It’s an age old question:
What relevance does Pythagoras’ Theorem have for everyday life? As we may scratch around for an answer we may begin to wonder about maths itself.
I taught a lot of maths to young children; twenty two years in all. I’ve had to deal with such questions many times.
If you were to type either question into a search engine, the results would be totally unsatisfactory. Even specific statements like “Ten important reasons for learning maths” produce lists of vague nonsense barely relating to the heart of the subject.
For starters, most of the results are American, where they call it math. It’s maths. How can such a massive multi-aspected complex array of information, concepts and formulae be referred to in the singular? It’s not a word like fish.
A lot of the “reasons” do not go past the ideas of sorting and gathering before going on about helping us to get a good job, dealing with finance and earning a good wage.
This is frustrating for someone (through teaching) who has developed a blood relationship with the subject. But it’s difficult. I can feel the relevance of maths. I instinctively know how it helps us in our daily lives but putting it down on paper takes weeks, nay years of focused thought and organisation. (There are two significant factors linking maths and real life for starters.)
I’m now going to attempt to explain it all in a clear succinct manner without inducing the usual soporific vibes which have haunted far too many corners of learning when the “expert” spouts and the “victims” try to fight off the yawns.
Such is my arrogance, I assume everyone will read to the end of my posts but this time I will simply say “please read to the end”.
By the time children get to year six, the different areas of maths should be clear:
Within each subtitle lies a multitude of factors designed specifically to stress out pupils, parents and teachers alike.
Any teacher will know that parents’ questions pertaining to maths and real life can create severe twitching and nausea before spouting a garbled bag of nonsense. In the early days I would blind them with science. My highly specific esoteric references would create that familiar blank smile when you have lost them by the second sentence.
Of the four above, measurement explains itself. The statistics area has been rebranded from “Handling Data” which again, has obvious links to real life. From experience it’s the other two; number and geometry which can leave many people jibberish, sitting nonsensically in a pool of befuddled swirling sticky matter. And that’s as technical as I’m going to get. So what use is number?
The bane of so many children and parents is times tables. The chanting, the testing and the whole apparent detachment of them from anything resembling reality gives them a unique air of mystery.
Aleady, I can feel myself creeping into a mire of detail which would have us arguing about finicky details, sinking away from the salient points in a vessel of despair and frustration.
I will therefore use the word “modelling”. Number is a tool through which we learn routine methodology and problem solving. Number gives us strategies to make sense of our everyday lives. In every aspect of learning and living we need memory. Hello times tables. I’m tempted to go into great detail of their value but I stop because I’m hearing someone shouting “but we’ve got calculators”. True. So what? Isn’t technology wonderful?
Times tables are a key to opening up the more complex operations which “model” the daily problems we encounter. In relation to the more difficult processes in maths, times tables at the very least show the value of memory. They also show how anything, and I mean anything, can be can be expanded (or exploded) by one other factor. It’s a basic scientific premise. Yes we might learn things instinctively and through experience but number models how to make sense of it.
Sorry, I’m drifting into teacher training text book mode here.
Write it down!
In maths we write things down in a specific order with numbers and signs. That’s a great model for so much.
To do lists, staff rotas, working out cause and affect, expanding ideas etc etc. For me, the most valuable use of number is working out the unknown from what we know. We generally call it detective work. Hercule is a fine example.
This is where I go back to Pythagoras. If you know the formula, (let’s call it a recipe. That word has more practical significance) you can work out the unknown length of the side of a triangle from the length of the other two sides. Short of finding the height of a tree or a telehraph pole, this does not appear useful. But learning to put things on paper in an organised way is. It can even be related to shape.
The trouble is, Pythagoras Theorem is a complex matter using number and shape in an abstract form and can leave the poor old student in a mess because they are right out of their zone.
There lies another highly significant aspect of maths. Taking yourself to the edge of your knowledge, experience and comfort need not be a cause of anxiety.
Through mathematical processes, we can begin to make sense of these danger areas by applying what we are familiar with and drawing conclusions.
This is very much a whistle stop attempt to make sense of maths and well done if you’re still with me here but I will finish with a reference to geometry; that’s shape and space in junior school talk.
In geometry we learn about classifying through observation, explanation, accurate (and rough) drawing and number. We learn to use instruments such as protractors, rulers and compasses. Isn’t that such a useful model for so many things we do?
Maths is the mini beast of learning. We learn so much from its processes but because it uses number and vague terminology it’s easy to get lost. This is where the skill of the teacher comes in; sometimes missing unfortunately. If a child “doesn’t get it” for the fifth time, the teacher needs to make subtle changes rather than saying the same thing, only louder.
