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New 13+ CE Publishing: Mathematics for Common Entrance

I was very excited to be alerted that a new Mathematics specification had been drawn up by the Independent Schools Examination Board (ISEB). Perhaps most people may not find such things exciting, but this was at the beginning of lockdown in March 2020. With all my work with schools cancelled and the prospects of several weeks of boredom ahead of me, this was something to get my teeth into.

Key features of the new books

The first draft of the new spec really tickled my interest. ISEB have moved forward dramatically from their aims in 2017 and for 2022 have diversified to include problem solving and reasoning skills; working logically; instilling confidence and resilience, learning from mistakes; understanding the applications of Mathematics in other disciplines and enabling pupils to recognise the beauty of Mathematics.

In addition, the aims also expect schools to provide a course that enables pupils to demonstrate cultural and environmental awareness and empathy and developing an understanding of their place in the world.

Schools are used to providing spiritual, moral, social and cultural elements but there has always been much debate about how to interpret ‘spiritual’. The use of the word empathy is therefore extremely helpful. I have still been asked to explain the use of empathy in Mathematics. The word empathy means sharing the feelings of others. Mathematically this could be used, for example, to show the similar use of Mathematics in civilisations around the globe, as well as their differences. There are shared emotions particularly when experiencing the beauty of Mathematics, whether it be through mystic roses and cathedral windows, the magical symmetry of a snowflake or finding Fibonacci numbers in nature.

The natural world gives us many examples of Mathematics, not only through its design but also through topics such as nutritional content of fruit and vegetables. Then there are marvels such as the Romanesco broccoli, its fractal structure reinterpreted geometrically in Additional Mathematics.

In reflection of the ISEB aims, the new books direct pupils to reflect on the topic under consideration in the following ways:

  • Cross-curricular notes: These explain how this piece of Mathematics could be applied in other subjects. This includes PSHEE.
  • SCEE notes: Links to themes on Social, Cultural, Environmental and Empathy topics.
  • Beauty of Mathematics: Directing pupils to look at broader mathematical concepts.

ISEB changes

But first, what exactly is changing in the ISEB examinations and syllabus for 2022?

11+ remains fundamentally the same, the main changes are for 13+.


The good news for all pupils is that they will all sit the same Core Mathematics papers: mental arithmetic, a calculator paper and a non-calculator paper. This makes preparation of pupils more straightforward for schools. It also reflects another of ISEB’s new aims to promote the idea that everyone can be successful in Mathematics.

Whilst all pupils will be taught the same Core Mathematics course, some will also be taught the Additional Mathematics course which will prepare pupils for the optional Additional Mathematics paper, or scholarship examinations. There is still the option for less confident pupils to take Foundation Papers as an alternative to the Core Mathematics papers by agreement with senior schools. Schools can determine for themselves how they wish to group and teach their pupils, either in the same lesson with fully differentiated work or in different teaching groups.

Course content

Specific changes to course content are:

For both Core and Additional Level:

Bearings Map scale drawings will not be examined, but candidates will still be expected to know compass directions.
Constructions     Accurate drawing will not be examined, but candidates will still be expected to measure lengths and angles accurately.
Drawing of pie charts Candidates will not be expected to draw pie charts but will still be expected to interpret them.
Significant figures Candidates will be specifically asked to round to nearest whole number, multiple of 10 or decimal place. Estimation may involve 'sensible' rounding.
Averages Frequency tables will be used, and mean, median and mode will be examined, but not from data extracted from a frequency table.

For the Additional Level:

All the above from the Core level except significant figures which will be examined. Questions ending with informal algebraic or geometric prof are included. Solving inequalities will not be examined.

However, it is noted that although these topics are omitted from the examinations does not infer that they should not be taught. They are all on the National Curriculum (except for the complex constructions of bearings and scale drawings that were previously a feature of CE papers) and are therefore covered in the textbooks.

How the new Hodder Education Mathematics textbooks align to the new specification

In order for schools to prepare pupils for the new specification at 13+, the Hodder Education (formerly Galore Park) team have rewritten their textbooks.

Maths for Common Entrance 1 and 2 have merged into Core Mathematics and Mathematics for Common Entrance 3 has become Additional Mathematics.

