Misconception or Mistake?
by Mel Muldowney, a secondary school maths teacher working in Warwickshire
As teachers, we come across students’ work all the time that is just plain wrong. However it is important that we understand the difference between mistakes, which are generally due to carelessness (the student will have demonstrated the skill elsewhere correctly) and misconceptions, whereby a misleading idea is applied or a belief that a certain rule that applies in one set of circumstances will always apply.
Misconceptions are often deeply entrenched ideas which can prove stubborn to shift because at a cognitive level the disparity of what a student is being told conflicts with some earlier learned idea. Research suggests that teaching is more effective when misconceptions are identified, so I’ve been on the hunt for common misconceptions and lo-and-behold I found this example from a year 9 student:
Having spoken to the student it was evident from the response “oh yeah, obviously anything multiplied by zero is zero … what an idiot!” that one of these was a mistake brought about through lack of concentration and could have been avoided by them checking each stage of their working. When we discussed the second idea of “1 × 1 = 2” the student was adamant that it was correct and it wasn’t until we did a bit of “pattern sniffing” looking at 1 × 2, 2 × 2, 1 × 3, 2 × 3 etc that a look of realisation spread across his face.
What I’ve learnt is that identification of misconceptions isn’t enough - they need to be challenged directly with the student. Ignoring misconceptions should not be an option and to simply mark something wrong with an “×” often leaves the student knowing that something is wrong but may not necessarily leave them with the understanding required to address the matter.
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