"Why are we learning algebra?"

It had been several weeks since my Year 7 class had the discussion of why we were learning algebra, so I was taken off guard when the perennial question came up again: "Mr Zuber, why are we learning algebra (again)?" 

I have a whole range of answers I like to offer to this favourite question but this time something unexpected came out of my mind.  "Have you seen those amazing new pictures of Pluto that came in this week from the Horizon spacecraft?"  I was pleased to see many students in the class start to get excited - they certainly were inspired by those photos.  

Global mosaic of Pluto in true color (NASA) July 2015

"Well", I said, "that was algebra. Algebra brought us those pictures. Very complicated algebra, and physics and engineering worked out by smart people helped get that spacecraft just at the right place, at the right time above Pluto, millions of miles away from Earth, to get that photo and send it back to us. That's why we're doing algebra."

I think that was the best answer I gave in class all week - and the students seemed to like it. Thank you NASA!

Here are four reasons for learning algebra that I like to offer students when I start the introductory algebra topic.  

Firstly we have some utilitarian reasons:

Algebra is a tool to help solve problems.
We use it to find values of something we don't know.

Algebra allows us to record information about relationships between numbers in a formula.
We can then put values into those formulas to find related numbers. This could be the area of a triangle, or the dosage of medicine to give a child based on their weight.

At a deeper level, algebra has an important place in our discovery of the world:

Algebra allows us to describe how the world works.
Students like this image. The picture in the centre is a matter-antimatter collision and the formula is Heisenberg's Uncertainty Principle.

and in supporting our exploration and representation of mathematical ideas.

Algebra allows us to represent and explore mathematical ideas and mathematical objects.
At least some students in your class will have seen the Mandelbrot Set and know how complicated it is - they will be very surprised how 'simple' the algebra looks.

Putting all these ideas together, I like to summarise with the one big idea: algebra is a language.

So - for those people who say "but I will never use the quadratic formula in my future work", I would respond: "Wouldn't you like to learn this amazing language? It will open up so many career possibilities to you (a utilitarian argument) and it's also a fascinating and rich language that will let you access a whole new level of knowledge and ideas (a sheer pleasure argument)"

What's even more amazing about this language is that it's an international language. I can speak algebra with a Russian or a Chinese mathematician. Somewhere out there in space, a class of Year 7 students with green skin and three eyes is also learning algebra.  Can you think of another subject you're learning at school which is also being taught in Alpha Centuri?  (OK - science... but let's pretend that's the same as maths :-)

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Postscript: Should I have mentioned that algebra helps us develop reasoning skills? Possibly.... but I'm not sure most students buy the "it's good for your thinking" argument. So I take the "what algebra will offer you" line, and make sure I give emphasis to its role in abstract thinking as well as in 'practical' applications.