Asking Diagnostic Questions in class

In previous posts I have talked about what is a diagnostic question, and what makes a good one. Now I want to turn my attention to how we might ask and respond to a diagnostic question in the classroom environment. After all, if we cannot do this, then all our efforts in writing and choosing good questions will be wasted. The power of formative assessment is that it allows us teachers to respond to the needs of our students in the moment — without quick and accurate information as to what those needs are, we are simply powerless to help.

When I interviewed Dylan Wiliam for my podcast, he said many memorable things. But one that really stuck out in my mind was that students rarely forget to bring their fingers to lessons. They may forget pens, pencils and homeworks, but fingers are always there. Likewise, fingers do not tend to be subject to the whims and fancies of unreliable technology, nor are they as easy to create inappropriate gestures with… well, apart from two notable exceptions. And so, when asking and responding to diagnostic questions in my classroom, I always get my students to use their fingers.

The process for asking and responding is one I have tweaked and developed over the last five years and I am quite particular about it. It goes like this:

Phase 1 — The Initial Question

I project a question such as the following up on my whiteboard:

The students are sitting in silence and I give them between 5 and 10 seconds thinking time. The exact time depends on many factors, ranging from the complexity of the question, the age and set of the students, and most importantly my gut feeling observing them thinking. It is very rarely more than 10 seconds — as discussed in the previous post, one of my criteria for a good diagnostic question is that students should be able to answer it in less than 10 seconds — but it is always more than 3 seconds. Wiliam (2011) explains how when the question requires thought, increasing the time between the end of the student’s answer and the teacher’s evaluation from an average wait time of less than a second to three seconds produces measurable increases in learning. However, according to Tobin (1987), increases beyond three seconds have little effect and may cause lessons to lose pace. That is where my gut feeling and experience come into play. When I sense that students have had sufficient time to think and settled upon the answer, I continue.

I then say 3, 2, 1, vote, at which point my students indicate their choice by holding one finger in the air for A, two fingers for B, three for C, and four for D. Again, this is all done in silence.

I should also say that I am not at all opposed to the use of mini-whiteboards. I find they are an excellent way for students to illustrate their thinking, and the fact that students can rub out all record of their work in an instance means the less confident ones are more willing to participate. I use mini-whiteboards for longer form questions, and for the problem part of the example-problem pair approach to worked examples, but not for answering diagnostic questions. Remember, diagnostic questions are short, snappy questions that assess one skill or concept. There is rarely any need for working out, and the time saved from leaving the whiteboards and temperamental pens in the cupboard can be significant.

Following the vote — and assuming that the question is a good one that I have studied in advance — a quick scan of the room immediately gives me some accurate and useful information about my students’ understanding of interpreting algebraic expressions. I know how many have got the question right, how many have it wrong, and based on their choices I also have a good idea of exactly why they have gone wrong. I may choose to leave it at that, and simply use this information to dictate where I take the lesson next — do I need to go back over the basics of algebra armed with my new knowledge, or can I move on?

However, more often than not I like to dig deeper into students’ answers. This is a relatively quick process, and it has a number of benefits. First and foremost, it provides me with extra information about how my students are thinking. This is particularly important if I suspect some students may be guessing, or if if the question is not a particularly good one and an answer can be arrived at via two different ways of thinking. But there are also benefits for my students. Being asked to explain their answer compels students to reflect on their reasoning and organise their thoughts. Moreover, it provides a useful opportunity to hear how their peers have approached the question.

So, I ask for a student who has chosen A to give me their reason. I always start at A (and move through the alphabet), regardless of whether this is the correct answer or not, so students do not learn that I am always either starting with the right or wrong answer. Lemov (2015) might refer to this as managing the tell, and we discussed this very instance when I interviewed Doug on my podcast.

The student may say something like: I added them together.

I would simply say thank you, ensure the rest of the students in the class are listening and being respectful, and then ask for someone who has chosen B to give me their reason. Something like: In algebra, if letters touch it means multiply.

This process would continue until I have collected a reason for each of the answers. If there is a particular answer that no-one has given, I wouldn’t usually refer to it at this stage, but I will certainly use this in Phase 2.

After we have heard reasons for all the correct answers, it is time for a re-vote. Students can keep to their original answers or switch. The majority of the time, most people now choose the correct answer. It is here, for the first time, that I announce what the correct answer is. Giving the answer straight away — for example, saying “B is correct, now who can tell me why?” before any discussion — misses a golden opportunity. It stops my students thinking. Those who have got it right have no need to listen any more, and those that have got it wrong may feel disheartened. By doing what Lemov (2015) calls withholding the answer, I am giving students an incentive to keep listening and thinking throughout the whole process. If I have not been entirely happy with the clarity of the correct explanation given by my students, or I have something extra to add, I will do it at this stage.

Now, it may be tempting to move on here. Indeed if most students got the question right first and second time, I may well do so, but not before having made a note of any students who are still struggling so I can go and help them out later on. However, if there are still plenty of students who have the wrong answer, I need to go into Phase 2. Likewise, if not many got the question correct first time around, but then during the re-vote everyone got it right, I might be a little concerned that maybe they are just copying the perceived smartest student in the class, or they have picked up on some subconscious cues from me when students were discussing their answers. In that case, I may also opt for Phase 2.

And Phase 2 is coming to a blog post near you soon…

If this has whetted your appetite for more diagnostic questions, I have good news — there are more than 40,000 of them (including 30,000 for maths), all freely available at diagnositcquestions.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 Educational Ltd.

References

  • Lemov, Doug. Teach like a champion 2.0: 62 techniques that put students on the path to college. John Wiley & Sons, 2015.
  • Tobin, Kenneth. “The role of wait time in higher cognitive level learning.” Review of educational research 57.1 (1987): 69–95.
  • Wiliam, Dylan. Embedded formative assessment. Solution Tree Press, 2011.