Menon mathematics
Private tutoring in Stockholm and online
MSc in Mathematics · MSc in Engineering Physics
As long as the problem looks like the example in the book, things go well. The moment it looks different, everything stops. The Friday test goes fine, but little survives the weekend. Most parents recognize the pattern, and tend to put it down to carelessness – or to maths simply not being their child’s thing.
I have taught mathematics from lower-secondary fractions to university analysis, and I believe in a different explanation. What is taught as mathematics at school is largely rote knowledge and mechanical calculation: the symbols, the recipes and the special cases, but rarely the thing itself.
An example: why are 13/15 and 26/30 the same number? Most students know the rule (“multiply top and bottom by two”), but few can answer the question, because nobody has told them: a fraction is a way of writing a number, not the number itself, and the same number can be written in many ways. (That, by the way, is what the equals sign means: one thing, written twice.) The rule changes the notation; the number stays put. Anyone who knows what a fraction is never needs to memorize the rules – they follow on their own. Anyone who does not can know a hundred rules and still not see which one applies.
The same pattern recurs higher up: students in upper secondary have often worked with functions for years without once being told what a function is, and derivatives are taught as though each student were expected to reinvent the intuition Newton and Leibniz had. They were hardly average.
So I teach in a different order. First comes the intuition: what kind of thing this is, and what it is for. Then comes the formal definition, because a concept has to stand firm before calculation can become more than following recipes. It may sound like a slow route to exam results, but in my experience it is the surest one: grades that grow out of understanding hold, term after term. And the grades are a by-product. What is really being trained is reasoning in steps that hold, and saying exactly what you mean – the kind of thing that stays with you long after the last exam.
“He has a philosophy behind teaching math that helped my son see past the confines of typical gymnasium math teaching. Top marks all around.”
Parent of a gymnasium student
About me
My name is Axel Zibirov. After a degree in engineering physics and a master’s in mathematics, I pursued doctoral studies in algebraic topology and worked as a mathematician in industry, before turning to teaching. I hold a Swedish teaching degree for upper-secondary mathematics (ämneslärarexamen).
I take on a few students at a time, so that I have time to think about each of them between lessons as well. The students I work with are in lower secondary, upper secondary or at university – it is the same subject the whole way up.
Practicalities
Lessons take place at the student’s home in central Stockholm, or online. A lesson lasts 90 minutes and costs 1,350 kronor.
The first conversation
Get in touch and we’ll book a free first conversation to see what I can contribute in your case. A couple of lines is plenty: who the student is and the maths in question.