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How to form cross curricular links in the new CE mathematics textbooks
By Serena Alexander
08 Nov

It was very exciting to be invited to write new mathematics textbooks for Galore Park reflecting the new specification from the Independent Schools Examination Board (ISEB). There is much that is new to the examination specification but not new to educators. It was wonderful to see that the examination board expects pupils to be educated beyond the constraints of an examination. It is also recognised that there are some topics that need to be taught but do not lend themselves to a timed examination and that such an examination should focus on mathematics, and not tricks of the English language.

When I wrote my first mathematics textbook back in the 1990s, I was aware that there were many pupils who may have been competent mathematicians but were not inspired by the manipulation of numbers and symbols. The challenge was to write a book that would capture their imagination in other ways. This is now reflected in the new specification. One of ISEB’s core aims is the expectation that pupils who have pursued a course of study based on CE specifications and assessments will understand how subjects connect with each other. For mathematics, an additional aim is to instil in pupils the importance of the subject and its associated skills, including the applications of mathematics in other disciplines. It should be noted that this is also reflected in the independent schools’ inspection criteria, as schools need to ensure that pupils not only develop competence in numeracy but also apply their knowledge and skills in mathematics to other areas of learning.

As literacy is ranked as important as numeracy from a child’s earliest years, then language is a good place to start. Did you know that many early civilisations had no word for three? They would count one, two and then ‘some’ or ‘several’. They developed words such as ‘flocks’ of sheep, ‘heaps’ of grain, or ‘lots’ of people. The language of mathematics reflects so much of the history of the world, starting with the ancient civilisation of Babylon and then moving though ancient Greece to Rome and then picking up symbols for the area we now call the Middle East but was once known as Arabia. Many of the words we use in mathematics have prefixes that are used more generally, such as parallel and paramedic or polygon and polythene, and the study of these can put these, sometimes strange sounding, words in context.

Whilst literature is a good source for studying subjects such as history and geography, there are not many books for this age group that specifically feature mathematics. However, many pupils enjoy puzzle books and detective stories. The idea of looking for clues and then using them to solve a mystery is fundamentally the basis for mathematical investigation. Most importantly, such experimentation helps pupils to appreciate how they learn from their mistakes and that there is no dishonour in getting something wrong. New to the books are a look at number puzzles in newspapers, an understanding between proof and paradox and an investigation into Fermat’s theory (not his last theorem).  

History is embedded in the development of number theory and there are some fascinating characters who are worthy of investigation. Pupils are directed not only to look at well known names such as Pythagoras and Fibonacci but also the life and times of al-Khwarazmi, from whose famous work the word algebra is derived.

Pupils will be familiar with using mathematics when they study geography, as they interpret maps and calculate distances using a scale. They will also apply statistics as they compare climate and population. A study of famous buildings around the world can bring together many areas of the curriculum, such as the Alhambra palace in Spain with its colourful history, its important geographical location, its religious significance and those beautiful mathematical tiling patterns, that can only inspire.

It is often forgotten that mathematics is an essential tool for designers. At its base is geometry, with the study of angles and carefully drawn constructions. In the books, pupils are encouraged to apply technology to develop their own patterns, such as tessellations inspired by the work of Escher. Works of art and architecture have their own beauty and pupils are shown examples of how the appreciation of symmetry and of the golden ratio have been an inspiration for generations.

Mathematics is very much part of science with the use of formula, graphs and tables. It is recognised that this generation of young people are particularly aware of environmental science. In the books, pupils are directed to look at the mathematics and science behind headlines describing, for example, the loss of large areas of rainforest. Science also includes the study of nature and here again, we find many examples of symmetry. Pupils are also directed to look at the prevalence of Fibonacci numbers in nature. There is a study of the use of technology to generate a pattern to replicate the natural fractal found in Romanesco broccoli. Finally, there is the recognition of the wellbeing that is generated by finding a peaceful place by the water and quietly looking at the reflections whilst contemplating the wonders of our world.

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! Learn more about Serena here.

The new Textbooks, eBooks and Textbook Answers for Core Mathematics and Additional Mathematics for ISEB CE and KS3 are for first teaching from September 2021 and for first examinations from November 2022. Find out more about our new Mathematics for Common Entrance series, view samples and order online here.

Tags: 13+, 13+ Common Entrance, 13 plus, CE, CE 13+, Common Entrance, Entrance exams, Independent School Examination Board, ISEB, Mathematics, Mathematics at Common Entrance, Mathematics for Common Entrance, Maths, Maths 13+, Serena Alexander

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