The Challenge

There's a challenge to taking on new students. You have to dig deep, work on the puzzle for a few weeks, and then try to find the way to lead them through the barrier that's keeping them in the dark. Most of the time, you make it through, but it's still difficult enough to be a challenge. How do you get on the inside, to see what's blocking the way?

Sometimes, it's obvious. There's a misunderstanding that can just be put right, and then they roar away and you help them catch up. On other occasions, it can take hours and hours to reach the problem, and only then if they allow you to get there. Deeper problems come with a defensiveness that can defy many attempts to help. Everyone has a deep-seated tendency to say 'I can't do it.' when they find something difficult, after all. Everyone can do arithmetic, though. It's a minimum level reachable by all, if the student hasn't been undermined at some crucial stage.

Why do people say, 'I can't do it.', so easily. Is it all down to the inherent laziness of the brain? It's fairly well known that the brain is fundamentally conservative (small 'c') and that it discourages the formation of new patterns of grooves in its structure. A therapist told me that on a passing occasion, so I choose to believe that it's true. That's why people are so prone to not learning new things as they get older. It's not just that it's harder, which it of course it, but that biology itself resists. This is a reason why pessimism is hard-wired into the human psyche in many ways.

So, if you have one student who is convinced that arithmetic is hard and that they can't do numbers, then you really have to start to find leverage and work not on the arithmetic so much as the mental block. That's the hard part. That's the challenge beyond the challenge, and it's where a slip up can make things so much worse than better. Oh, for an easy life!

O.

It Doesn't Have To Be Dull, Surely?

(Originally posted on sister blog, 'The Quirky Muffin'.)

While writing numeracy questions for my GCSE students, which is often an onerous chore, I sometimes get to thinking about how to make things more interesting. Or funny. Or both. It shouldn't be impossible to make practice questions interesting, should it? For that matter, why do exams and examples have to be so humourless in general? Students might do a little better if they weren't locked into quite so grim an examination mindset. Ah, for the good old days which never happened! I don't remember that time when the whole exam wasn't themed on raising dragons in Hyborea...

How can numeracy questions be made more interesting? It's a tough question. The standard and most substantial numeracy question is often about a business and its dry income and outflow, and how it all adds up to a net result. How on Earth could that not be dull as ditchwater? (Note: Must find out why ditchwater is the epitome of dullness. With that much life in it, the results of consumption would be anything but dull!) Well, what if we changed from a business to a person, some kind of unusual person? Or a spacegoing cruise line? Or the president of the United States? What if we looked at the bizarre budget of Count Dracula, Baron Frankenstein, or Sherlock Holmes? What if we had to go through the oddities of conversions in barter cultures, or societies that trade via pigments, odd rocks or the sculptures they make in the backs of their caves?

We can literally do anything while making up practice questions. They don't have to be super-conventional and super-dull, they only need to cover the material that will be presented in the exams. It's early days, but progress is being made, and the beginnings of a portfolio are being put together. It's amazing how even the brightest of students have been stunned by new numeracy papers, and presumably were similarly stunned by their previous analogues. We'll get there in the end, with some examples that lead and some that challenge.

In other affairs, if anyone runs into a camel marked 'Abu Dhabi Or Bust', please contact the Quirky Muffin. The story is long, involved, and connected to the mysterious disappearance of said camel from the audience during a recent performance of 'Ooh, That's Not My Fish', a satirical comedy on the connections between frozen strawberries, maniacs moving into the White House, idiots running Downing Street, and the reasons why triangles are under-represented in nature. The camel is a material witness.

O.

Results Day

It is finally here. The results day for my first bunch of GCSE students has been and gone, and they did pretty well. Congratulations, examinees! The only annoying part is that the Maths Numeracy paper scuppered practically every single one, garnering grades one rank lower than the mainline Mathematics paper. It's supposed to be the other way, if there's a difference at all... In any case, it seems highly suspicious, and I'm sure a huge load of re-marking is even now being requested of the exam board, whose name shall not be mentioned. However, we all know who they are...

It was a good results day overall, apart from that institutional snafu, with everyone hitting their targets in Mathematics proper. The tension is over for another few weeks now, before the next exam season kicks in. And then the next. It's a maddening system! Oh, why so many exams, exam board who will not be mentioned? Four exam sessions doesn't seem excessive at all?

Back in the old days, when I had to actually sit the exams instead of prepare other people to sit them, it was never a particularly tense day. At school, you would turn up and get handed a very unattractively shaded piece of paper with some titles and grades on it, and then you would just go back to your usual day. At university, you had to sign in and look at a badly designed web page. It was never very interesting or nervous, from the point of view of a confirmed idiot savant. It is only now that results day actually provokes nerves.

Well, that's not entirely true. There was one results day which was nerve-inducing, one examination process that couldn't be predicted. You have to feel nervous for your doctoral viva voce exam. It's impossible to not be so! That was a nervous day indeed, and not just because I had to go to London and do it there because of freakish scheduling!

