I’ve become very interested in the use of diagnostic questions in mathematics lessons. I’ve always been a big believer in learning from mistakes and have often given pupils work for them to mark but which I’ve tried to include common misconceptions so they can see these errors and, so the theory goes, they don’t make these mistakes themselves!
Craig Barton of the mrbartonmaths fame is developing a website which houses many diagnostic questions as well as a discussion of what they are and how they can be created. You can view the website here.
In this post I’d like to explain how (I believe) a diagnostic question works by means of an example diagnostic question I’ve created and used myself.
A diagnostic question consists of a question with four possible answers. Obviously only one answer is correct. However the power in the diagnostic question is that the three incorrect answers are derived from common misconceptions, hence a pupil selecting one of these answers could point the teacher to diagnosing this misconception and allow them to address it.
The diagnostic question above I have used after delivering a piece of work on parallel and perpendicular straight line graphs. The correct answer is of course B (y = 2x + 7). The teacher could just collect the information in some fashion (white-boards, post it notes) and from this data could diagnose which, if any misconceptions are present. Another approach is to actually get the pupils themselves to discuss WHAT misconceptions were made in producing answers A, C and D. This is no easy thing to do and requires training the class but really delves deep into a topic and hopefully develops an understanding in the pupils of what misconceptions are common with a topic.
In the example above, in A they have clearly understood the negative reciprocal nature of a perpendicular line but failed to notice the 2 in front of the y.
In C they’ve notice the 2 and realised two lines that are perpendicular have different sign gradients, they’ve just forgot about the reciprocal part.
In D they’ve done the opposite of the error in C.
The wrong answers should come from one single mistake and preferably through a single stage approach to solving the problem. If not, the diagnose part can become muddled and messy because there are too many variables involved in getting to the answer.
I think they are really useful things to do to start a lesson and refresh understanding from the last lesson maybe or to check understanding after delivering a topic or part of a topic.
I’m also playing with the idea of the pupils themselves creating their own diagnostic questions with their own commentary surrounding the misconceptions.
I’ve developing a bank of my own diagnostic questions which you are free to access and use for yourself (would love some feedback on how useful they were) by hovering over the diagnostic questions menu at the top. I’m categorising them under number, algebra, shape and data.
Please let me know if anyone else is using diagnostic questions and how they are using them.