Mathematics

The Purpose of Learning Mathematics in School

We believe that the value of learning mathematics in school is to learn to think analytically and to be able to apply logical deduction in the solution of problems. It is not purely to memorise methods which have dubious applicability later in life, or an exercise in passing exams.

Educational Philosophy

We strongly believe that students should be guided towards the discovery of mathematics, rather than have mathematics thrust upon them. We see the role of the teacher as a guide in this process, rather than as a lecturer or mobile textbook stating the facts and expecting the students to memorise them. We introduce each new topic by setting a problem and asking the class to solve it. Our role isn’t to solve a problem for students, but to facilitate the students’ discovery of a new aspect of mathematics through solving the problem themselves. We provide them, as they work through the problem, with the new definitions and terminology they need in order to articulate the mathematics they are suggesting, and to correct any mistakes they may make along the way.

Teaching mathematics in this manner ensures that the mathematics taught is always at an appropriate level for the class as the new material always comes from their suggestions rather than being imposed from above. Of course, individual students will make these leaps of understanding at different rates, and so the teacher must work to keep everyone on board at all times. This will inevitably mean speaking individually with some students to ensure they have thoroughly understood the material. The hardest part of this task is in the selection of appropriate questions to inspire the correct creativity in the students. One of the most delightful aspects of this method is that sometimes the students’ suggestions are better than the one you were expecting!

Examinations

All students at HCH are prepared for the 11+, 13+ and GCSE examinations; however the prescribed syllabus does not drive our curriculum. Instead we are driven by the natural flow of mathematical progression, the passions and interests of the individual teachers and, most importantly of all, by the questions our pupils ask.

GCSE Policy

The HCH Mathematics department follow a linear GCSE, which all students will take at the end of Year 11.

Although some schools ask their more able students to take the GCSE exam at the end of Year 10 the arguments in favour of this seem flawed, hinging mostly around the idea that finishing the GCSE course early allows the time to work beyond the syllabus once the course is complete. This argument does not hold water as any good Mathematics department, and indeed any good teacher of Mathematics, should be looking to stretch their more able students beyond the confines of the syllabus at every stage of their education. The exam syllabus must necessarily be contained within the department’s scheme of work, but shouldn’t be the entirety of it. A good Y11 course will as a matter of course contain much of the Mathematics AS syllabus, such as completing the square and the ambiguous case of the sine rule. It may also choose to contain ideas such as combinatorics and binomial expansion; or draw it’s inspiration from outside common examination syllabus, such as working in different bases or Diophantine equations.

The way develop strong mathematicians, capable of taking on Maths and Further Maths at A-level, is to challenge them with problems which require them to independently think rigorously through multiple stages of calculation, rather than to simply give them a cursory grounding in ‘more mathematics’.

To rush students through examinations early only puts unnecessary limits on the curriculum that can be covered, and is therefore is in our opinion more detrimental than it is advantageous: our policy is one of enrichment rather than acceleration.