# Conceptual understanding

Concepts are thoughts or ideas to be understood as opposed to facts that are statements that can be memorised.

It is easy to remember the fact that momentum = mass x velocity but not so easy to understand the concept of conservation of momentum.

There are lots of big concepts in physics, the list reads like chapter titles
• Mass
• Motion with constant acceleration
• Conservation of momentum
• Newtons Laws of motion
• Work energy and power
• Thermal concepts

etc.

There is an excellent text "Conceptual Physics" by Paul Hewitt but is it at all possible to teach physics without the concepts? Well I think it is but you wouldn't really be teaching physics. Let's take the example of conservation of momentum.

Momentum = mass x velocity

The total momentum of 2 balls colliding is always the same

example Momentum before = 5 x 1 = 5 Ns

Momentum after = 1 x 1 + 4 x 1 = 5 Ns

With this information, plus some mathematical skills, a student could answer simple problems involving conservation of momentum but would have no idea of the concept. They probably wouldn't be able to answer the question

Use the principle of conservation of momentum to explain the operation of a jet engine.

Having said that a very good student would probably be able to fill in all the gaps and work it out for themselves but we haven't helped them along the way. IB questions are written to test conceptual understanding at least the ones testing objective 3 are. To have a complete understanding of physics requires that a student remembers some content (Definitions of quantities and laws), have skills to use the knowledge (mainly mathematical skills) and understand the concept (see the bigger picture and how the different parts are related to one another). Once a student understands the topic they can apply their knowledge to the sort of novel situations found in practical work and sometimes the exam. If one bit is missing then things go wrong.

• A student could have a good understanding of the concept of momentum but lack the skills to solve problems.
• Another student has excellent mathematical skills, solves problems easily but can't work out why a pool ball doesn't rebound with the expected angle.
• Finally a student has a good understanding of the concept, can solve problems but thought that momentum = mass x velocity.

To fully understand a concept means that you can apply it to unfamiliar situations and the best way to be able to do that is to practice as many situations as possible. As physics teachers, preparing for class, we often go through a process of testing our own understanding by self questioning.

If angular momentum is conserved how do balls start spinning when they hit each other?

I can answer this simply by saying that the angular momenta cancel each other out so I try this out with a simulation (you may have relaised that I do like using simulations in this way) and find its not the case. Look, they don't even spin in opposite directions. I obviously don't understand this properly so I refer to texts and find an explanation that helps me to explain what I have observed, in this way my understanding of the concept of angular momentum gets better.

Most students are not so good at self questioning so need us to ask the question for them.

##### Misconceptions

I sometimes feel that I spend most of my time trying to show students why commonly held misconceptions are incorrect rather than concentrating on reinforcing the right way of thinking. Part of the problem is that we don't want our students to fall into the examiners traps. Examiners have an annoying habit of trying to trip up our students by playing on misconceptions.

In which direction is the resultant force on a helicopter flying forward at constant velocity?

The feeling that the helicopter wouldn't be moving forwards without something pushing it leads to the misconception that the force is forwards. This question (not from the IB exam) would be rather unfair as it leads the student into thinking that there is a force. Why ask the question if the resultant is zero. To answer the question one must also understand the language. The word resultant is very important. There are of course many force acting but the resultant is zero.

To overcome misconceptions it is necessary to see why the flawed understanding doesn't work and how the correct explanation leads to a better result. In this example of Newton's first law we could look at examples where the forces are clearly balanced but there is still motion, an ice skater for example. The problem we often have is that if we try to show this in practice it doesn't actually work, an ice skater does have some friction and air resistance. We can pull a cart along a table with a hanging mass and show that when the forces are balanced it travel at constant velocity but if we want the cart to have constant velocity with no horizontal force we have to cheat by angling the track. Here simulations can help.

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