The Portrait

You know your marks. Nobody has told you how you think.

Two short sittings, and a written account of how you actually work.

Two students get the same answer right. One saw the shape of it straight away and used a method they had used a hundred times. The other had no idea where to start, and built it out of something they understood properly. Same mark. Two completely different mathematicians.

You have been measured for years. Tests, exams, class positions, predicted grades. All of them tell you how you did. None of them tell you how you did it, and that is the part that decides what you should learn next.

That is what the Portrait is for. Over two short sittings you work through questions designed to show how you read a problem, how you set your reasoning down, and what you do when you are stuck. Afterwards I write it up for you. No score, no ranking, no label.

Most students have never had anyone describe their mathematics back to them. It is a strange thing to read. Almost everyone recognises themselves straight away, and almost everyone finishes it knowing what to do next.

A gold fountain pen nib resting on watermarked writing paper

Read

How you take mathematics in. Whether the symbols read easily or slowly, and whether you can tell the difference between really understanding something and just recognising it.

Fluency · Calibration · Reading

Write

How you put it down on paper. Whether someone could follow your working without you sitting there to explain it, and whether it is an argument or just a set of steps that ends in the right place.

Expression · Argument

Think

What you do when you are stuck. How long you stay with a problem before you give up on it, what you try, and how you handle mathematics nobody has taught you yet.

Independence · Abstraction

Ninety minutes cannot show everything. How you work over a whole term, and the ideas that only turn up on the fourth day of thinking about something, will not appear in two sittings. I say so in the report, because you should know what it could not see as well as what it could.

What it does see, it tells you clearly. You will not get told what kind of student you are. What I watch is what you actually do, which question you opened with, where you slowed down, what you reached for when you were stuck. That is what the feedback is about, and every bit of it is something you can change.

R1 500

Credited in full to any course that follows.

Two sittings · About ninety minutes
A written assessment of six to eight pages
A covering letter to your parents
A report for your teacher or tutor, if you want one
Book a sitting

Sittings are arranged personally.

Leave your details and I will write to you to arrange the two sittings and to settle the fee.

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Thank you. I will write to you personally to arrange the sittings.