What is the hardest part of teaching? part 1

On of the weirdest things about teaching is how aware one ends up of the multitude of contradictions and paradoxes that infuse education, and do so at so many levels. In a sense I think this is an expression of a very deep expression of the complexities and contradiction inherent in adult expectation of children. Parents not only want their children to well, but also want the same children to face down the ghosts those  parents were haunted by a generation before: More than that their kids give then younger eyes on the world again, a world that has shifted from when they were young, a shift they want the education of their kids to reflect (but not too much).
  Moreover the wider adult community is incapable of seeing kids for the tangle they are. It rather resolves them, and what we teach them into crypto mythological debating points, about behaviour and standards, and duties and success and failure:: A constant stream of platitudes from the media/political classes that is about ideology, or perhaps mythology. It is an a series of statements and expressions, tied together in a loose argument (but really a legend) about where WE (Britain) are in the world, and the FEAR about where likely to end up... We as a nation project then our fears of failure on kids, and what we teach them.b All of which in a sense is ok, and natural, but adults are so pompous about all these feelings, and think that they must not confess them to their kids (who know them anyway), or to themselves.... 
From which it follows that the 'debates' we think we are having are frankly senseless or at least so abstract as to become pointless, be they about standards or teaching method or whatever. and the result is of course by and large a lot of pointless meaningless, if passionate discussion, which is more about the society 'living' being a democracy, than it is anything real (and so a myth). It certainly does not really reflect life teaching. The only direct link that exists between the two worlds comes when one of these debates creates a movement in the syllabus which rips though the class room, changing what is taught (and forcing the school to by new products or send teachers on training days - so spend money)... Occasionally one scoops the gold with these reforms. Those of you have read my blog will know I am a fan of the current GCSE syllabus, finance and tax  is so much better when taught by mathematicians who really understand the maths, than it is by any other set of teachers (or at least that is my prejudice). It also allows one to generalise and to show how maths and our treatment of statistics underlines the way we think about society.... but the reform clearly will not last very long, and we will be back to the mythology of teaching soon.
 As a teacher one is therefore attempting to hold down all these fears and allow them expression, while also actually helping individual kids learn about the world they are meant to be learning about. That is the topic one is also trying top teach them. The problem of course is that this topic is so far down the agenda. One has so much more to manage first. For as I said before kids know that what they are being taught has more to do with adult fears and feelings than actual reality, and they really resent it , and why not. It is after all an abuse of power, if one made in the name of education. Getting them through this antipathy and towards what actually matters, and showing them that some of what they are being told is useful and even vital, is for me the hardest part of teaching. The problem is one of trust, as much as anything. A trust that this mythological debate with all its inappropriate passions does not help at all.. The problem is therefore one cut through all the guff to the actual reality of how how helps another person restructure their minds (for that is what teaching really is).
 Or to put it another way, we have created in schools a real paradox. In most human history, myth and education are the same. The myths structure then mind and that is it. But here and now, in our schools, teachers must run counterfactual to this age old truth as they teach. Our knoweldge is almost opposed to the myths we have about it (or at least it is in maths). This single fact makes teaching so very much harder, but if I am honest it also makes it so much more fun!

When is the time to get a maths tutor?

Just in case anyone is thinking shall I get Maths tuition for a summer exam?
 - Now is the time to do (November). Just just before Christmas.
If you wait until February or even even April a tutor will do there best, and make some difference (firming up grades) but it is very hard to make a really significant change as it is hard to cover the entire syllabus in detail, and do the necessary practice for questions. What one can do effectively is therefore restricted (there is only about seven teaching weeks, given easter from end of march on June...)
If you start in November though, everything is still up for grabs. One can make a really big difference, as one can cover all the syllabus, and have time to look at questions in detail.
 So if know you need help, do not wait for the mock in a few weeks time, act now, and make that difference!

