Each answer has been specially selected to draw out a particular misconception. In answer B it would appear that the student has confused squaring with multiplying. In answer C, the student has either forgotten to square three or has not realised that the square function applies to the whole bracket. In answer D, the student has squared the three but is perhaps unsure of how the squaring affects the algebraic variable. All three wrong answers encourage a rich discussion into the depth of understanding required to master this particular law of indices and allow the teacher to pre-empt any possible misconceptions.
There is an argument that by presenting incorrect answers as part of the choice could encourage and embed certain misconceptions. This is why it is so important to consider and discuss the incorrect answers and confront the misconception head on. Moreover, if a student confidently choses an incorrect answer and then subsequently receives immediate feedback into why it is wrong, they are more likely to experience the “hyper-correction effect” and have a greater likelihood of remembering the correct answer in the future. Andrew Bulter and Henry L Roediger III write that “feedback enhances the positive effects of taking a test and helps students correct their errors, thereby reducing the acquisition of misinformation”. The evidence is clear in that if you are going to use diagnostic questions, be sure to give feedback to the students so that all misconceptions are dealt with.
Zofia Reeves
Research School Associate