How to Solve Problems

Teaching is a constant learning process. At least it should be. One problem with being a teacher is that you often get into situations where you think you're right, which can make it difficult for you to change what you're doing. In the classical model of the teacher, you can be expected to be right in your knowledge, otherwise you wouldn't be there. But when it comes to how to share that knowledge, or in what order to present it, there is less clear right and wrong and just a whole range of choices.

I believe in the power of problem solving for teaching. This translates to a belief in the power of learners to solve problems, and for them to learn something in the process. The problem is, not all learners are good at solving problems, and many have been through educational systems where they have not been expected to solve them. At least not the kind of problems that I give them. 

So how do I solve this problem?

Given that I want to teach problem solving skills, I probably just have to be a lot more open and transparent about it. I have been mentioning a few things to the students in passing: like suggesting they draw diagrams to help them work out problems, or advising them to write their calculations out carefully and clearly on lots of paper so it's easy to go back later and see what they did. I need to be much more explicit about the steps of the problem solving process, and give them a bit more practice in each step rather than just throwing a problem at them and hoping they'll work it all out. Too often the problem I've been throwing at them is how to solve problems, which is way too abstract.

Here are some steps:

• Formulate the problem

The first step is to work out exactly what the problem is. Draw a picture. Write down what you know. Draw another picture. Put question marks where you need to find an answer. 

• Find solutions

Now that you know the problem, you can think about solutions. What strategies are available? Are there different ways to solve the problem. Make a list!

• Choose a solution

Which is the best way to solve the problem? What are the steps? 

• Prepare tools

If you are calculating, your main tools are equations. If you are using a computer, the tool is the software. You also needs data. There will be physical properties that need to be looked up from tables, some things may need to be measured. Some will need to be estimated.

• Calculate

Use lots of paper. Avoid any shortcuts that will not be obvious to someone looking at the calculations later. If you miss out steps on paper, there's a higher chance you'll make a mistake.

• Check the calculation

Ideally get someone else to check your calculation. It's often difficult to see your own mistakes.

• Check the answer

Eyeball it. Compare it with your real world experience. So you calculated that this pencil weighs a million tonnes? Maybe you should think again.

• Check the error

Answers in the real world are never perfect. Their accuracy depends on the accuracy of the numbers going in, and the accuracy of any equations you used. Know how wrong you are!

That's eight steps, and no fancy acronym to go with them. I can start building them into my lessons and watch what happens.

It's probably also worth talking about engineering problems and how they are different to the problems that come up in education. They have often been conditioned to find one correct answer, but over in the real world there is usually more than one answer, and more than one way of finding the answer. Good engineering will find the best solution to a problem, given a range of criteria. The most important considerations are often cost, safety and performance, and the best solution may be optimised between them. Cost itself can be in materials, equipment and construction processes. 

Of course one factor in this optimisation is the length of time the engineer spends on the problem itself, since engineers are a scarce resource and their time precious.

So I think I've written enough on this topic for now.

[Image taken from https://schooltutoring.com. not sure where they got it from!]