Why Being Stuck in Math isn't Actually a Problem
Whenever I found myself stuck on a math question at school, my teacher would smile broadly and say: "Great! If you're not getting stuck once in a while, you're not trying hard enough."
As a student, that irritated me no end; as an adult - and as a tutor - I understand where he was coming from. Kids naturally tend to enjoy solving the the simple problems that they get right first time. This is important and shouldn’t be overlooked as it does wonders for confidence levels, but we know that in order to improve at math (or anything, really) we need to stretch ourselves.
The further your child gets into learning mathematics, the more time he or she can expect to spend being stuck. This isn't exactly surprising - the problems get harder!
At the very top end of the 'stuckness' scale is a math puzzle known as Fermat’s Last Theorem which baffled mathematicians for centuries. Fermat, in 1637, wrote down the theorem in the margin of a book basically saying ‘I’ve proven this but don’t have room to write it down here.’ This was the ultimate tease for generations of mathematicians who spent more than 300 years falling over themselves trying to solve it with no success. (So, as you can see, being stuck in math is fairly common.)
As a parent, it's tough to watch your children struggle with something. Your instinct is usually to help out but that's not always the best thing to do - it can be like telling someone the ending of their favourite TV show, or spoiling a riddle. Being stuck in math is part of the process, so rather than guide them towards the answer, you can help them develop strategies for getting unstuck themselves.
Talk about the question... without giving away the answer
One of my favourite ways to get unstuck is to explain the problem to someone who doesn't understand it. It doesn’t even need to be an actual person - I’ve had pretty good results discussing my problems with teddy bears. To explain a problem this way, it helps the child to:
organize their thoughts
get specific about what's holding them up
remember what they've already tried and think about why it didn't work.
This is often enough to crack the problem wide open!
You can also ask your child questions that force them to look more carefully at the question they’re doing, and to look at it in a different light. Asking:
'What do you know?' helps children to clarify what bits of the answer they do know and find out where the gaps are - better still, ask them to write everything they actually know on a piece of scrap paper and see if they can turn the problem into a picture or diagram.
'Is this like any other question you’ve done?' or asking if they can break the question into parts that they do recognise helps children make links between different parts of their learning.
'How is this different than the last question you did?' encourages a student to try similar methods and see where they fall down.
'Is there anything in the question you haven't used?' reminds them to read carefully.
'What do you understand by this word/symbol?' can start a conversation about the question.
Talking about the question without giving away the answer is a good habit to get into: the odds are, at some point in your child's school career you'll be asked to help with something you don't know the answer to yourself, and this way you’ll still be able to help!
Experiment
In the 1980s, a professor called Andrew Wiles dedicated himself to proving Fermat’s Theorem after becoming entranced with the problem when he was just a boy. He worked alone and in secret for the best part of a decade, making lots of mistakes and getting stuck many times along the way.
Normally, mathematicians prefer reason and method to experiments, but when someone is properly stuck, anything goes. Some ideas are:
Can you do it with easier numbers? Build up a recipe and then follow it again.
Can you get close with trial and error? Figuring out roughly what the answer should be can be a huge push towards doing it 'properly'.
There's often more than one way to solve a problem. Children who get used to tackling things from different angles generally turn out to be better problem-solvers.