In any case, it was results day, everyone made it through. Let's all be happy.

O.

A Sonnet

A sonnet is a type of poem, most popularly mastered by Shakespeare, who wrote far too many of them! It is a sequence of three quatraines, culminating in a couplet. A quatraine is a four line poem, and a couplet a two line poem. They can all have independent rhyming schemes but should be in the same meter, which is normally iambic. (Iambic meter is composed of pairs of syllables called 'iambs', the second of each emphasized.)

Here, to prove my credentials as an English tutor, is a rudimentary sonnet, composed in a great hurry, and with awful meter. Iambic it is not, but a good start is a good start. All writing is a study in multiple drafts, after all...

'Sonnet I' by Oliver Bain (2016)
(also known as 'The Time Travel Sonnet')

I fly through time, a rover back and forth,
Righting wrongs and seeking a pathway home.
With each flash of light, facing south or north,
My feet might touch past sand or future loam.
The first time was a trip to Rome by boat,
The next a jaunt to the Moon by balloon.
The third was a meal with an old dragoon,
But next I was chasing an angry goat!
How long have I been bouncing to and fro?
How long until this tale is fully told?
It was meant to be a test, a brave go,
With our time machine, which will our past fold.
When will I land this time, when that flash fades?
Home at last, the past, or green future glades?


O.

Five Tidy Squirrels

Who doesn't need a little help with mathematics from time to time? It's a hard subject, after all. It's not just adding up numbers like a human calculator, but a whole set of related skills, all embedded into a greater system of puzzle solving.

Helping people with mathematics is one of the greatest parts of being a tutor, and knowing the right way for any given student can only be the product of experience. Do we need to go back to the basics for a primary school student? Does this student need to have things explained visually in order to understand and prepare for their GCSEs? Why do we learn long division at all? How does it all fit together?

Having gone through the whole education system, from primary school to PhD - with GCSEs, A Levels, an HND and a first class honours BSc between - I know how it all fits together, and why. That holistic knowledge is the advantage of getting a private tutor for one-to-one mathematics tuition. It does all fit together, and if someone is confused at school then they've probably missed the important connections.

That's enough promotional blather for now. Let's have a maths puzzle instead!

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The Tidy Squirrels

There are five very tidy squirrels, who have thirty five acorns in total. One day they decide to line up so that each squirrel has one more acorn than the one before, for a group photograph. How many acorns does the squirrel with the least have?

Reading Material

Working out good reading material for your English students can be a daunting task. Do you stick to approved texts, matched to whatever teaching system is used at school, no matter the flaws? Do you go for classics stories that will drag in anyone who starts reading them? Do you aim low or high for your students, who might have been let down in the past? Do you classify some books 'for girls', and others 'for boys'? It's tricky. However, here's a selection of books that might hit the mark, although they might aim a little high, given my own precociousness at school.

Key Stage 2 Lower

'Mary Poppins' by Dorothy L. Travers
'The Story Of Dr Dolittle' by Hugh Lofting
The 'Secret 7' stories by Enid Blyton
The 'Engine' stories by Rev. W. Audry
'Winnie The Pooh' by A. A. Milne

Key Stage 2 Higher

'The Magician's Nephew' by C. S. Lewis
'Five Children And It' by E. Nesbit

Key Stage 3

'The Hound Of The Baskervilles' by Arthur Conan Doyle
'Pawn Of Prophecy' by David Eddings
'The Last Dragonslayer' by Jasper Fforde
'Amazon Adventure' by Willard Price

O.

Times Tables

One of the ways in which the teaching of Mathematics can go badly wrong is in not providing enough context for why you're teaching something to someone. A classical example is that of the times tables. Times tables are useful for a number of reasons.

Firstly, when taught well the times tables provide the basis of pattern recognition. Look at a grid of numbers in rows of ten. Every time you add eleven, you move up a row and across one, and build a diagonal on the grid. On the other hand, every time you add seven you move up and a row and across three in the opposite direction. This, along with the use of musical rhythm is an important aspect of the topic.

Secondly, and more obviously, times tables assist in the formation of multiplication ability.

Thirdly, learning a pattern of multiplication is immediately useful for learning the basics of division. Witness in wonder:

3 x 6 = 18,

3 x 6 ÷ 6 = 18 ÷ 6,

3 = 18 ÷ 6.

This means that for every line of a times table you learn, you also learn two division facts. Actually for every line of a times table you also learn two multiplication facts, as:

3 x 6 = 6 x 3.

It's not just simple division that runs on knowing tables, though, as short division becomes incredibly easy if you know these facts. Just last week, I demonstrated that by knowing short division and the thirteen times table, you can divide any number, no matter how large, by thirteen. Every real number. What's a real number? Well, that's a question for another day.

How you teach things is important, and it's not wrong to explain why you're doing it.

O.