What really impressed

I am, as a teacher, always endless impressed by the sheer pluck and commitment of most my pupils. Oh you get some who are time waisting, but very very few. Most do actually want do well, and it is one job as a maths tutor to make sure they do (and know they can). More than that it is also part of the job to nurture this desire, and make it matter, in the face of natural laziness, but also, even more of school expectation.
This desire to achieve is sometimes (well, to be honest in the maths tutors world, it is often), frankly in spite of their school's expectation of what they can do, and were they have been set in class. An expectation that of course a self fulfilling prophecy. For most schools only teaches the full syllabus to those it thinks are up to it, and the rest are often taught much less (so they can only get a C), - and what is more many of my pupils (and their parents) have not been told this fact. One of the jobs of the maths tutor is therefore to tell them this, and see what they want to do. At this point pupils face a simple choice: Do they want to achieve what the school expects or do better? And if they want to do better (and they all want to), are they going to work hard enough to ensure that they will get where they want to be? And what so impresses me about my pupils is that they not only want to do better that they are meant to, but, if suitably inspired, will work hard to do so.
It is my job therefore to ensure that this work makes the difference, and that they can really get where they want to be. It is this aspect of maths tutoring that I love, and that keeps me teaching, and keeps me inspired.

GCSE - and the thrust of the written

When all is said and done - as I have made clear in this Blog, maths is more a game of writing, than counting. Write it in way that tallies with your eyes, and your expectations, and it is clear and easy - but if you do not you have not got a hope.
Yesterday's lessons were a classic example.
 Yesterday's three separate sessions (with maniac drives between in the devon-county dark, with famers harvesting, and forcing me and the transit to reverse half a mile, in the dark....But that aside), illustrate this point very well.
Each of the pupils I saw I taught caught a different aspect of this problem. The first, who was sitting an exam for a second time, in the hope of firming up a C into a B, is in an exam where one needs to experiment greatly with numbers-  and hates it. For him maths is all about getting the answer done (a reasonable proposition - unfortunately one not shared by AQA linker maths GCSE). For AQA numbers are about play and experimentation. The Examiners want you to  pull out formulas which you have never seen, and things you do not know from the maths you do know. To do this one simply has to write down the formulas, and then pull them around, again and again until one gets the answer. It takes a lot of trust, but also a lot of confidence in the fact that one is writing it down right and well. If one does not have either the show cannot get going. The problem for this pupil is, as is so often the case, he does most of this maths on My Maths and no one has ever (well apart from me), really worried him about the writing down of equation (I have always thought he has been taught them by his school in a way to make them easy at the simple level, but so much harder at the level he is now on). The result is that he will not even start to play. He sees what I have done, but cannot get going  himself. What I will do is attempt of the weeks to persuade to starting on the pretext that he 'might get a method mark if he always does this...' - only once we have got going do I think he will turn round and suddenly get it!
The second pupil (three tractor reverses away), is younger and had another version of the same problem. For her it is all about narratives. She understands (although does not belief she understands) the individual calculation quite well. But what she cannot do is tell a story with the figures - and unfortunately she is in an exam (Linear Edxcel GCSE ) which loves its stories. One does not therefore only need to count, but also describe in figures, and keep the narrative going. In teaching her therefore I am still very much trying to explain to her what she cannot do - because she does not really know. What she thinks is that she cannot DO MATHS, what I think though, is that she cannot make maths tell stories.... Once this become clearer to her (and we will need to do a little more method work I think to make it so), then I am optimistic she will be fine, if I can get her through the collywobbles that far.
 My final lesson (another long drive to the coast though back lanes away), same problem, but again in another setting. This one was a pupil half way through a foundation GCSE exam. She had done one exam yesterday (and was very confident), but had others to do. What she lacks, again is the basic ability to know where to being in any question if it is at all complex. She can do perfectly well short questions, but does not want to try longer ones. My break though with her (she is a dancer) was to persuade her that maths is just another performance (which it is). To understand the kind of wordy questions she is having to do in her GCSE exam one needs to role play! That is one needs to pretend the numbers make sense and are about ones own life, and not merely a faceless set of nothings. It was this basic move that made the difference I think for her. It made the numbers feel like something, and do so even when they do not make sense (and actually her mental maths is a little weak).  Once she gets the part, she understands the problem, and how to write it down.
 Three very different pupils, three different solutions, and yet one real problem, Modern GCSE is a game of reading and writing in a  weird way - and one needs to be endless creativity to teach that oddity.

