For the first 10 years of my teaching career, I used to believe for any given question there were two groups of students: those that could do it and those that could not. Those that could do it were fine to get on with the next challenge, and those that could not needed help. Crucially, they needed the same help.
I now realise I was completely and utterly wrong.
Diagnostic questions are designed to help identify, and crucially understand students’ mistakes and misconceptions in an efficient and accurate manner. In future blog posts we will look at exactly how we can collect in this information and respond to it in the heat of a lesson, but here I want to focus on what it is that makes a question a diagnostic one, and why I have been getting things wrong for so long.
The best way to explain a diagnostic question is to show you one.
Take a moment to look at the question, and in particular the four different answers. What would each of these answers tell you about the understanding of a student who gave them?
Answer A may suggest that the student 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 student 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 student is aware of the concept that angles on a straight line must add up to 180°, but has included all visible angles in their calculation.
Notice how each of these answers reveals a specific, and different mistake or misconception. Imagine you had a group of students who answered A, another group who answered B, and a final group who answered D (we will cover exactly how we go about collecting this information in a later blog post). Would all three groups require the same intervention from you, their teacher?
I don’t think so. Which brings us to my erroneous belief. It is not always the case that students either can or cannot answer a question correctly. Sure, there may be a group of students who get the question correct for the same or similar reasons. But there are likely to be students who get a question wrong for very different reasons, and it is the reason they get the question wrong that determines the specific type of intervention and support they require.
For example, students who answered B and D may both benefit from an interactive demonstration (for example, using Geogebra) to illustrate the relationship between angles on a straight line. Students who chose B could then be presented with an exercise where they are challenged to match up an assortment of diagrams with the angle fact they represent. Those who selected D may benefit more from a selection of examples and non-examples of angles on a straight line. But what about students who answered A? Their problem lies not with the relationship between the angles, but with their mental or written arithmetic. This may be a careless mistake, or it may be an indication of a more serious misconception with their technique for subtraction. Either way, it is not a problem that is likely to be solved by giving these students the same kind of intervention as everyone else.
However you choose to deal with these students, there is little doubt that there is an advantage to knowing not just which students are wrong, but why they are wrong. And I have never come across a more efficient and accurate way of ascertaining this than by asking a diagnostic question.
So, what makes a question a diagnostic question? For the way I define and use them, there needs to be one correct answer, three incorrect answers, and each incorrect answer must reveal a specific mistake or misconception. I can — and indeed do — ask students for the reasons for their answers as I will explain in a later post, but I should not need to. If the question is designed well enough, then I should gain reliable evidence about my students’ understanding without having to have further discussion.
The set of criteria that I impose in order to deem a question a good diagnostic question will also be discussed in a future blog post. For now it may be useful to see a few more of my favourite diagnostic questions, just to get into the swing of things. Each time, ask yourself what you would learn about your students from their choice of answers without them needing to utter another word?
And if this has whetted your appetite for more diagnostic questions, well then there are more than 40,000 of them (including 28,000 for maths), all freely available at diagnosticquestions.com
Subtle advertisement alert: my book How I wish I’d taught maths, which contains an entire chapter dedicated to the practicalities, benefits and considerations when using diagnostic questions in the classroom, is available to buy from Amazon and John Catt Education Ltd.