"If maths were food, what food would it be? MajorLeagueTeacher
I'm not being that clever with my title here - many, many people have used the connection - as in this photograph above, which I now see, as I look at it, has all sorts of maths in it. Not just the symbol for pi, the shape of the pie or the numbers. What about all those lines on the tea towel - there must be maths in that? and I'm guessing - because I am not a a maths expert - there is also a lot of maths involved in the folds of the tea towel and the degrees of browning on the pie's surface - not to mention the shapes of the numbers and the pi symbol.
And what about fractals? There's got to be some fractals in there - a pattern that repeats forever. Such a wonderfully mysterious and philosophical concept it seems to me. The tea towel itself and the pattern of the lines, must have some fractal component I would have thought. If you look up fractals and food you get the romescu cauliflower a human creation through selective breeding. So I imagine there might well have been some maths involved in its creation - as well as biology and a whole lot of other science - not to mention maths' close relative, economics.
But back to maths in general and food - and please note I am saying maths not math. Why did the Americans decide to drop the 's' I wonder? Perhaps a topic for the food and language curriculum.
In fact before I embarked on this particular curriculum topic I thought I might not find much. How wrong can you be? So much so that I don't really know where to begin. Perhaps with my own basic maths education. I don't remember maths ever being directly related to food either at primary or secondary level, apart from the occasional problem involving fractions and counting.
I used to be reasonably good at maths in school - I was in the lower half of the top stream for maths at my school - I think we were streamed into three classes. I thought algebra and trigonometry and logarithms were rather neat and pleasing. Mind you I wasn't that great at mental arithmetic or calculations - those sums about taps dripping and filling up baths and trains potentially colliding. I wasn't all that interested in theorems which seemed to make up most of our geometry classes, but when we got to calculus, and even ratios I lost it. A step too far for me. I never got to learn to use a slide rule or get into the more abstract concepts of algebra and so on.
But then most of us don't. And yet. Even the home cook uses maths every time they cook, even if they are not cooking from a recipe - winging it. In your head you are doing mental calculations about how much of a particular ingredient you need. How much salt is too much, is that too much liquid, if you've got that many tomatoes how much basil do you need? That sort of thing. And yes, it's as much about taste and just general judgement, but you don't arrive at those kind of things without some idea of weights and measures and proportions.
And if you are working from a recipe - well there are numbers everywhere. Take, for example this recipe picked almost at random from the latest Coles Magazine. Not quite at random because the picture featured three different geometrical shapes - which could be useful language to transmit to a small child - a concept and words at the same time.
Quantities, time, temperatures - the quantities being offered in two different systems - cups and spoons, versus the metric system of weights. If this was an international publication you might have pounds and ounces as well, and Fahrenheit and Gas mark temperatures. Thus you can deduce - if you're good at these things - how many grams in a pound and so on. Size - also given in metric, but you might have to convert to inches - or even more difficult - you might only have a round tin - oh dear do I have to do a conversion here? And how many portions can I get out of this? They say 16 but is that true? Can I create more? Or less?
Then at the end we have percentages, with all the nutritional information.
Of course, these days, it is possible to look up the conversions you might have to make on your phone - but what if the battery has died?
For chefs the use of maths is even more crucial:
"A chef’s routine includes simple to complex math calculations. Examples include counting portions, increasing a recipe yield, determining a ratio for preparing a stock, calculating a plate cost, or establishing a food and labor budget. Culinary math begins with the basics of addition, subtraction, multiplication, and division along with ratios, yields, and percentages. Ingredients must be measured and scaled accurately, food production quantities are calculated, and recipes are increased or decreased to scale based on demand. Math is used for portion control, to maintain consistency in production, and to compute food costs. Mastering math leads to better results in the kitchen through accuracy and consistency." The Culinary Pro
And all of that, of course, applies to industrial food production - along with all the maths involved in creating the machines to do the production and delivery.
Did prehistoric man, or even Neanderthals use maths I wonder? Did they count things? They would surely at least have had some idea of how many people were in their particular tribe - would notice if any were missing - and how much food was needed to feed them all - or am I giving them too much credit? If you went missing maybe nobody noticed, or if they did they probably couldn't do anything about it. If there wasn't enough food then there wasn't enough food.
