Mathematics

“Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.”

David Hilbert, mathematician (1862-1943)

 

Mathematics at Kings Langley School

Mathematics is the study of logic, pattern and number and is unique amongst the academic disciplines for its absolute rigour. For some, the truth found in mathematics is the purest form of truth there is. To study mathematics is to train oneself in the art of reason, assembling the facts before making logical deductions, a skill very much in demand in today’s world full of conflicting data.

There is a rich history of problem solving in mathematics and the methods developed to tackle these problems have their applications in modern economics, science, industry and business. There is also satisfaction in applying one’s own mind to a problem and the study of mathematics is a worthy pursuit in its own right.

Mathematics knows no borders, knows no race, religion or gender and knows no social background. It has the power to transform a young person’s life and every child has the right to the opportunity to engage with a rigorous and aspirational mathematics curriculum.

Staff:

Mr B Wilshaw (Learning Area Leader)

Mrs L Bishop (Lead Practitioner)

Mrs R Jennings

Miss D Khatri

Miss Y Li

Mrs N Ndlovu

Mr E Tembo

Miss S Slade

Mr J Jakubowski

Mr V Ogunba

Curriculum Intent:

Mathematics knows no borders, knows no race, religion or gender and knows no social background. It has the power to transform a young person’s life and every child has the right to engage with a rigorous and aspirational mathematics curriculum.  Society values the skills of interpreting data and solving problems and students have the right to access roles, in the workplace and in academia, which require these skills. 

At Kings Langley School we recognise this right and support it through teaching which develops accurate recall of facts and procedures so that the students cultivate fluency and automaticity in their work.  We train the students to form chains of reasoning to solve multistep problems and we help them to make connections between different areas of mathematics so that their knowledge is powerful.   

We understand that our students will experience numerical and logical challenges in every walk of their adult life and the mathematical education that we provide will help them to quantify, codify and then solve these problems, making them a valuable contributor to society. 

Mathematics is the study of logic, pattern and number and is unique amongst the academic disciplines for its absolute rigour. For some, the truth found in mathematics is the purest form of truth there is. 

At Kings Langley School we believe that being able to engage in mathematical thinking in an enriching experience and we prepare our students for this by teaching them to translate problems into a series of mathematical processes, to make deductions and inferences, and to draw final conclusions from their work.  We also teach them to prepare proofs of their arguments as an expression of this ultimate academic rigour. 

We understand that mathematical fluency and insight is blunted if the student cannot communicate their ideas and solutions effectively.  We teach our students to communicate effectively, by valuing oracy and an accurate use of notation.  We also teach them to assess the work of others, to evaluate the validity of an argument and to critically evaluate a given way of presenting information.  This is a vital skill to possess in a world where they will be bombarded by contradictory or biased data.    

There is a rich history of problem solving in mathematics and we believe that every student should see themselves as a mathematician.  They should be given the chance to engage with problems and to interpret their results and evaluate their methods, whatever their prior attainment in the subject.  Only then will we have prepared our young people properly for their place in the modern world. 

Implementation:

Key Stage 2 into 3

Starting from the end point of Key Stage 2 we build and broaden students’ confidence with the number system and its operations. 

We develop students’ knowledge using a mastery maths approach.  This means blocking together related topics at Key Stage 3 so that the students acquire a depth of knowledge and fluency in one area before they are ready to move on.  All the students are taught the same core curriculum but are placed in sets so that they can acquire the required knowledge at a pace suitable for them.  This also allows us to stretch the students with problems which are challenging, whilst not being out of reach for their current attainment level. 

A mastery approach means that the students can represent their knowledge in multiple ways, for example using bar models to support algebraic thinking or multilink cubes to support work in ratio.  This approach helps to make the students more resilient when it comes to tackling problems in unfamiliar contexts, as they have the tools to support their initial ideas.

The curriculum at Key Stage 3 develops the students’ ability to move from concrete representations to increased levels of abstraction and this is a key component in the introduction of algebra.

The end point of the Key Stage is a solid foundation of knowledge with a set of core problem solving skills which they will use to access the developing subject at Key Stage 4. 

Key Stage 4

We follow the Edexcel course 1MA1 for GCSE mathematics. 

At Key Stage 4 we maintain the central elements of mastery teaching such as multiple representations and the development of fluency but now the content is covered in a spiral curriculum.  This means that smaller blocks of topics are studied from the main areas of Number, Algebra, Geometry, Probability and Statistics, and Ratio and Proportion.  This is intended to help the students to develop cross topic links between related areas of maths as the spiral curriculum moves outwards into ever more sophisticated areas of the main topic areas.  This approach teaches the students to solve more sophisticated problems which relate several topic areas.

The end point of the Key Stage is a broad knowledge of mathematics together with an increasing range of strategies for problem solving and proof.  This leaves the students with the confidence to tackle problems in their workplace or in their further studies.  They will be ready to access the developing rigour of the subject at Key Stage 5. 

Key Stage 5

Finally at Key Stage 5 we provide a traditionally broad A level offer consisting of pure maths, mechanics and statistics as this broad base allows students to be successful in a wide range of highly numerate undergraduate degrees at university.

