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!]

Low Energy Building First Class Fact Checking

The first lesson has some background on the energy problem. I have the carbon graph, showing the emissions taking off around 1800, driven by a smooth exponential growth in coal production. Actually the coal was not really being produced—that happened back in the carboniferous period 300 million years ago—it was being moved around and then burnt. The graph shows oil starting, then gas a little later, each in its own exponential variant. Meanwhile, the emissions from coal have still been increasing. 

I've been saying "until this year" with a quizzical optimism, and finally it looks like "production" of coal is down, which is a sign that we will eventually burn less of it. 

This graph from BP is still pretty scary.  That gray coal line definitely seems to be getting thicker. Also alarming is the sandy bit at the bottom, which is biomass. Before coal that was the only source of heat, and it was more or less constant until the middle of the twentieth century. Now that is on the rise. I'm not sure how much is in industrial use of biomass, for example replacing coal in thermal power stations, and how much is domestic use from fuel-poor burning what they can find. 

If you look carefully you can see the thin yellow strip of renewables at the top, like a sprinkling of snow on a mountain top. While this has increased from its previous levels of invisible and insignificant, it is still a long way off replacing any of the behemoths beneath it.

It should be noted that while BP's data can probably be trusted, their main business is still in selling fossil fuels, and their business model is still based on selling more. The graph goes up to 2013. 

The next graph is from the International Energy Agency, and gives us hope that 2013 was around the high point of coal, with production in China and the OECD decreasing. It's tempting to see that as a peak, and look forward to a steady then rapid decline in coal extraction.

However, Dick Van Dyke nostalgia has been strong in the US, and production was up last year. So, once again, it's too early to tell.

I guess it depends on who wins between the people selling fossil fuels, and people promoting energy efficiency and renewable energy. 

While checking figures, I also revised the proportion of Japanese energy that is imported from 80% up to 90%. The lower figure was pre-Fukushima, which had got into my slides at the beginning, and I've now corrected several years late. (Japan was 20.2% energy self-sufficient in 2010, and 8.3% self sufficiency in 2016 according to METI.)

I had been telling student that Japanese houses use 30% of the country's total energy, while in fact its more accurate to say that buildings in Japan use around 30% of the total energy. 

Whichever way you look at it, the amount of energy imported can be reduced if we get serious about low energy buildings.

I also found some interesting changes in energy use, which I may need to mention some time, although should probably work out more carefully first. 

Between 1973 and 2015, residential energy use in Japan increased by 90%, office energy use increase by 140% and industrial energy reduced by 20%. 

I'm not sure to what extent this is a sign that houses and offices have become much less efficient, while industry has become more efficient, or whether it shows that Japanese industry is producing less, and people are spending more time in offices and more money on energy-consuming appliances in their houses. 

(Dick Van Dyke from trailer screenshot - Mary Poppins Trailer, Public Domain, https://commons.wikimedia.org/w/index.php?curid=34700974)