Best of luck!


 So here we go again - it is another exam day (there are so many in a year). This time it is aGCSe: some school are doing the EdXcel Unit exam, while others are taking the full foundation GCSE now, so that they have a chance of retaking it later, or upping their grade to the higher exam. It is an exam school are putting their weaker candidates in, or else those who are out the proof the school is wrong in their setting or treatment of the pupil. I am therefore peculiarly interested in the results, which are due in January.
So keep your fingers crossed today!.

What makes a maths tutor different? Part 1

The second great thing I think one to one maths coaching can offer, is that it alone can actually watch where you go wrong/ i spend my time in tuitions teaching certainly, but also listening y really carefully to what I am being told by my pupil as the work though a problem, but also watching their face and their pens. one therefore spends ones time actually watching thought as it happens - in all its hesitant beauty, and layered complexity.
 The job is then to work out exactly how and when one needs guide the other persons thought process. I personally am a great fan of doing a little as possible, But doing soemthing. I will tap the paper therefore on a sing, or raise an eyebrow, or sometimes re-ask the question. thee point being that i am trying to teach how one notice and then reacts to that observation in maths. the game in the subject is never not to be wrong, but merely to write down in such a way that one naturally notices or looks for ones own error.
If I get the 'correction' right, therefore it should feel like for other individual it is them that is noticing the problem, it is their eyes and their brain - I am merely showing them where and when to do it.
 And yet of course this isa  risky strategy. when it works it is great,but you have to be so careful. It is so easy to not be helpful, and merely be irritating. Each pupil is different not only in the way they  think, and the exact place they make errors, but also, and just as importantly in the way the way they like to locate those errors. one needs then to have also ready the 'stock tutor' methods which allow for one to find errors through very formal writing down of methods - a formality that is certain aspects and at certain times is astounding useful and powerful.
 What maths makes tuition so difficult, and so powerful at times (and given the right relationship), is that one can teach the real brain on skills that gets you through maths exams, skills that one cannot teach anywhere else i think, and ones always worth having - they the skills that allow one to be self critical, and reflexive.

Getting them grade up

What is it that really makes the difference in grades?

This is a question that haunts all maths maths teachers I guess - the job is after all to make a real difference to grades, and so lives.
There are of course many answers to this question.One needs good written methods, one needs patience, one needs confidence..., All of which it is of course the maths tutor's job to add.
And yet the philosopher in me knows this is not really it. What one really needs for maths is rhythm. Maths is a game of noticing, writing, checking and experimenting. Problems then come in maths because no one really teaches (or even seems often enough to appreciate) exactly how one orchestrates these facets of 'doing maths'. This is a real problem, as kids want permission, they crave to be old what to do next, and the point of the maths exam is exactly that one is not told, on has show initiative, and think: One needs therefore to impose ones own rhythm, ones own inner knowledge of what is next (and why). This is genuinely terrifying - it is what scares adults about maths: They never know what to do next....
 It is no surprise that most of the time when a maths teacher is called in it it is because one or other of these elements is out of sync with the rest and the rhythm has broken down. It is your job, as a maths tutors to get them all lined up with one another, as best they can.
 What do I mean when I say maths is rhythm. Only this, to successfully navigate a question, one needs to know what one is doping and when: all too often mistakes happen because one tries to do every at once. Or even worse one gets right, but at the wrong moment, and that stifles ones ability to think what one has done, and actually know what one has worked out. It is only rhythm that defines when one is thinking, when one is looking and when one is writing: whether one is good or not at maths in the end is all about rhythm. A rhythm some kids have innate, and other have to be taught.
 To teach maths one first needs  always to check that pupils know how to notice, think, write and correct, (all of which are real skills in their own right, and again never formally taught) - but in the end grades are made or lost of rhythm. If you know what should happen next, what you should look for, or check or write it is all so much easier.
It is the rhythm that makes the difference between knowing what to do in  question, and seeing that it is so easy, and being at sea with it all. It is therefore the first and last job of maths teacher to give thought rhythm!