From first teach last year, mechanics became a key part of the UK A Level Mathematics syllabus for both OCR A and AQA students. Below, one of our expert mechanics authors Nathan Barker discusses his top tips for teaching the subject.
“A good place to start is by using the Standards Unit A6 Interpreting distance-time graphs, or if you do not have access to this by looking at the introductory kinematics resources on NRICH (part of the University of Cambridge) to find something that will work for your students.
Then, I like to define what kinematics is, explaining that together with dynamics, it is the area we call mechanics.
Discussion is important in mechanics; it allows students to practise articulating what they think is going on and allows the teacher to find any misconceptions. Graphical representations also play an important part in understanding what is happening in any given kinematic situation. Getting students working with these graphical representations and suggesting functions that could describe them is the first connection that will lead to the use of calculus.
Using Underground Mathematics (also part of the University of Cambridge) – discussing distance and speed vs velocity – works well at getting students talking and also helps to identify who is not interpreting the difference between a scalar and vector in this context.
From here, we can discuss the different features associated with these graphs. This is the first place I like to talk about rates of change and link the topic to calculus. I also like to distinguish the idea of average speed, and average acceleration from velocity or speed at a specific time. This idea is then used in the Walk-sorting resource on Underground Mathematics to liken the ideas of calculus to kinematics.
Summarising what we can learn from these graphs allows us to talk about mathematical models for each of these situations and the possible realistic nature of some of the journeys.
After this, we can consider the following: what would we have if acceleration was set as a constant with this starting point:
A particle is moving with constant acceleration a. Its initial velocity is u ms-1 and its velocity after t second is v ms-1. During this time the particle covers a distance of s metres.
- Can you sketch a velocity-time graph for this information?
- Can you write down any equations connecting the information given?
- Where can you “see” these equations in your sketch?
Then from here, take the calculus idea from before and look to exploit the connection between velocity and rate of change of displacement.”
Nathan currently teaches A Level Mathematics, Further Mathematics and the International Baccalaureate in Jersey after moving from Cambridge University where he was a resource designer for Underground Mathematics (a Department for Education funded project) and worked as a teacher of mathematics for Comberton Academy Trust (now Cam Academy Trust). Nathan is also a member of the Mathematical Association Post-16 subcommittee and is currently completing the pilot Chartered Teacher programme through the Chartered College of Teachers.