A mathematician, like a painter or a poet, is a maker of patterns… The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test.
How are most children taught writing?
Eight weeks ago I took over an AS English Language class in which none of the students had a clear understanding of the difference between a noun and a verb. How is that they have got so far through formal education with absolutely no explicit understanding of how sentences work? The answer, my friend, is that teachers’ own language skills are just not up to snuff.
I had an argument with Phil Beadle recently in which he maintained that he’d never met an English teacher who a) knew what a sentence was and b) knew how to use a comma. I was shocked. Could this really be true? Obviously I proceeded to demonstrate my own understanding in true show off style but this merely disguises the problem he was trying to describe. It really doesn’t undermine his argument to say, I’ve only met one English teacher who knows what a sentence is. (See below for definitions.)
Like most English teachers, I’m a graduate of English Literature and, like most people my age, I escaped any hint of grammar teaching in my own education. My great good fortune was to teach English as a Foreign Language (EFL) before becoming a ‘real’ teacher. I had to get to grips with my trusty copy of Michael Swann’s Practical English Usage in fairly short order to be able to field the steady stream of questions about present participles and phrasal verbs.
As products of this system, the modern English teacher is very comfortable discussing metaphor, alliteration and other literary techniques but is often rather out of their depths with semi colons and conjunctions. Needless to say, if we don’t know these things, there’s little chance they will!
My personal bête noir is the lie that you put a comma where you take a breath. I’ve lost count of the number of children that I’ve had to disabuse of this misapprehension: it is simply not true. That said, knowing that punctuation marks were originally notation for actors on how to read scripts does give some credence to this theory and while it’s still fairly useful advice that you might take a breath where you see a comma, it’s certainly bad advice for our putative writer. So what to do?
Well, the teaching of punctuation deserves a post of its own; here it is my intention to demonstrate how approaching sentence construction from the logical and precise stand point of the mathematician might be helpful. Basically, one has to start by knowing that a sentence contains the following elements:
- A subject. This is the noun (or noun phrase) about which the sentence is about
- A verb. This is the process by which the subject interacts with the object. It is not a ‘doing word’.
- An object. This is (usually) the noun (or noun phrase) with which the subject is interacting. Sometimes it isn’t, so if you’re not happy with object, refer to it as ‘other’. It’s all good.
For instance: I (the subject) am (the verb) a teacher (the object).
The observant among you may have noticed that I failed to label ‘a’ (an indefinite article) and that’s deliberate. For one, I don’t want to over burden anyone and also they aren’t required in a sentence. A better, purer example perhaps might be:
David (subject) loves (verb) English (object).
This understanding of the SVO structure can then be applied to existing sentences. Here’s one entirely at random from earlier in the post:
Like most English teachers, I’m a graduate of English Literature and, like most people my age, I escaped any hint of grammar teaching in my own education.
Now, this is a fairly complex sentence made up of 4 different clauses which I’ll try to deconstruct into its component parts:
If you were then to transcribe this sentence as part of an equation it would something like this:
P O, S V O C, P O, S V O.
The commas are doing a similar job to that of + signs and help us see the different clauses within the sentence.
This is useful when marking students’ writing and you encounter something like this:
As I ran down the street.
Because it starts with ‘As’ (a coordinating conjunction) it’s a subordinate clause and cannot therefore be a sentence in and of itself. Our response to this fragment (unfinished sentence) is to scream, “What? What happened when you ran down the street?” Students need to know that where this happens a sentence needs to look like this:
C S V O, S V O.
And that anything that is left merely as C S V O is wrong. It’s also worth knowing that if a subordinate clause begins a sentence it is always followed by a comma. So in effect what you would be doing is leaving the comma dangling and then just starting a new sentence with a capital letter. Obviously, you wouldn’t do that because the vast majority of people know that you end a sentence with a full stop. But what if commas were understood in the same way? What if we knew, deep in our souls, that you only ever use a comma to divide single items (nouns or adjectives, or phrases if you want to get technical) in a list or when a subordinate clause begins or is embedded in a sentence?
If we knew that we could teach it. If we knew that a sentence describes the relationship between a subject and its object then maybe we’d have more luck communicating this knowledge to our students.
We could then instruct them to write a sentence which did this:
S V O; S V O.
V, S O.
And, by God, they’d know how to do it!
But language is messy. Maths on the other hand is neat and ordered. If algebra makes sense to you, it is a realm of certainties. So, could writing harness some of this logic and precision (while remaining mindful that “fiction that does nothing but follow rules is cold arithmetic”?) Can we, as English teachers (and don’t forget that every teacher in English is a teacher of English) give students the mental tools to be able to construct technically accurate sentences? And does it even matter?
Some may argue that all this emphasis on grammar stifles creativity. To them I say, pah! We wouldn’t value a mathematician so focused on a creative solution to a problem that they couldn’t add up, or an architect whose ‘creative’ buildings were unbuildable. We value precision in so many other fields, why is it OK for writing to be sloppy?
I’m pleased to report that after 8 weeks of an intensive crash course in grammar, my AS class are now able to write. They are so much more thoughtful about how they’re writing rather than just dumping their thoughts on the page. I would argue, and so would they, that this has allowed them to be much more confident and creative in their writing. Most of all, it’s allowed them to decide when, where and why they might want to break the rules.
And crucially, none of this need be dull. Just as there are bucket loads of creative, exciting maths teachers out there, so too can there be regiments of outstanding grammarians. Take a leaf out of the wonderful Dancing about Architecture for some excellent ideas on how to combine the physical with the abstract.
And finally, a plea
Please note that am in no way an expert in grammar. I do my ‘umble best with the little I know. I accept that having the temerity to write about these things opens me up to all sorts of criticism from the sort of people I’d fear to meet down a desk alley. Be gentle with me. I know that ‘object’ is often wrong and that we could dance for hours discussing predicates and compliments. But to what end? This level of knowledge is sufficient to vastly improve students’ knowledge of and ability to improve writing. And that’s what matters. I thank you.
Lisa Jane Ashes on the fusion of Maths and English: Manglish!