Problem Solving Rules

My 8 year old son and I have figured out some problem solving rules that help him tackle unfamiliar material: they work for many adult sized problems too.

I enjoy helping Jonathan, with his homework. I particularly enjoy working with him on his Number Work. Maths was one of my favourite subjects at school, and I like to share my enthusiasm for the subject. Best of all are those moments when something dawns on him for the first time: his whole face lights up, he often begins to laugh and he feels so proud of himself for getting – not just the answer – but the concept.

Over time, we’ve started to work out some “Rules of Maths” that help Jonathan deal with unfamiliar material. Recently, I’ve begun to see that these same problem solving rules work for many grown-up sized problems too.

Rule 1: Look Like You’re Learning

It took me a while to work out the importance of this rule, but these days, whenever I sit down with Jonathan to start his homework, I begin by reminding him of our first Rule of Maths: “Look like you’re learning”.

If Jonathan doesn’t feel like working, he usually shows it by looking distracted or by slumping at the table. If he’s daunted by his work, he tends to bury his head in his arms or to look away from the page. Whilst I understand these behaviours, I also recognise that they don’t help him overcome his difficulties. Indeed, there is a marked difference in when in Jonathan when he’s sitting up straight and when makes and effort to appear attentive and interested in what he’s supposed to be doing. He genuinely tends to focus better and to engage with the work. His mind seems clearer and his attitude more positive. Additionally, it certainly encourages me to work with him. Hopefully, “Look Like You’re Learning” will carry over into other areas of Jonathan’s life. I am sure that his teachers find it easier to help him when he looks engaged and enthusiastic. Fore these reasons, then, I absolutely insist that Jonathan shows me – by his posture and attitude – that he’s ready to learn.

The challenge for me is this: when I’m faced by something I don’t want to do or which I find hard, what do I look like? Do I adopt an enthusiastic, “ready to learn” posture myself? I recognise that the way I hold myself is partly the result of what is going on inside, but at the same time my demeanour can also be a significant influence on my inner world. I’ve noticed that I feel happier when I smile, I feel more alert when I stand up, and I feel more reverent when I kneel to pray. And this works regardless of whether anyone else is watching: it appears that adopting the right physical posture can help me develop a healthy mental attitude towards my work. Consciously adopting a positive stance towards a problem is good first step towards finding a solution.

Rule 2: Don’t Guess

One of the things I found when I’ve worked with young children is that they do like to please adults (at least most of the time). One the ways they aim to do so is by trying to get the right answers. Unfortunately, children often fall back on their default answer-obtaining strategy: guessing. And I’ve seen children who are very good at guessing: they perform a kind of cold reading, getting the right answers by watching the questioner’s body language or speech patterns or by following patterns in what has gone before. Or sometimes they look for clues in other children’s behaviour or in their environment. And in Sunday school they say that the answer’s “Jesus” because it almost always is.

Curiously, adults often become complicit in this “guess-what’s-in-my-head” game. They mouth the answer or say the first letter. They sign the answer or point to something that’ll give the child a clue. And all of this is fine, as far as it goes, because children do need to learn to look for clues to get right answers, and because many of these strategies work perfectly well in social situations.

Unfortunately, however, none of these strategies works well for Maths. Whenever you guess the answer in Maths, one of two things will happen: more often than not, you’ll just be wrong. Occasionally, however, you’ll be right but for the wrong reasons. Then you’ve got some unlearning to do as well as the original learning. So that’s why we have the rule, “Don’t Guess”.

So, here’s the challenge for me: when I face life’s knotty problems, how often do I ever just guess? Because that’s exactly what I’m doing when I try to apply the wrong strategies or use faulty principles in my problem solving. I need to recognise that, when my approach to a problem isn’t working, I may need to step back and ask myself if the strategy I’m using really does apply to the problem at hand. As it has been said:

Insanity: doing the same thing over and over again and expecting different results.Albert Einstein

Rule 3: Look for Patterns

One of the things that really helps in Maths is looking for patterns. Here are some simple examples:

• Whenever you add two even numbers you always get an even number
• When you multiply a number by 10, you always end up with that number with another zero at the end
• Whenever you half an even number you get a whole number, but whenever you half an odd number you get something and a half

The benefit of looking for patterns is that they help you find principles, and can lead to strategies for finding answers to problems you’ve not encountered before. For example, Jonathan probably knows that 2 x 10 = 20. But he also knows – by applying a principle – that 1,933,452 x 10 = 19,334,520. More importantly, he knows that even if he had never encountered the number 1,933,452 before.

For me, the takeaway from this is that looking for patterns can help me with my problems, too. It is important, of course, that I’m careful not to see false patterns. It is all too easy to imagine meaningful patterns in random events, just like we see animals and faces in clouds. Nevertheless, when I do see a genuine pattern, I have made a significant step to understanding principles, and as I’ve written previously, principles are the key to success in any endeavour.

Rule 3½: Take a Break

Sometimes, when we’re doing his homework, Jonathan needs a break. He just can’t work effectively when he’s fatigued. Moreover, he often finds that a problem that he really battling with before the break is suddenly much easier afterwards. It is as if his subconscious was still working on the problem even he wasn’t thinking about it.

I often find this in my own experience – that mulling things over sometimes causes my thinking to get fuzzy and treacle-like. But when I leave things alone for a while, the sludge seems to have been flushed out of my brain by the time I come back.

Speaking of taking a break, this seems like an ideal opportunity to take 5. I expect I’ll write more about these rules in another article.

References

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