The students spend two-thirds of their time studying pure maths, developing their knowledge from GCSE.  There is a move towards developing greater rigour in their use of notation and their writing of proofs at this stage.  This bridges the gap to undergraduate study where these skills form the mainstay of a degree in mathematics.

In the remaining one-third of the time the students follow courses in applied maths, namely statistics and mechanics and the students begin to experience how the subject can branch off onto varied areas of application.  The problem-solving skills acquired at Key Stage 3 and 4 support the students during this branching of the subject and now the students are expected to show greater levels of independence in their study.  

We also offer further maths A level and this offers the students the opportunity to study a very broad curriculum which dips into the material covered in the first year of many science and maths degrees.  

Studying further maths alongside a core maths A level provides the student with the opportunity to see the vast interconnectivity of the subject and to makes surprising links between topics.  These links are further explored at university.  

Top universities require further maths for entry onto their mathematics degrees and students at Kings Langley have this aspirational path open to them through our curriculum development from Key Stage 3 to 5.

Super Curriculum:

Top 5 books to read (The school library will have copies of these books)

  • Why Do Buses Come in Threes?: The Hidden Maths of Everyday Life: The Hidden Mathematics of Everyday Life (Rob Eastaway).
  • Things to Make and Do in the Fourth Dimension (Matt Parker).
  • Alex's Adventures in Numberland (Alex Bellos).
  • Fermat's Last Theorem: The Story Of A Riddle That Confounded The World's Greatest Minds For 358 Years (Simon Singh).
  • Journey Through Genius: The Great Theorems of Mathematics (William Dunham).

Places to Visit 

Useful Websites:

Mathematics Extra-Curricular Programme:

Maths challenge - This is a national competition open to top set students in Year’s 7 to 13. There are age categories comprising of the junior, intermediate and senior challenges.

Royal Institution masterclasses - These ‘hands-on’ interactive sessions are led by experts from academia and industry. Each year a handful of students are invited from Year 9 to take part.

Further Studies and Careers:

If you’re a talented Mathematician, a maths degree can be a good option. The fact that there is a right answer to questions means that it’s possible to achieve high marks, most courses offer the chance as you progress to specialise in the areas that most interest you. Your skills will be useful in many careers.
More information about studying for a maths degree, types of A levels you need and the careers it leads to can be found here:

Maths Degrees and Careers

Options after a Maths Degree:

Studying Maths helps you develop skills in logical thinking, problem-solving and decision-making, which are valued by employers across many job sectors.

Jobs directly related to higher maths qualifications, such as A-levels or a degree, include:

Acoustic consultant, actuarial analyst, actuary, astronomer, chartered accountant, chartered certified accountant, data analyst, data scientist, investment analyst, research scientist (maths), secondary school teacher, software engineer, sound engineer or statistician.

Jobs where higher maths qualifications would be useful include:

CAD technician, civil service fast streamer, financial manager, financial trader, game designer, insurance underwriter, machine learning engineer, meteorologist, operational researcher, private tutor, quantity surveyor, radiation protection practitioner or software tester.

Remember that many employers accept applications from graduates with any degree subject, so don't restrict your thinking to the jobs listed here.

Top Mathematicians to research and learn about:

  • Leonhard Euler 1707-1783. A Swiss mathematician who produced more original mathematics than any other mathematician before or since. He is behind a lot of the symbols you use in your maths lessons, such as the symbol for pi, f(x) etc. He went blind in later life, but the loss of his sight actually increased the amount of work he produced. He discovered so much that often other mathematicians are credited as being “the second person after Euler to have discovered it”.  He is Mr Wilshaw’s favourite mathematician.
  • Ada Lovelace 1815-1852. A female mathematician in a world that didn’t easily accept that such a thing could exist. She worked on programmable machines and envisaged how a machine could be programmed. Some say that her work amounts to one of the first ‘computer’ programs ever written.
  • Henri Poincare 1854-1912. The last mathematician to have understood all the areas of maths that were around in his lifetime. These days the subject is too big for any one person to understand all parts of it.
  • Srinivasa Ramanujan 1887-1920. An Indian mathematician who had no formal training in mathematics, but his self-taught ideas were ahead of some of the most advanced western mathematicians of the time. He came to England to study and made many outstanding contributions until his unfortunate death at the age of 32.
  • Andrew Wiles 1953- . It’s easy to think that all of mathematics has been discovered but Andrew Wiles proof of Fermat’s last theorem (another thing to look up!) is a very modern discovery. Andrew Wiles found Fermat’s last theorem in a library book as a schoolboy and wondered why something that could be understood by a ten-year-old had not yet been proved. After studying at Oxford and then Cambridge he proved it but then found an error in his work. It took a year to fix this error and he finally achieved his life’s goal in 1995.

Revision documents: Topics covered each half term matched to the mathswatch website

Y7 Mathswatch (Autumn term)

Y7 Mathswatch (Spring term)

Y7 Mathswatch (Summer term)

Y8 Mathswatch (Autumn term)

Y8 Mathswatch (Spring term)

Y8 Mathswatch (Summer term)

Y9 Mathswatch (Autumn term)

Y9 Mathswatch (Spring term)

Y9 Mathswatch (Summer term)

Y10 and Y11 Mathswatch