# Mathematics – ideas to help students who find mechanics hard

*Hints and tips - 7 minute read*

**Steven Walker, OCR Maths Subject Advisor**

*This blog was originally published on 17 October 2019 and has been updated.*

*We offer two specifications for AS and A Level Mathematics:*

*While both specifications have been accredited against the same DfE criteria, they are slightly different in approach. This means we can offer choice to centres so they can deliver the course that best suits their students. While much of the content is similar, one difference in the mechanics section is with moments in A Level Maths. A section on the differences has been included in this republished blog to support students studying remotely during the current lockdown.*

There have been three examination series for the reformed A Level Maths qualifications, with 2019 being the only ‘standard’ cohort of students:

- 2018: A small cohort of students, the majority sitting the examination after one year of study and expecting to progress to Further Maths in 2019.
- 2019: The first full cohort where the majority had followed a standard two year programme.
- 2020: A small cohort sitting an autumn series after disruptions to education due to COVID-19 restrictions.

The examiners’ reports make clear that mechanics is one area where a significant number of candidates struggle.

### What are examiners’ reports and how do I use them?

The examiners’ reports provide a detailed commentary on the A Level Maths cohort’s approach to the whole exam paper, followed by an analysis of the paper question by question.

If you want to know more, we’ve a specific blog to help with tips about how you can make the examiners’ reports work for you.

You can find the question papers, mark schemes and examiner’s reports for 2018 on the qualification webpages for Maths A (H230/02 and H240/03) and Maths B (H630/01 and H640/01).

You can access the 2019 and 2020 material with your Interchange login. If you’d like to request access to Interchange, everything you need to know is on our website. See our past paper schedule of moving material from Interchange to the open website.

### Why do students find mechanics so hard?

In the legacy A Level Maths, many centres did not offer mechanics (choosing instead to offer S1 and D1) and of those centres that did M1, the majority delivered it in year 13.

Mechanics was also identified as one of the Big 4 changes of the reform. To support teachers during the reform in 2017 we published a recording of our webinar ‘Teaching mechanics’ - part of a series of events for the Festival of A Level Mathematics.

### Students’ perceptions about mechanics

There is a perception among students that you need to be good at physics to succeed here. In fact, the prior knowledge that underpins mechanics can be seen in everyday life, for example:

- gravity acts downwards
- friction only acts in the opposite direction of movement.

The rest of the content simply builds upon the GCSE (9-1) Mathematics work on kinematics and the understanding of gradient and area under the graph of velocity-time graphs.

### Ways you can use mechanics as a vehicle for teaching pure

Mechanics does build upon the pure content more directly than statistics, so this can cause problems for students that are not yet confident with the underlying pure maths and provides some of the rationale for the common legacy approach of leaving M1 until year 13.

An alternative approach to explore with your students could be to get them to embrace mechanics as a concrete, real-life example of the abstract pure maths, as shown in the below calculus example:

The use of ‘hands-on’ experiments and computer simulations can support students’ understanding of the pure content alongside the mechanics.

For a selection of useful resources you can work with, see the delivery guides within the planning and teaching section on the qualification pages for Maths A and Maths B.

### Using diagrams to help understanding

Questions set in context always add an extra dimension to maths problems. In mechanics, the situation often needs to be translated into algebra first and then the calculations performed.

Encouraging your students to visualise the problem in a sketch can help to focus their minds.

Let’s look at Q10(a) from the Mathematics A H240/03 Sample assessment material as an example.

Here an initial sketch of the context can be used to determine a force diagram, from which the algebra can be stated.

This allows a sense check between the directions of each force and the arithmetic.

The subsequent algebraic manipulation is not too complex. While mark schemes may not explicitly reward a diagram, any sign errors made by a student can be quickly identified to support the awarding of partial credit.

### Modelling assumptions

A common type of question in mechanics is where candidates are asked to make a comment on the model used in the calculations.

Examiners often note that candidates tend to offer extended prose when short bullet points will suffice.

Another issue is where candidates offer generic textbook responses rather than providing an answer that is based on the context of the information provided in the question.

### Differences in mechanics between Maths A and Maths B

The key difference between the mechanics content in Maths A and Maths B is the depth of study of moments in the full A Level.

In the A Level Maths A (H240) specification, the 3.04 Statics content includes the note ‘To determine the forces acting on a horizontal beam or to determine the forces acting on a ladder resting on horizontal ground against a vertical wall’.

In the A Level Maths B (MEI) (H640) specification, the Rigid Bodies content includes the note that when calculating the moment of a force there is an exclusion of ‘Vector treatment'.

This means that while A Level Maths A may involve the need to resolve forces using trigonometry, the focus in A Level Maths B (MEI) is with forces that are parallel or perpendicular.

For example, the ladder problem seen on Q14 from the Maths A H240/03 Sample assessment material could not be set in A Level Maths B (MEI), but the horizontal beam seen on Q9 from the Mathematics A H240/03 Summer 2018 exam could be seen in A Level Maths B (MEI).

### In summary

Mechanics should not be seen as a separate subject to pure maths. Students should be encouraged to recognise that it is simply the application of the pure content to everyday events. The use of careful diagrams helps visualise the mathematical model and provides a sense check of the generated equations.

### Stay connected

If you have any queries, you can comment below, email us at maths@ocr.org.uk, call us on 01223 553998 or Tweet us @OCR_Maths.

You can also sign up for monthly email updates to receive up-to-date information about resources and support.

### About the author

**Steven Walker, OCR Maths Subject Advisor**

Steven originally studied engineering before completing a PGCE in secondary mathematics. He joined OCR during the recent qualification reform period, working on the redevelopment of Entry Level, GCSE (9-1), FSMQ and the suite of A Level Mathematics qualifications. He now focuses mainly on supporting the Level 3 qualifications, although during the current home-schooling period is also supporting his daughter with year 1 arithmetic.

#### By the same author

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