Counting and calculating however, are the first forms of writing, maybe even the root cause of man creating writing:
"Cuneiform was a mnemonic device designed to aid accountants and bureaucrats" Jeremy Black.
Commerce indeed has a long history. This tablet apparently recounts the receipt of some oxen.
Prior to maths being written down it would still have been used - for recognising the passing of time, for counting things, for measuring things, constructing, and so on, although the counting methods may well have been different - using the natural world, the numbers of fingers, sticks ...
But I'm straying somewhat from the notion of a food-based maths curriculum. Mostly food is not involved at all in the maths curriculum, although if you tackle it the other way around - learning about food - then maths will inevitably creep in. Maths probably creeps into almost everything. Indeed like writing itself some of the first picture books we encounter are counting books - those and alphabet books. Children are fascinated by numbers - I distinctly remember at one point thinking that they saw everything in terms of numbers.
At a primary school level you can imagine contriving various food related maths topics but what about secondary school? Well I found one example from a British organisation called STEM Learning which, along with other projects had a food based maths curriculum which it described thus:
"In these activities students use a variety of mathematical skills in order to complete the tasks, each set in the context of the production of food and drink."
The curriculum is explained in outline - each segment having a foodie based title - for example:
"Fruit pies - In this task, students are presented with the problem of finding how many circular pie tops and bottoms they can cut from a rectangular sheet of pastry. Students are given the diameter of the top and bottom of the pies, which are different, and the initial size of the sheet of pastry. There is an added twist to this problem as students can take the left over pastry and make a second sheet of pastry from which further tops and bottoms can be cut. Students are required to break down the problem into smaller steps, use logical reasoning, perform accurate calculations and communicate their findings effectively." STEM Learning
I assume they don't actually have the pastry in front of them. They have to do the calculations in their heads. So much more than maths involved there really or perhaps a bleeding into other fields of knowledge - philosophy, communication, writing.
"People focus quite a lot on, ‘Do you know how to solve a quadratic equation?’ And actually, the really important skills are about critical thinking and looking at something and deciding whether it makes sense or not. I don’t think you need to be particularly numerate for that.” Hannah Fry
Other topics covered different concepts, and I'm sure there are ample opportunities for elaboration - even complication. Take this example from Eugenia Cheng on the Science Friday site - and here we are back to pi - as the problem posed is: "Methodically slice up four pies to reach the irrational number pi." As part of the preamble she says:
"Every child knows how to make their pie last: Eat half, then eat half of what’s left, then eat half of that…and so on. The part that’s left over will get smaller and smaller until eventually you can’t even see it any more, and the total amount of pie eaten will get very, very close to one, although it will take forever." Eugenia Cheng/Science Friday
Which possibly takes us back to fractals, and infinity - another very abstract mathematical concept, but then I'm not a mathematician so I'm not sure about that.
Mathematics is perhaps, maybe physics too, which involves a lot of maths, it's perhaps the most abstract of subjects that we learn at school - well maybe philosophy as well - not that I learnt philosophy at school - and that too is related to maths through logic. Truly everything is connected - once you start looking into one very particular thing, you find yourself leaking into everything else.
One final thought on linking two apparently disparate subjects such as food and maths, from the learned Nutrition Journal:
"Nutrition education programs in schools have been effective in improving children’s knowledge and behaviours related to food and nutrition. However, teachers find it challenging to implement such programs due to overcrowded curricula. Integrating nutrition with core subjects such as mathematics could potentially address time constraints and improve the learning of both."
POSTSCRIPT
I almost forgot this. I'm not sure how I would fit it in to my mini discourse on maths in the food curriculum, but I thought it was so fascinating. A completely everyday thing, with such a complicated mathematical history - so complicated that a supercomputer had to solve it. This is advanced stuff. Should we be distressed that such ingenuity went into creating something so - so - what? Irrelevant, bad, wonderful, imaginative, pleasure giving .... Maybe if we can do this we can solve the climate change problem pretty easily. I have to say that I often think that it's engineers who will save us all and make our lives better.
Like wow really.