Using diagnostic questioning in the Maths department

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Posted by Head of Maths

​This year the Bethany Mathematics department has been focusing on using diagnostic questioning in lessons.

It allows teachers to respond in the moment to pupil needs, by gathering as much accurate information about pupils’ understanding as possible. This is a technique that has been developed by Craig Barton, an Advanced Skills Mathematics teacher, advisor to the TES for Secondary Mathematics and author of the fantastic mrbartonmaths.com.

Often pupils arrive at Bethany with a fear of making mistakes or wanting to opt-out of giving answers. So, we have been looking to find a way to ensure that all pupils actively and honestly participate when asked questions. Fortunately, the use of diagnostic questions brings mistakes (and misconceptions) into the open, treating them as the learning opportunity that they are, whilst at the same time encouraging full class participation.

So, what is diagnostic questioning?

Previously, for any given question there were two groups of pupils, those that could do it and those that could not. Those that could do it were fine to get on with the next challenge until they got stuck, and those that could not needed help.

However diagnostic questions are designed to help identify and crucially understand pupils’ mistakes and misconceptions in an efficient and accurate manner. Mistakes tend to be one-off events, the pupil understands the concept or the algorithm but may make a computational error. Misconceptions, on the other hand, are the result of incomplete knowledge. The same misconception is likely to occur time and time again, and stop pupils progressing.

The best way to explain a diagnostic question is to show you one.

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Answer A suggests that the pupil understands that angles on a straight line must add up to 180°, and is able to identify the relevant angle, but has made a common arithmetic error when subtracting 65 from 180.

Answer B may be the result of the pupil muddling up their angle facts, mistakenly thinking this is an example of vertically opposite angles being equal.

Answer C is the correct answer.

Answer D may imply that the pupil is aware of the concept that angles on a straight line must add up to 180°, but has included all visible angles in their calculations.

Each answer reveals a specific, and different mistake or misconception. There is little doubt that there is an advantage to teachers knowing not just which pupils are wrong, but why they are wrong. They are then able to adapt learning in the lesson to best suit the pupils.

As a department, we have been using diagnostic questions at varying different points in lessons. They have been used to assess baseline knowledge at the start of a topic. By knowing where pupils are in their learning, in particular, which misconceptions they hold before teaching new knowledge is key. It also primes pupils’ long-term memories. When pupils are compelled to retrieve knowledge, that very process modifies and enhances what is stored in long-term memory. As well as this, being questioned on the material you have not studied before actually enables you to better understand and remember the material when you do study it.

They can also be used in the middle of a lesson, as a hinge. They provide a perfect way to quickly assess where certain pupils are going wrong, but why they are going wrong. This allows teachers to intervene where needed, conversely, if everyone gets the question right, then onwards and upwards!

Finally, diagnostic questions can be used at the end of the lesson, to inform the starting point and the planning of the next lesson. It is also an opportunity to give pupils a question based on what they will be studying in the next lesson, allowing assessment of pupil understanding of key concepts so planning can be adjusted accordingly.

Parents may also start to see diagnostic questions on their children’s preps, with pupils not only answering diagnostic questions but also writing them which demonstrates the depth of their knowledge of a particular concept.

Adam Manktelow Head of Maths