**Steven Walker, Maths Subject Advisor**

In this blog I will look at using legacy comprehension papers from the MEI Mathematics – 7895 qualification (Paper 4754B) in classroom or independent learning activities.

Whilst Maths B (MEI) – H640 is unique in having a distinct comprehension section as part of the A Level assessment, the ability to engage with published mathematical articles is a valuable skill for all students to develop as they progress through their A Levels and into Higher Education and employment.

### What is mathematical comprehension?

A Level Maths is one of the most popular A Levels studied post 16. However, the majority of these students do not go on to study maths at degree level but study subjects that require the application of mathematics produced by others.

In recognition of this, the DfE Mathematics AS and A Level content (April 2016) includes in its aims and objectives that:

*AS and A Level specifications in mathematics must encourage students to: *

*Read and comprehend mathematical arguments, including justifications of methods and formulae, and communicate their understanding.**Read and comprehend articles concerning applications of mathematics and communicate their understanding.*

### When should students start preparing for the comprehension section?

Students have been developing these skills from the start of their maths education. GCSE and AS papers all have questions that require students to extract the relevant information and solve problems. The difference is that this is an extended piece of writing and mathematical formulae, often with some accompanying diagrams.

September in year 12 is a good time to start thinking about the comprehension section, perhaps using some articles that are solely reliant on GCSE techniques. This allows some revision of the assumed knowledge while highlighting that the A Level course is more than just answering a set of questions with a gently increasing level of demand.

The synoptic nature of techniques brought together in the comprehension section also means that time spent practicing for this provides good revision for the full course at Easter in year 13.

### Legacy 4754B assessment

A bank of legacy papers (from 2005 to 2018) can be found on the teacher section of the MEI website; the comprehension paper was 4754B on Applications of Advanced Mathematics (C4).

There are slight changes in style between the reformed and legacy qualification comprehension assessment:

- H640 will only focus on maths content taken from the Pure Maths section of the specification.
- The comprehension forms section B of the H640/03 2-hour examination rather than a separate exam (H640/03 has 75 marks rather than 100 to reflect the ‘reading time’ needed for this section).
- The H640 comprehension passage is shorter than the 4754B passage.
- The H640 assessment of the comprehension is only 15 marks rather than the 18 marks on 4754B.

This means that the legacy papers could be used as a one-hour activity in its published form, or as the starting point for a larger investigation to review content knowledge.

Some of the topics covered in the legacy qualification focus on material that is fully accessible to able year 11 GCSE students, while most can be attempted once the AS course is covered. A few articles need some basic knowledge of concepts from the A Level only content, such as radians or logarithms. A couple do cover more complex techniques (for example June 2012, involving differential equations).

#### Sudoku puzzles (June 2008)

In this article students look at the development of the sudoku puzzle from the more generic Latin square. The mathematics involved only needs students to be familiar with finding factorials, recognising that objects can be arranged in equivalent ways through transformations and general confidence with algebraic manipulation and substitution.

This would be a good introductory activity for students near the start of their A Level course.

#### Curves of constant width (January 2012)

In this article students investigate an unusual group of shapes that, like a circle, have a constant width. The mathematics involved is limited to surds and algebra so is an ideal opening introduction to mathematical comprehension.

The fact that oneapplication of this seemingly abstract property is the design of coins that can be used in vending machines is a nice way to demonstrate the usefulness of maths. It also makes this a great activity to start the course.

The article would also make a useful year 13 resource to practice content studied in year 12.

#### Modelling sea waves (June 2007)

In this article students are introduced to the idea that the waves seen at the beach are not modelled as sine waves, but by cycloids that are defined parametrically. The article defines all the vocabulary that will be used and then gives an outline of how the formulae are derived.

The questions require students to use trigonometric functions, parametric equations, curves, mathematical modelling and general algebraic manipulation and substitution.

Additionally, as an activity, students could use dynamic geometry to investigate different waves, using the equations given in the text.

The mathematical techniques involved in this article mean that it is best left until towards the end of the A Level Maths course.

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### About the author

**Steven Walker, OCR Maths Subject Advisor**

Steven joined OCR during the major qualification reform period of 2014-2017. He now focuses mainly on supporting the Level 3 qualifications. Steven originally studied engineering before completing a PGCE in secondary mathematics. He has taught maths in England and overseas, including the legacy MEI A Level Maths course at a couple of schools.