Thursday 10 October 2013

When Will I Use Algebra in Real Life?

There is one question my students ask me that I hate far more than all others. Far more than "Why are you just a teacher?" and "Do you have a boyfriend? What's his name? What's his job..." etc.

That question is: "When will I use simultaneous equations/ the laws of indices/ completing the square in real life?"

A good maths teacher, of course, would have a bank of answers to such questions. "Satellite dishes are in the shape of a parabola!" etc. Urgh.

Even though I do happen to know a few applications of algebraic principles to "real life" (picture me making air quotes with my fingers), I never tell these to my students. I refuse. 

First of all - real life? I'm sorry, are my maths lessons not real? When you enter room 204, are you entering some kind of alternate universe? Is a  maths lesson merely a state of mind? Some kind of lucid dream that looks real and feels real, but can't possibly be real because instead of English the teacher is speaking in an alpha-numeric jumble?

Secondly, where did students (and, for that matter, teachers) get the absurd idea that everything one learns has to have some kind of practical "use"? Can't we simply enjoy learning maths for its own sake? Does everything we do have to have a useful purpose? What kind of depressing life would that be?

Maths is beautiful. It is deep and interesting. It is a language. It is an art. It is a self-contained world with its own rules, patterns, and mysteries. So don't try to spoil my beautiful maths with your ugly "applications". 

I will leave you with some profound quotes from mathematician G H Hardy: 

"Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics". 

“Imaginary’ universes are so much more beautiful than this stupidly constructed ‘real’ one; and most of the finest products of an applied mathematician’s fancy must be rejected, as soon as they have been created, for the brutal but sufficient reason that they do not fit the facts.”

"I have never done anything 'useful'. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world."

Of course G H Hardy was wrong with that last one - his work was actually widely applied to genetics and thermodynamics. But the point is, that wasn't why he did it. And he didn't need these applications as motivation for producing this work.

Do you agree with me or are you someone who sees maths as a "tool" with which to get things done?

Emma x x x

Friday 4 October 2013

7 Habits to Get Your Year 7s into

(Substitute "year sevens" with "seventh graders" if you're American, "S1s" if you're Scottish, or "first years" if you're posh/old/a wizard).

Year 7s are so cute, aren't they? So eager to learn, so willing to please. Some are actually shorter than me, which is nice. By Christmas they'll have had their growth spurts and be taller than me. That's why I like this term. (FYI if you want a mental picture of me, I'm 150cm tall, 50kg, and look a bit like Garth from Wayne's World but slightly more feminine).

The thing with year 7s is that they are lovely little blank slates. They're a fresh batch of play-doh just waiting to be moulded. At my academy, we keep our classes throughout their school career. So it's important that you get your year 7s into good habits early on, to make your life easier later.

Here are the good habits I'd like to get my year 7s into:

1) Leaving the answer as a fraction

To some students, an answer of 3/5 doesn't look finished - because you haven't actually carried out the division. They would much rather put 0.6 because it looks like a proper answer. We need to stamp this out! Fractions are infinitely superior to decimals. The use of fractions should be encouraged from day one. Don't you just hate A level students who convert all their fractions to decimals? Think ahead, teachers!

2) Lining up the equals signs

Some teachers are very anal about this and I admit I'm not really one of them. But it does make algebra look a lot more beautiful when there is neat line of =s down the page.

3) Drawing margins

Why do maths exercise books not have margins pre-printed like all the other exercise books?! It drives me mad having to remind students to draw margins every day. It's amazing how some of them still forget - even my top set year 11s! We need to try some Pavlovian conditioning to get them to automatically reach for a ruler and pencil as soon as they open their books.

4) Drawing diagrams

To solve any geometrical problem, the first step should be to draw a diagram. This is something good mathematicians do automatically. I don't know which is the cause and which is the effect, but it's worth getting our students into this habit.

5) Resilience

Perhaps the most important characteristic of a mathematician is resilience. Try something. If it doesn't work, try something else. Don't tippex out your first attempt. Don't sit there with a blank page because you're scared of writing something that's wrong. If we can instil this attitude into our youngest students, they will grow up to be good mathematicians, whatever their attainment level.

6) Using a calculator properly

Calculators are great. I can honestly say I haven't done bus-stop division with pen and paper for a good 10 years. Because I own a calculator. My computer has a calculator. My phone has a calculator. Even my tape measure has a built-in calculator. Don't diss calculators. However, some students become instantly stupid as soon as they pick one up. They don't question whatever answer it spits out. Students need to be taught to estimate the answer first to check if it's roughly right. Also, calculators are really sophisticated these days, and for example you can type in the entire quadratic formula in one go without pressing equals in between or using complicated nested brackets. Teach students how to do this. Teach them about the magical s<=>d key. Explain how the fraction key works. Get them to make frequent use of the "ans" key. And most importantly, get them to buy their own and bring it in every lesson. But make sure it's a Casio! (Sorry Sharp, but you make my life so difficult. Please stop making calculators.)

7) Taking pride in their exercise book

That's "jotter" if you're Scottish. Or "notebook" if you're American. (Or "parchment" if you're a wizard).
When an exercise book gets filled up, students are supposed to keep it. What do most students do? Throw it away. How awful is this? The problem is that many students see their exercise book as the place where they do work, not the place where they write down things to help them understand. Also some books are just horribly messy! I find that if your work is neat, you take more pride in your book, and hence you put more effort into your work. I know presentation is not about learning and hence presentation-focused comments is considered ineffective marking, but I think good presentation does lead to better learning.

Those are my personal picks. Are there any you would like to add?

Emma x x x