Last week I challenged you to play the another round of Guess the Misconception. I asked you to predict the most popular incorrect answer that students from all around the world gave to the following question on calculating the gradient:
Well, it is safe to say that it was all kicking off on the emails! I have no fewer than 43 people writing to me, not to wish my Happy Birthday for Friday, but to say I had missed a key misconception! They explained (very politely) that by far the most common misconception their students displayed when tackling gradient questions was doing the change in x divided by the change in y, and because in this particular question the correct answer is 1, you would reach that answer no matter which way around you did the division, and hence the misconception would not be revealed.
Well, all I can say to that is… yes, you are absolutely correct.
Whilst I feel suitably embarrassed – after all, a decent chunk of my Diagnostic Questions training course involves looking at the features of good and bad diagnostic questions – I have decided to take heart from the fact that teachers understand the importance of ensuring all the key misconceptions are covered. Indeed, maybe this question was merely a devious ploy to check that? (it wasn’t!). And I would further try to dig myself out of this hole by stating that so long as this question was part of a quiz involving other gradient questions, then all misconceptions should be revealed.
Anyway, temporarily putting my uselessness to the side, let’s see what this question did reveal.
Well, once again teachers correctly predicted that the most popular student misconception was D, giving an answer of 2. Why did students think that? Well, let’s have a read of their explanations to find out:
“because the difference between 1,3 is 2 and the difference between 5,7 is 2″
“Because you minus both x co ordinates so 3-1 and it equals 2 :)”
“because its the distance between each number”
It is also worth having a quick read of explanations arguing for an answer of x. I find this is a symptom of emphasising that “the gradient is the number by the x”, and before you know it that little x has found its way into their answer as these students explain:
“2 up and 2 across. 2 divided by 2 = 1. So you need 1x, which is just written as x.”
“The gradient on a line is the x bit, which in this case is 1x.”
So that’s 2-0 to you lovely teachers! I wonder if I can get you back with next week’s round of Guess the Misconception. Keep an eye out on the blog for the announcement on Sunday evening…