"Factorise: x2 - 13x + 40," said Edwin’s Maths homework sheet.
I detested my year of doing Maths AO level when at school, hundreds of moons ago. I had a rubbish teacher who gave all his attention to growing a shabby beard and the greasy haired boys on the front row who were destined for Mathematical greatness and super-strength spot cream.
In my first year at school, for some reason unknown to me, I was considered to be good at Maths and so I was rewarded with the joy of doing the O level one year early. Great. I was then given the exciting, apparently it was, opportunity of taking the AO (Additional Ordinary) level course. Rewarded as I was with a grade C at O level Maths I thought that I could improve on it and soon afterwards got another grade C in the second sitting of the exam. I had clearly peaked, twice, and so mentally gave Maths up. I still had eight months of the AO lessons to endure and no amount of pleading would convince the tweed-jacketed, dandruff generating teacher to allow me to drop the subject. So I did the sensible thing. I sat at the back of the class and worked on my German instead. Being a good lad at heart though I did leave my maths books open on the desk and even looked at the board and teacher at the front of the class occasionally, appearances are important after all. And I am pleased to report that, after much struggling and hard work, I got a grade C, in German. I also obediently, sat the two AO Maths papers and, having little idea or interest in them, I came out with quite a creditable grade E. In the nearly thirty years since that last exam I have not given my Maths studies a second thought....
….Until recently that is. Edwin is currently doing Maths at school and has been introduced to the world of wonder and confusion that is Algebra. This week he has been inducted into the topic of factorisation. Teachers are consistently encouraged to explain to students why they are studying key topics and if I was told why I was tortured by Algebra 30 plus years in the past then I have buried that knowledge long ago. I have no desire to return to the distant days of 1986 to relive those Maths lessons, despite it possibly helping to improve my German. Being a supportive Dad and teacher I did ask Edwin why he was studying Algebra. Doubtless he had been told why but he did not appear entirely sure beyond saying it was just something that he had to do. Not satisfied by this answer I read a range of web pages suggested to me by google as the answers to my question: Why Study Algebra? The suggested pages were little help and could be summarised (a skill I learned in O level English) as because it is both good for you and will help you. Prunes, marathon running and supportive underpants are also good for you but one doesn’t have to study them three times a week at school.
But now I reckon I have found some, possible, use for one of the skill sets learned while battling the mysteries of Algebra and factorisation in particular.
Firstly though my understanding of factorisation, which I know might be wrong, but here goes anyway.
When the Maths student is confronted with such beauties as ab2 + 5ba - 36a and told to factorise it my sources tell me that they should not seek to find the answer, which to the Maths numpty like me, seems counter intuitive. Surely every question needs an answer. Apparently not. Factorisers should seek to break the collection of letters and numbers into the constituent parts of the sum by expanding it. My Drama teacher’s brain immediately wants to ask why, but that of course is an elementary mistake. I should simply expand it and expand it until I can expand no longer.
But hold on though, my Drama teacher’s brain thought earlier today. While I have absolutely no interest in the answer to 6x2 - 9xy - 81y2 (oops, remember factorising is not answering, Robin) I might just have some use for the skill that expanding this seeming gobbledigook could provide me with…
… When students are first confronted with IGCSE Drama monologues their initial reaction is “Have I got to learn all those lines?” As any Drama teacher knows, that is the wrong question. What they should be asking is “Why does the my character say what they say?” And to find out the answer to that question they need to factorise. What? Expand the words that are in front of them and start thinking about who the character is, what are their given circumstances, what do we know about the character that the character does not know yet (oh, the beauty that is Dramatic Irony), who are they related to, how do they like their eggs cooked and all the other questions that help us know the whole Juliet, Romeo, Leah (the DNA Leah, not to be confused with her kingly ancestor Lear) or any other popular character. Expand until the actor can see all the sums that make up all the parts of the whole character.
Next the IGCSE actor simplifies and combines all the sums and parts of their character and so performs it right (having of course conquered minor factors such as knowing the lines, getting their costumes spot-on, conquering their nerves and turning up on the right day)
So, there you have it. Factorising, expanding and simplifying Algebraic combinations is full of the same skills as those that are needed to tackle top quality monologues. It is finally useful to the dramatist and it has only taken me 30 years to discover it. Phew. And I got a German qualification too.