Mathematics uses number and other representative symbolism because like music, it is a universal language. In our modern age however, technology is obscuring our essential learning needs. All I can say is that the most successful mathematicians learnt their times tables and success in maths sets you up well for life.
My final hint?
If you find a complex problem, try it with easy numbers as a “model” for the more complex numbers. I can never remember how to do percentages on a calculator so I remind myself by doing 25% of 200.
I believe modelling is the real essence of maths.
Thank you for reading.
Just let it sink in and then reflect of the first thing you thought of. I see the bottle; a traditional squeezy thing with a tapered neck.
Then I realise that I haven’t bought a bottle of it for over twenty years. After that is a pang of irritation.
How could anyone prefer it to brown sauce?
Is this where I sigh and say “each to their own”?
Never. Ketchup is for sweet-toothed chocolate lovers too scared to risk the tongue tingling sensation of a feisty bit of brown.
At the risk of a vociferous lambasting from the freedom of taste thought police, I will proudly wear the symbol of the brown sauce champion.
I say this but some time ago, I found the tradtional ferocity of HP had given way to something a lot fruitier. It was an outrage. How very dare they start to dumb down its unique flavour just to suit the more modern palate?
There was only one thing to do. Look up brown sauce recipes on the internet. I developed my own; a truly beautiful thing. I even made a version with mint to go with the things that mint goes with.
Last week there came a revelation. In the spirit of that ridiculous Holman Hunt painting I stood up and cried “eureka”.
Well I didn’t actually stand up. It was a more “slap yourself and mutter words of mock self admonishment for missing the bleedin’ obvious” thing. On Masterchef someone made carrot ketchup. Oh my giddy aunt! The recipe was sitting on the printer before our two belicose brothers in gluttony had even tasted it. Then I made it.
Allow me to present my version of carrot ketchup.
450g (ish) carrots
1 big onion
5 garlic cloves
225ml wine or cider vinegar
225ml water/ tomato juice/tinned tomatoes
(I mixed a good squirt of tomato puree with water.)
2 tbs Worcestershire Sauce
1 tsp ground coriander
half tsp chilli powder
seasoning to taste
In a large pan, gently fry the onions. Allow the onions to caramelise a bit.
Add the garlic and fry until softened.
Add the carrots and let them soften.
Add the sugar, water (or your choice of liquid) vinegar, seasoning and spices and gently simmer until everything is soft. (About 45 minutes.)
Remove from the heat and allow to cool a little. Using either a food processor or a hand blender, whizz it all up until smooth and silky.
Check for thickness and either reduce over heat or add more liquid to your desired consistency. I went for the same as commercial tomato ketchup. It will thicken as it cools.
When cool, store in sterilised jars.
This is open to all sorts of variations. Make it as hot or as sweet as you fancy. I avoided malt vinegar; that’s strictly for chips. You can mix the carrots with any other root vegetable. Beetroot, sweet potato, a small turnip and parsnip come to mind. There are other classic combinations for carrots. Orange, ginger or celery for example. If you like celery it could be some celeriac or celery salt; celery itself might be a bit too stringy. Like the smug faced pouting Nigel Slater, I’d say “recipes are not to be followed”.
Actually, recipes are really useful. We need the guidelines.
Finally, what does carrot ketchup go with?
I have no idea but I’ll enjoy finding out.
Thank you for reading.
Fenwicks, Tunbridge Wells. I don’t much like going shopping but I promised Rose shoes followed by some cake and juice. The disabled toilet was clean but who the hell put the mirror there?
It only allows hair brushing.
The journey to Tonbridge was long. It will always be that way if you use public transport. But it was a chance to get out and be a human being:
Yes, I have decided that certain parts of the world are anchored firmly in times past. These are times we consider to be uncivilised. This extract relates to the streets of London in 1790:
“Tread wisely,” warned His Lordship gesturing to the ground. It was good advice. The surrounding floor was filthy. In amongst the dried mud and general litter were little patches of stuff too disgusting to contemplate. It seemed to have three different stages of decomposition. Firstly there was the new stuff, resembling the contents of a baby’s over filled nappy. It was slightly shiny and that is all I wish to say about it! Secondly there were the older deposits, looking pale and withered. Finally, the really old stuff had transformed into dried flakes which rose with the dust as people walked by. Then something moved out of the corner of my eye.
At the base of one of the buildings, I noticed the scamper of feet and flash of a tail. It was too big to be a mouse. Then there were more. Looking further along, a whole family of rats appeared to be going about the business of sniffing and inspecting every piece of human waste. As a group of men approached, they scattered and disappeared. I felt afraid to walk on such ground. It was as if the whole street was nothing more than an open toilet.