# How to Teach Problems…

Physics is all about the problems.

In my last post, I picked apart the knowledge I needed to solve this physics problem:

A bottle of water is suspended from a fixed point by a inextensible rope. The bottle is set in motion and the system swings as a pendulum. However, the bottle leaks and the water slowly flows out of the bottom of it. How does the period of the swinging motion change as the water is lost?

200 Puzzling Physics Problems (with hints and solutions) by Gnadig, Honyek and Riley (2001)

The knowledge included:

• knowledge of useful strategies to use

But I didn’t go into how you teach someone to solve problems. This post is about teaching problems.

# Part 1 – Know lots of stuff…

The key to being able to solve problems is to have lots of knowledge. In the pendulum examle above, I needed to recall knowledge from two physics domains:

1. pendulums (the length is important; the mass of the bob isn’t)
2. centres of mass (and how to combine two centres of mass).

When knowledge is properly learnt, it takes no effort to recall.

So, how do you help students to “properly learn” it? Here is my suggestion for part 1:

1. Start with a story. The story is the scaffolding to build the schema on. The story of Galileo’s invention of the pendulum is neat – a version for younger students is here.
2. Pendulum experiment: the practical work adds to the story skeleton. It is there to hang knowledge onto. It turns a story into a nascent schema.
3. Teach the knowledge. The first pass at the knowledge is important. It starts the process of builing out the schema. But be warned, when you have “taught” something, for example pendulums, it isn’t learnt. Learning takes months and years. Like a gardener, you have planted a seedling, which will take lots of care and maintanance to mature.
4. Practice the knowledge. By practice, I mean retrieval practice. I mean spaced practice. I mean interleaving. If you don’t know about these yet, here is a good place to start. The idea is that returning to what you have taught in a planned, regular way, your students will gradually move new knowledge into their long-term memories.

Daniel Willingham categorises knowledge as flexible and inflexible (here). So far, if all goes well, your student has developed inflexible knowledge: knowledge they can recall effortlessly, but which they can’t yet apply to novel problems and examples. They now need to make that knowledge flexible. They need to do problems.

# Part 2 – Do lots of problems…

Inflexible knowledge isn’t enough. It refuses to fit problems. When faced with a problem, flexible knowledge pops into our minds. Inflexible knowledge is hard work. How do you make inflexible knowledge flexible?

Build a programme of problems. Start simple and build up. Spread the problems out over the months and years but don’t leave too long between each one. Mix them up with questions from other topics. At first you may need to give lots of support. You can always set the same question again in a month with less support. The idea is that your learners gain famliarity with the questions. They learn to bend the knowledge to fit the question. They make knowledge flexible.

So start with knowledge – it will be inflexible at first. Practice the knowledge until it becomes permanent. Then make the knowledge flexible by giving loads of problems. There, you have built a physicist!

In my next blogs, I am writing more about physics stories and practical work. Until then, here is a taste of problem practice using Doug Lemov’s excellent strategy: Write/Rewrite from Reading Reconsidered.

1. Answer the problem below. If you are stuck, write down any information you think may be relevant.

A bottle of water is suspended from a fixed point by a inextensible rope. The bottle is set in motion and the system swings as a pendulum. However, the bottle leaks and the water slowly flows out of the bottom of it. How does the period of the swinging motion change as the water is lost?

200 Puzzling Physics Problems (with hints and solutions) by Gnadig, Honyek and Riley (20

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2. Read the my solution here (half way through the blog).

3. Now, in your own words, improve your answer. If you can’t complete the whole problem, write down what you can remember. Try not to go back to the solution.

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