Bringing together two sets of constraints

Focusing on the learners:

Distinguishing–eliciting–connecting. How will you:

• respect the understanding about force and motion already achieved
• develop the current understanding of forcing motion, without undermining it

Teacher Tip: These are all related to findings about children's ideas from research. The teaching activities will provide some suggestions. So will colleagues, near and far.

Focusing on the physics:

Representing–noticing–recording. How will you:

• state and represent Newton's third law
• clearly present the task that the third law fulfils
• simplify situations, to get back to a single object acted on by a resultant force

Teacher Tip: Connecting what is experienced with what is written and drawn is essential to making sense of the connections between the theoretical world of physics and the lived-in world of the children. Don't forget to exemplify this action.

Stating the law helpfully

Wrong Track: Action and reaction are equal and opposite.

Right Lines: An interaction between two objects can be replaced by two forces, one acting on each object. These forces are equal in magnitude, but opposite in direction.

Thinking about the learning

The neat and seemingly concise and precise statement:

Jo: Action is equal to minus reaction

is easily memorised, but has proved hard to use well as a way of thinking about situations.

One line of thinking that it sets in train is first action, then reaction, which leads to reasoning in chains rather than seeing the forces as replacing an interaction. The former view tells stories as a linear sequence; the latter emphasises that the forces on both objects arise simultaneously. There is no first one force, then the other force. It's not action, then reaction.

To use a form of words, however memorable, that encourages this line of thinking is to send students off down the wrong tracks.

Thinking about the teaching

Learning to think of complex interactions as being processes that happen all at once is not easy. Our natural causal explanations tend to be narrations in time, involving a temporal sequence (this leads to that, that leads to the other). We'd suggest that working with a longer version of the third law helps this transition.

Then you'd be well advised to think about the role that the third law might play in your students' thinking. If you've followed the development in the SPT: Forces topic and in the SPT: Force and motion topic, you'll already be able to predict motions of isolated objects, and have learnt how to isolate objects and to find the resultant force. So what does the third law add?

Some will prefer to start with the third law (and we think this might be appropriate if our teaching of forces started with older children), but met here, at this late stage, it looks like a short cut. That is, once you've worked out the force on one of a pair of interacting objects, you can simply write down the force on the other, using the third law. No further analysis is necessary.

Not empirical

Newton's third law is not empirical. There wasn't an experiment you could do to show that it was wrong in Newton's time. Rather, it's a statement that allows the whole Newtonian description to be precise enough to get a grip on the lived-in world, and to be able to mimic certain elements of that world. It's an essential part of the whole, so can be shown to be helpful by association – the whole apparatus of Newton's laws is certainly reliable.

As you cannot do an experiment to either confirm or falsify the third law, how can you present it?

We'd suggest that you encourage students to see it as a law connecting pairs of interacting objects, that allows you to switch focus from isolating one object, to isolating the other. As you switch focus, so the law enables you, given the forces on one object, to immediately write down the forces on the other.

Teacher Tip: Treat Newton's third law as a way of correlating the descriptions between two different facets of the same process: one facet corresponding to the isolation of each object.

Choose very simple situations to think about interacting systems

Choosing apparently simple situations to promote discussion can result in a clear understanding of what interacts with what, and how to model the situation. The essence is to learn to see a new situation in terms of one with which you're already familiar.

Teacher Tip: Promote lots of discussion about simple systems, asking how they can be redrawn to make them more familiar.

When I act, and when I don't

Wrong Track: I push on the table, and then it pushes back.

Right Lines: Isolating the table, there's a force exerted by you, acting on the table. Isolating you, there's a force exerted by the table, acting on you.

Equal, but symmetrical descriptions

Thinking about the learning

The idea that one thing pushes, and then another pushes back might grow naturally from the suggested introduction to forces in the SPT: Forces topic, where the force exerted by an inanimate object is likened to the actions that you can take to effect changes in the world.

Teacher: You can push and pull, and so can other things

.

