The straight lines debate
For a long time I’ve been confused about straight lines. Not because they confuse me, or that I don’t understand them, but the prolific use of the formula y-yo = m(x-xo). I personally prefer the y = mx +c version, and I couldn’t see a benefit to y-yo at all. I certainly couldn’t fathom why at A Level is was so heavily favoured by teachers and markschemes alike. I had asked around a few times, and the only coherent point I had got that made any sense to me was that when the gradient is fractional students who weren’t any good with fractions could multiply up by the denominator and deal with integers more easily. But my experience showed me that students used y-yo in a mechanical manner, and weren’t building any deep understanding of the geometry of straight lines.
I then noticed, while reading his blog at flying colours maths, that Colin Beveridge (@icecolbeveridge) was very heavily on the side if y-yo, and called y=mx+c “the baby formula”! I thought, perhaps “Colin can explain why there’s such a preference.” I asked, and sparked another “blog off”.
Colin wrote this excellent piece on his blog setting the case for y-yo. He argued that y = mx + c is a special case of the other, also mentioned the aforementioned fractional gradient argument, and made a few other (occasionally compelling occasionally contradictory) points. I felt that it did give me a better understanding of why people preferred it, but still did nothing to persuade me that it was the better version to use. (If you haven’t read Colin’s post, you should!)
I then responded with a guest post on Colin’s blog setting out my counter arguments. Since the post was written I’ve discussed these formulae with teachers and students alike. I have noticed something about the students views, those who I taught in year 12 ALL prefer y=mx+c, but those my colleague taught in year 12 mostly prefer y-yo. So I wonder if I had somehow imparted my preference to them. A friend of mine who is also a maths teacher summed it up pretty well for me when he said:
“Ok, well so full honesty then- y=mx + c is probably better, however, when working with weaker students I find it easier to use the mechanical form, rather than the one which provides the most information about the line itself!” (Steve Atkinson 2014)
Which version do you prefer? Do you have any strong views? I’d love to hear them.