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.
Relax, don’t worry about being stuck
Quite often, the problem isn't that a student can't do a problem, but that a student has become convinced they can't, which is a self-fulfilling prophecy. Coming up with ways out of the spiral of doubt can be the difference between a successful homework session and a big argument.
Being stuck in mathematics isn’t failure, it’s part of the process. Andrew Wiles was unusually persistent in working on one of the greatest unsolved problems in math, but being stuck is perfectly normal in math, whether it’s spending eight years on Fermat's Last Theorem or twenty minutes on a tricky percentage problem.
Some things that might help include:
Use positive language. Remind your child that they're smart, and they will crack it eventually. Make sure they're not bullying themselves.
Get moving. Sometimes having a little dance or run-around is enough to get the blood pumping and give a fresh perspective on the problem.
Have a change of scene. Move to a different part of the house, put some music on, work on a fresh bit of paper - just do something differently.
Come back to it later. When Einstein got stuck in his thinking process (yes, even geniuses get stuck) he took breaks to play his violin. Taking a break to do something else gives the subconscious some time to work on things in the background.
Albert Einstein, who was responsible for some of humanity’s most famous intellectual discoveries, was also known for his daydreaming, violin breaks and unusual approach to thinking. We also know about Archimedes making one of his great discoveries while relaxing in the bath (Eureka!) and Isaac Newton coming up with the theory of gravity while having a cup of tea in an orchard. They weren’t alone - many celebrated musicians, scientists and other people considered to be geniuses depended, and still depend, on the power of taking breaks and ‘doing other things’ to help them connect what they know to what they want to know.
It’s always tricky to find the right balance between helping your child stick at a task and making a strategic retreat - the tactics here will help you to help them build resilience, try harder for longer, and solve problems for themselves.
A puzzle for you to get stuck on
Since we're talking about unsolved problems, let's look at one that doesn't need much math to play with - it's known as the Magic Square of Squares.
A *magic square* is a grid of numbers where each row, column and diagonal add up to the same number. For example:
This is a 4-by-4 magic square in which each row and column adds up to 34.
Click here to download a printable worksheet for the following activities
Activity 1: Complete the 3x3 square
Activity 2: Can you find other patterns in this magic square that add up to 34?
(We know the rows and columns add to 34)
Activity 3: Can you use the numbers 1 to 9 to make another magic square in a 3 x 3 grid?
A Magic Square of Squares takes things a step further; as well as the rows, columns and diagonals adding to the same total, each number in the grid has to be a square number - a number you can make by multiplying something by itself (for example, 16 is a square number because it's 4 × 4).
Nobody has so far found a Magic Square of Squares, although a few people have come close.
Activity 4: Complete the 4x4 square:
Activity 5: Try to find a Magic Square of Square numbers. (Download your printable worksheet here) Get stuck. Keep trying!
Here’s a list of the smallest square numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144...
Andrew Wiles was just ten days away from giving up on Fermat’s Last Theorem when he finally made the key breakthrough that led to a solution. After more than 350 years of the entire mathematical world being stumped, he finally solved the problem with tenacity, persistence and his ability to accept that math is all about being stuck and the valuable journey that (eventually) getting unstuck takes you on.
Answer 1: Complete the 3x3 square
Answer 2: Can you find other patterns in this magic square that add up to 34?
Answer 3: Can you use the numbers 1 to 9 to make another magic square in a 3 x 3 grid?
This is just one example out of hundreds:
Ask yourself:
- Do the rows and columns add up to the same number?
- Do the diagonals?
If so then it’s a magic square!
Answer 4: Complete the 4x4 square:
Activity 5: Try to find a Magic Square of Square numbers. Get stuck. Keep trying!
Hmmm...I'm stuck!
Hi, I'm Colin Beveridge - a math tutor, former NASA researcher, and writer of math books including Basic Maths for Dummies.
About Komodo - Komodo is a fun and effective way to boost K-5 math skills. Designed for 5 to 11 year olds to use at home, Komodo uses a little and often approach to learning math (15 minutes, three to five times per week) that fits into the busy family routine. Komodo helps users develop fluency and confidence in math - without keeping them at the screen for long.
