At first sight, Maths, languages and Chess may seem like very different subjects.
I have taught Maths, French, Spanish, Italian and Chess for many years, and one of the things that has always interested me is how much they actually have in common.
All of them are built around patterns, rules and logical connections. The real aim is not simply to memorise information, but to understand the underlying system well enough to apply what you know when something unfamiliar appears.
That principle has become an important part of the way I teach.
Maths is perhaps the most obvious example.
A pupil can memorise a procedure and successfully complete several questions that all look alike. The real test of understanding comes when the question is presented differently or combines several topics at once.
In an examination, a question is unlikely to announce exactly which mathematical ideas are being tested. Pupils therefore need to recognise the structure of the problem for themselves.
This is why I place considerable emphasis on understanding why a method works, rather than simply remembering a sequence of steps.
For example, my approach to mixed numbers is not simply to tell pupils that they must always convert them into improper fractions. For addition and subtraction, it can often be much more efficient to understand that a mixed number consists of a whole-number part and a fractional part and then work with those parts directly.
Once the structure is understood, the pupil has choices.
That ability to choose an appropriate method is much more valuable than following one routine automatically.
Languages may appear less mathematical, but the same idea applies remarkably well.
French, Spanish and Italian are full of recurring grammatical and pronunciation patterns.
When learning the French subjunctive, for example, simply memorising individual sentences is of limited use. It is much more helpful to understand what is happening between the main clause and the subordinate clause and why certain structures require a particular mood.
Spanish irregular verbs provide another good example. Something may initially appear highly irregular, but often only one part of the verb has changed. Once the irregular stem has been identified, familiar endings can frequently be applied.
Italian pronunciation works in much the same way. A learner who understands how the pronunciation of C changes according to the letter immediately following it can work out the pronunciation of unfamiliar words rather than learning every word individually.
In each case, recognising the pattern reduces the amount that actually has to be memorised.
Chess brings the same principle into a completely different setting.
A beginner can memorise the first few moves of an opening, but that knowledge quickly becomes useless if the opponent plays something unexpected.
Understanding why the pieces are being developed, which squares matter and what each side is trying to achieve is much more useful.
The same applies to tactics.
As players gain experience, they begin to recognise recurring patterns: forks, pins, discovered attacks, mating ideas and weaknesses around the King.
More advanced players also recognise positional patterns involving pawn structures, weak squares, open files and good or bad pieces.
The exact position may never have occurred before, but familiar ideas can still guide the player towards a sensible decision.
This is where I think Maths, languages and Chess come together particularly strongly.
The learning process often moves through several stages:
First, we learn a rule or idea.
Then we begin to recognise the pattern.
Next, we understand why it works.
Finally, we are able to apply that understanding independently in a new situation.
That final stage is especially important to me.
A pupil should not always need somebody beside them saying which method to use, which grammatical structure applies or which chess move to consider.
The aim is to develop enough understanding that the pupil can begin making those decisions independently.
This does not mean that memorisation is useless.
Certain things simply need to be known.
Times tables need to become familiar. Language vocabulary and irregular verb forms have to be learnt. Chess players need to remember tactical motifs and some opening ideas.
But memorisation becomes much more powerful when it is connected to understanding.
Knowing a rule tells you what to do.
Understanding the pattern helps you recognise when and why to use it.
That distinction becomes increasingly important as the level of the subject rises.
I have been tutoring since 2002 and have lived in Mill Hill all my life, so North London is not simply an area in which I happen to advertise tuition.
Over the years I have worked with pupils of different ages, abilities and educational backgrounds across North London.
Some pupils need help rebuilding confidence. Others are preparing for important examinations or want to move beyond what they are currently doing at school. Adult learners may have completely different goals again.
Whatever the subject or level, I try to identify the underlying structure and help the pupil see how the different pieces fit together.
Although I teach five subjects, I do not see them as five completely unrelated areas.
Maths, languages and Chess are all built on patterns, rules and logical connections. My teaching focuses on helping pupils understand these underlying structures so that they can apply what they know confidently and independently in unfamiliar situations.
That is the thread connecting the subjects I teach.
Whether we are solving a difficult Maths problem, understanding a French or Spanish grammatical construction, working out the pronunciation of an Italian word or deciding what to do in an unfamiliar chess position, the underlying skill is very similar:
recognise what is happening, understand the logic behind it and use that understanding to make a good decision.
For me, that is much more valuable than simply memorising the answer to a question that may never appear in exactly the same form again.
Please visit my home page for further details.