The first issue in maths is to know the difference between maths and arithmetic: arithmetic is just counting things, adding, subtracting, multiplying etc: this is what Piaget called “concrete” thinking. There are objects, you can count them. Maths is completely different: you can do arithmetic without maths, but you can’t do maths without arithmetic. So although the necessity of memorising times tables is an essential skill (for speed issues apart from anything else) maths requires the imagination, that’s why it is “abstract”: if you imagine a triangle, that is abstract thinking. In school many mathematical (not arithmetical) questions are abstract, they have no immediate reference to any particular real object or set of objects in the world, you are required to show you know how to do it, so-called “Formal Methods”. However, maths is a very historical subject, it’s origins lie with the Babylonians and the Greeks; in many ways a maths book is a history book and Pythagoras for example had an interest in arithmetic, maths and music: logic, sequences and suchlike form a major part of understanding maths and mathematical thinking.

The GCSE maths syllabus as shown below basically hasn’t changed for at least 50 years

Pure Maths/Number

Everything you know about maths including arithmetic, even and odd numbers, prime numbers, factors, percentages, ratio and proportion, decimals: the first maths you will learn is squared numbers and square roots.


Linear equations/straight-line graphs

Simultaneous Equations

Quadratic Equations

Geometry/”shape and space”

Pythagoras’ Theorem


Circle Theorems

Data Handling/statistics

Graphs, probability

In essence , if you can grasp those topics, you’ll get a “C” grade.

It is interesting and curious that Maths GCSE is essentially about the building trade: consequently it was seen as a boy’s subject and is essential for Chartered and Quantity surveying etc: subsequently girls were not expected to do it. However I personally am a big fan of algebra (an Arabic word for reconstituting, as in repairing a broken bone) as it teaches logic.

Another important issue is that maths contains many Latinate words such as linear, simultaneous, geometry, etc so a good understanding of Standard English is essential for maths and of course was socially-divisive in the past as that particular accent is seen as middle-class and posh: this is nonesense: standard English is BBC English, as in the Concise Oxford Dictionary and is simply intended that anyone who is a scientist should be able to understand each other from Land’s End to John O’ Groats, or as more the case today, from any part of the world