The books contain all the key features that are the hallmark of Hodder Education (formerly Galore Park):

  • Careful worked examples, with methods approved by senior schools
  • Helpful tips and guidance
  • Carefully graded exercises
  • Examples that relate to the everyday experiences of the pupils
  • Questions designed to stretch pupils’ reasoning skills
  • Investigations, activities and cross-curricular opportunities  

The questions have been revised and updated and there is much new content in both books to reflect the new specification. In particular:

  • More coverage of core skills and questions with fewer words
  • Questions with less scaffolding (i.e. less multistage questions leading to the final answer and less leading through problems step by step)
  • An increased number of thought-provoking puzzles and unfamiliar problems to encourage pupils to explore and experiment.

The familiar end of chapter activities have changed. There are still investigations and thought-provoking puzzles, but now an increased number of cross-curricular projects. These are designed to allow pupils to use their mathematical skills to explore themes such as current affairs and environmental issues.

In addition, there are sample schemes of work in the Textbook Answers and assessment sheets that can map pupils’ progress to the National Curriculum will be available for free on the Hodder Education (formerly Galore Park) website.

Tips for teaching the new ISEB Mathematics specification

Every group of pupils is different, coming from different backgrounds and experiences and with different interests and enthusiasms. Similarly, every teacher is different. Some will want all pupils to work through each exercise, whilst others will happily allow pupils to follow their own path through the curriculum; most are somewhere in the middle. It is intended and expected that teachers will adapt and supplement the course content covered in the two books to match their pupils’ needs.

When initially assessing pupils’ competency, there are a variety of strategies a teacher could use. There is always a written test, but this can be time consuming for the teacher and daunting to pupils. Question and answer sessions with the level of complexity slowly escalating can be useful, as can pupils' own self-assessment. Teachers could also consider allowing pupils working together in a small group to answer questions such as ‘what do you know about fractions’ and recording their thoughts on A3 sheets.

Much is written elsewhere about the need for differentiation. It should be noted that each exercise in the Hodder Education (formerly Galore Park) textbooks has questions that are carefully graded. More able pupils may be set, for example, odd numbers only or the right-hand column only, in order to move them rapidly through the basics to more challenging material. Depending on how your pupils are grouped, they may all work initially from Core Mathematics, with more able pupils extending each topic with the Additional Mathematics textbook. It should not be expected that every pupil will work through every question in every exercise. Some pupils will need to slowly go over the initial exercises as they revise material that may not have been well understood in their primary years, whilst others will be more than capable and will need to be stimulated and stretched with more demanding work. The books include a range of both content and level of difficulty in each topic allowing teachers to set work as appropriate to individuals.

Rather than teach every topic through the chapters and exercises, teachers should also consider using the Projects to develop skills. Exploring topics such as the Mathematics behind articles in the news on, for example, climate change, will require pupils to use their analytical skills as well as Statistical Mathematics in a way that will, hopefully, engage their interest.

There is always a need for pupils’ thinking to be extended through investigation, there are many examples in the books but teachers should not feel restricted by these. There are many others that may be better suited to their particular pupils.

Differences between the Core and Additional Mathematics textbooks

Core Mathematics covers the ISEB Core Mathematics syllabus. Each topic starts with revising any relevant content that should have been covered in Key Stage 2, before covering the additional topics for Key Stage 3. There is a focus on initially solving problems mentally, word problems follow once the mathematical skills have been covered. Each chapter ends with first an extension exercise for the more able and then a mixed exercise that could be used for revision, for homework or for assessment. Investigations, projects and practical topics supplement the exercises.

Additional Mathematics covers the additional topics in the ISEB Additional Mathematics syllabus. The book is structured in a similar manner. Although core topics are revised, the coverage is more compact. There is more focus on extending each topic both with new content and with questions of increasing difficulty. There are fewer questions with step by step scaffolding and more that encourage independence of thought. The projects and investigations require increased algebraic knowledge and skill as well as deeper understanding of other topics. The book also completes the Key Stage 3 programme of study, including all topics such as trigonometry that are not examined by ISEB.

Serena Alexander has taught Mathematics since 1987 in both maintained and independent senior schools. She is now an educational consultant and inspector but still helps to run Mathematics conferences for prep school teachers. She has a passion for Maths and expects her pupils to feel the same way. After a lesson or two with her, they normally do! 

The new Textbooks and Textbook Answers for Core Mathematics and Additional Mathematics for ISEB CE and KS3 will be publishing in Summer 2021. The new Mathematics resources are for first teaching from September 2021 and for first examinations in November 2022. Find out more about our new Mathematics for Common Entrance series here.

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