They could suggest 3-digit numbers, or adding three consecutive numbers, or adding two numbers vertically on the 100 number square. Always the question is ‘What did you find out?”, “Is that true all of the time?”. The possibilities of a simple investigation are endless but the child is using loads of maths knowledge and skills without even realising it; addition, multiplication and subtraction. They’ve organised their thinking, worked systematically and recorded their findings, findings which are backed up by hard evidence they’ve discovered. This investigation is a great starting point for algebra as it establishes rules which are never changed.
It’s important to help all children to understand what it means to be a mathematician, and to encourage them to develop mathematical habits of mind. One of the common cries of any classroom is “I’m stuck”. But getting stuck is good! It’s what mathematicians do because real maths requires some energy and perseverance to make progress, or get unstuck. It’s only by working out how to get unstuck that we learn. The ability of a child to explain the process they’ve been through to solve a problem, even if they’ve got the answer ‘wrong’ is of great value to any tutor or teacher. Just like a car that won’t start, it’s impossible to know what’s gone wrong without opening the bonnet.
In these days of online learning it’s simple to see ‘fun’ online games and videos as a way of keeping children engaged in maths. They have their value but rarely allow children to engage on anything more than a superficial level…it’s fun but what do they actually learn? So rather than offering them ‘fun’ activities that skate along the surface of maths, teachers and tutors can give children a mathematical experience. They can, and shouldn’t be afraid of, offering tasks that require a bit of intellectual work and perseverance, and being honest to parents about it. Parents need to understand that perseverance is likely to lead to success, which is valued precisely because of the effort involved. And success is a positive state, which means children are likely to think of maths as enjoyable…and fun!
© Neil Acford 4.11.20