Thinking about the teaching

We'd suggest that you develop a forces acting on object description from the interactions of an object with its environment for each occasion. Newton's third law is useful as you switch focus from one interacting object to another, but it applies to all forces equally.

In some ways that's the whole point of the forces-plus-masses world view. Once you have simplified to forces acting on a mass, then you can find the resultant and predict the motion without further reference to the environment.

Helping smooth the paths to Newton 3

All forces on an object arise as a direct result of the environment into which it is placed. Some of these forces seem more active and more like the actions the student might themselves carry out. Other seem more passive and result from local adjustments – for example, the object deforming its environment. It may help to smooth the full acceptance of the third law by explicitly discussing these differences.

The non-contact forces seem more like active forces (gravity, electrical, magnetic). They're the result of free agents, without limit to the forces they can exert.

The normal and frictional forces are a result of local interactions. These forces have evident limits (the buoyancy force is limited by the volume of water that can be pushed out of the way; the slip force by the materials of the surfaces; the compression force by the strength of the materials.)

It's worth noting that the active forces are thought to be the more fundamental ones in physics.

But, in both cases (active and passive), the forces are just forces, however close or otherwise they seem to our actions. The point of explicitly raising the issue is to point out its non-importance in the analysis.

Teacher Tip: Explore and revisit the kinds of forces to ensure that all are understood to be just forces and so all are equally described by Newton's third law.

Comprehensive diagrams

Wrong Track: The forces acting are obvious. There's always gravity and friction, and a bit of buoyancy, which we nearly always ignore – even if I've no idea why.

Right Lines: To build a model of a situation where there are a number of interacting objects takes skill and care. You'll need to be thinking about the interactions between each of the objects, then assign linked pairs of forces to each object – linked by Newton's third law, that is.

Thinking about the learning

There's a tendency to promote and encourage a rush to the answer. This often relies on cutting out several stages of the modelling process, which can lead students off down the wrong path. If they're ever to see what the Newtonian world view buys them, they'll need to engage with the modelling.

Thinking about the teaching

In the Physics Narrative, and again in the Teaching Approaches, we've encouraged the use of interaction diagrams for those who want to develop a full description of a situation. If these seem over-complex for the students you teach (we think that's likely, for pre-16 students), you can revert to use the approach suggested of isolating the object from its environment, and drawing only that object and the forces acting on it. That'll be enough to find the resultant force and so predict the changes in the motion of the object. This is the approach developed and suggested in this topic and in the SPT: Forces topic.

Working backwards can promote thinking

Starting out at different points in a conventional presentation, then working backwards and forwards from those, can result in illuminating discussions.

You could select an equation, such as: 30 kilogram metre inverse second = velocity  ×  50 kilogram, and get students to write down a question to which this could be the beginnings of a solution. Group work, where students assess the reasonableness of each other's claims, leads to lively discussions.

Selecting suitable equations can lead to a much deeper understanding of the significance of such relationships than is engendered by the question – choose equation – plug in numbers – give answer route. At least it provides some variety.

Teacher Tip: Hand out any equation and then ask students to write a question to which the equation is an answer.

Consistent representations support understanding

We've emphasised using arrows for representing physical quantities that are vectors, as a supplement to verbal and algebraic representations. The main reason for this is to emphasise the vector nature of the quantities – something that can all too quickly get lost if you focus on processes that can be described in one dimension.

It's important to be able to differentiate between the arrows, so be consistent. Either develop your own conventions for different quantities (different styles of arrowhead, maybe – but we'd suggest not different thicknesses as the primary differentiator), or use the SPT arrows developed here. In either case, be clear and consistent.

There's a good chance you could improve your teaching if you were to:

Try these

• using interaction diagrams
• connecting the study of Newton's third law to earlier understanding of Newton's second law

Teacher Tip: Work through the Physics Narrative to find these lines of thinking worked out and then look in the Teaching Approaches for some examples of activities.

Avoid these

• presenting the law as obvious
• presenting the Newton three pair of forces as both acting on one object

Teacher Tip: These difficulties are distilled from: the research findings; the practice of well-connected teachers with expertise; issues intrinsic to representing the physics well.