The Role of Problems in Physics

Recently, I have written about the imortance of frequent problem solving for physicsstudents. Thomas Kuhn, the philosopher of science, wrote that:

Students of physics regularly report that they have read through a chapter of their text, understood it perfectly, but nonetheless had difficulty solving the problems at the end of the chapter. Almost invariably their difficulty is in setting up the appropriate equations, in relating the words and examples given in the text to the particular problems they are asked to solve. Ordinarily, also, those difficulties dissolve in the same way. The student discovers a way to see his problem as like a problem he has already encountered.

Second Thoughts on Paradigms, Thomas Kuhn

This post explores this idea, demonstrating the importance of two types of knowledge: subject knowledge and procedural knowledge in learning physics. I have used an example to demonstrate the knowledge involved.

This example is adapted from a lovely physics book: 200 Puzzling Physics Problems (with hints and solutions) by Gnadig, Honyek and Riley (2001). The puzzles (without the hints or solutions) can be found here.

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?

There is a lot of knowledge hidden needed to solve this problem: Continue reading


Teaching Energy

The more abstract a concept is, the less useful learners find definitions or explanations. There is no lightbulb moment. Rather, our understanding grows by a gradual accumulation of experience, of problems solved.

Energy is a perfect example of this:

It is important to realize that in physics today, we have no knowledge of what energy “is.”  We do not have a picture that energy comes in little blobs of a definite amount.  It is not that way.  It is an abstract thing in that it does not tell us the mechanism or the reason for the various formulas.

Richard Feynman, in The Feynman Lectures on Physics (1964) Vol I, 4-1

mechanical energy
Conservation of Energy

We do not know energy what energy “is.” We cannot model it or visualise it. The equations highlight this: energy must always be calculated from more accessible quantities. We use mass and velocity for kinetic energy; mass and height for gravitational potential energy; the spring constant and the displacement for elastic energy; the mass and change in temperature for heat energy and the change in mass and the speed of light for nuclear energy.   Continue reading


How We Learn Concepts in Science

In my last flurry of blogs (here, here and here), I wrote about the limits of definitions for learning . Learning the definition does incredibly little to develop understanding. For example: Electrical current is the rate of flow of charge.

Even if you know what rate means and you have a clear understanding of charge, you still don’t really know what current is. You don’t know how to use it in calculations or how to use it in writing or discussion. You don’t have a proper ‘feel’ for current.


Thomas Kuhn, the philosopher of science, argues that we learn scientific concepts by ‘acquiring an arsenal of exemplars‘ – often the bank of questions at the end of each chapter in textbooks (Kuhn, second thoughts on paradigms, 1977).

So spending learning time to memorising  the definition is not a great use of time. Spend that time on learning exemplars instead. One effective way of doing this is by using worked examples. Hattie (in Visible Learning, 2009, p172/3) describes the worked example cycle as typically:

  1. exposure to the example question
  2. a training phase
  3. a testing phase.

Variations include: matching text to diagrams; fading (gradually removing steps in the example) and self-explanation of the stages.

In addition to learning to solve the exemplar questions, I would add: talk about models and practical work and reading and writing sentences containing the target concepts.

This leades to a far richer undrestanding of a concept – I know my definitions now, though I didn’t when I was using them as part of my degree. I didn’t need to know them – I understood them instead.


Electricity’s Colourful Past

Yesterday I wrote about electric charge and its confusing meanings (here). I had intended to write about voltage and current today, but after a discussion with Mary Whitehouse @MaryUYSEG and a troubled night’s sleep, I’ve decided to write about the word electricity instead. Much of the information in this blog is taken from Iwan Rhys Morus’s (@irmorus1) brilliant book: Shocking Bodies.

Among physicists, the word electricity has lost it’s usefulness. Instead, it is rather a nuisance: an idea with a colourful past. But that past is glorious.

Electricity’s colourful past

Continue reading


Electric Charge – why it is difficult to understand and how to help.

My heart has never been in definitions. It was set against them in Africa 20 years ago, when I was teaching physics in Ghana. The exams, and the students, prioritised the recall of definitions. And I didn’t know them – I just converted the equation into words (I=Q/t Definition: current is the rate of flow of charge). 

When my definitions disagreed with the examboard’s definition, I saw doubt, fear and sometimes anger on the faces of my students. So I learnt the exam board’s definitions, sadly, not with good grace.

Recently, I have begun thinking about definitions again. I often see teachers asking students to write their own definitions as either a warm-up or assessments task. But I think this is too hard. If you want students to learn a definition, learn the exam board one.

But definitions are not the key to understanding a concept. Daisy Christodoulou’s new book (Making Good Progress) quotes Thomas Kuhn when talking about definitions. She (and he) make the point that a definition doesn’t lead to understanding: repeated exposure to the concept through discussion, models and texts; solving the discipline’s standard questions about the concept and carring out the standard practicals leads the learner to a rich understanding. Then the definition becomes useful. Continue reading


Using Comparative Judgement to Rank the Importance of Concepts

If you haven’t heard of comparative judgement (CJ), it is the latest fashionable way for judging the quality of student work (see here and here) – although it’s not really new. I think it has great potential for judging longer written answers (or even short answers) beyond just right and wrong – some right answers (and some wrong answers) are better than others and this should be recognised and explored.

I had the idea of trying our CJ by ranking energy statements into order of importance for understanding energy. I took the statements from the ASEs Big Ideas in Science energy section here.

10 physics teachers ranked the statements using the CJ engine at Making 25 comparisons (each comparison taking, on average, less than 10s), the correlation was surprisingly high (0.82). The top 5 are:

  1. When energy is transferred from one object to others the total amount of energy in the universe remains the same; the amount that one object loses is the same as the other objects gain.
  2. Energy cannot be created or destroyed.
  3. Objects can have stored energy (that is, the ability to make things change) either because of their chemical composition (as in fuels and batteries), their movement, their temperature, their position in a gravitational or other field, or because of compression or distortion of an elastic material.
  4. An object at a higher temperature heats the surroundings or cooler objects in contact with it until they are all at the same temperature.”
  5. The transfer of energy in making things happen almost always results in some energy being shared more widely, heating more atoms and molecules and spreading out by conduction or radiation.

The full bank of statements, ranked, is here.

I’d be really interested if anyone has tried this with written exam answers.