I had intended this to be a three part series, however while trying to write the final post today, I realised I had left out an extremely important piece of the puzzle. In the first post I talked about ‘understanding’, in the second ‘thinking’ and now before looking at under whose influence we may be operating, I realised I need to add in something about questioning.
Then, in thinking I need write a brief note on questioning, I found it to be one of the most horrifically complex aspects of teaching I’ve yet tried to analyse! I can’t say I’m yet at anything that’s usefully conclusive to others, but perhaps the journey will spark a few thoughts in other people’s minds. It’s a necessarily long post, and so I’m splitting it into two parts. I’ll publish part two on Wednesday.
Questioning and I have a strange relationship. It’s something which is given a lot of attention during training, though I never really understood the point that was being made. It’s one of the staples that always comes up during CPD cycles, so there’s obviously a great deal of institutional focus on it; again I’m left a bit clueless as to exactly why, and what precisely is the point being made. There seems to be a vague idea that it leads to ‘thinking’ and therefore ‘understanding,’ but I’ve not yet seen any clear explanation as to precisely when, how or why this would be.
A strange relationship
It’s not something to which I’ve dedicated all that much thought, certainly not in comparison to other elements on my teaching. Yet, it’s something whereby I’ve been receiving praise in observations; I’ve been told that my use of questioning is good, and the reasons why it’s good have been articulated. Okay… that’s nice to hear… but I still feel something’s missing; really, why does it even matter? There are certainly some questions that I carefully plan, and there will be at least one example of this in a later post. But given the number of questions I do ask, I wouldn’t say I thoughtfully plan the majority of them. There are so many different kinds of question as well, looking to serve different purposes. I remember during training being shown the lesson plan of someone whose lesson had apparently been considered ‘outstanding.’ What we were supposed to take away from the plan was how it had been carefully constructed around the questions to be used. What most of us took away from the plan was how insanely impractical it was, and therefore useless to us in our particular situation – perhaps I should have mentioned that this single written lesson plan was some 6-8 A4 pages long, with almost a full page dedicated to each five-minute micro-section of the lesson.
All in all, the vague structure of the paragraph above probably well conveys my equally vague thoughts and feelings towards questioning, and yet, clearly we can see that it is considered to be of great importance.
At this point I need to make it clear that I’m writing almost solely from the perspective of a maths teacher. Through some discussion with colleagues teaching other subjects, I appreciate the rules may change across subjects in ways that are difficult for me to fully appreciate.
That said, on to a few anecdotal experiences, and the odd thought that follows.
First, when I’m speaking to anyone about something one to one, there are times when I slip into a particular pattern of dialogue. If I am talking on a subject of which I know something and the other person does not, then sometimes I will simply exposit what I know, while other times I will switch to making a point, and then asking questions of my interlocutor based upon what I have said. I haven’t thought enough about when I’m doing this to understand when I switch between each, and why. My gut tells me that if I’m simply recounting something, such as an event, story, history or any other kind of information, I will tend to just say it. On the other hand if the subject is something philosophical, logical or mathematical – particularly mathematical – I might be sometimes inclined to enter into this mode of questioning.
Next, thinking about the classroom, the same thing happens in different ways. When I started out, I was terrified of telling students anything, fearing it would lead them to such evils as relying entirely on me to learn, failing to think, failing to understand, rote repetition and so forth. There’s also this amorphous ‘sense’ that people don’t like it when you ‘give them the answer.’ This was supported again recently by a survey that noted students saying they preferred it when a teacher helped them find the solution themselves, rather than simply telling them what it was – for the life of me I can’t remember where I heard it or what the context was!
Now, I actually shifted from this position part way through my first year. I started to find that the persistent asking of questions was not always productive. It was the destroyer of pace, ate time and therefore was not always practical. Nor was it always sensible; take a child whose shutters have come down and sometimes the worst thing you can do is to keep battering them with questions.
Battered by questions
Something else particularly relevant to mathematics – not all the problems we ask students to solve are really ‘problems,’ depending on your definition of what a problem is. I’ll phrase that another way, through example: let’s say I’m teaching them to expand brackets. Having been shown a few times how to do this, asking them to now expand a few brackets for themselves isn’t really problem-solving, it’s direct application, and practice. Though the process is identical each time, the practice serves the dual purpose of building students’ long-term memories and building their confidence that they’re doing the right thing; it builds their fluency with the process – which is harder than you might imagine. By contrast, a ‘problem’ might be something relatively unique; the solution, once known, is not necessarily relevant to other problems. By giving the game away, the teacher would ruin the problem for the student.
Why is this important? Well, if a child asks me if they’ve expanded a bracket correctly, and they haven’t, there are now two different possible strategies. One is to ‘induce cognitive conflict,’ that is, ask questions until they realise their own mistake, and correct it. The other is to say ‘no, the answer should be this…’ Which is better? The one I have always heard promoted institutionally – though not necessarily by actual experienced teachers – is the former: ask questions. The one I get a sense teachers are expected to naturally tend towards, without training, is the latter. I also get the feeling that this expectation leads to fear, which in turn breeds the pushing of option (a) – ask questions. Which do I do? Well at the start, I’d always ask questions. Now, I’d say that 80-90% of the time I take the second option. Here’s an example of what the conversation usually looks like when I do:
3(2x – 4) = 6x – 4
“Sir, is this right?”
“Almost there. It should be 6x – 12.”
“Ah damnit, yeah, I forgot to multiply the 3 and the 4 as well. Thanks Sir.”
Total time taken: about 15 seconds.
To sit there and ask questions and ‘induce cognitive conflict’ might have taken us a good couple of minutes at least, it could also have actually overloaded the student, causing further confusion rather than clarity. In that time I could help eight kids by just telling them the mistake. I learnt that, often – not always – if I point out what the answer should have been, they quickly spot the mistake for themselves. If they don’t, I tell them where the mistake lies, and now we’re up to nearly 100% successful correction rate in little more time. Given the nature of the ‘problem,’ I haven’t ruined anything for them by given them the answer, quite the contrary, I’ve provided feedback on their mistake, and they have plenty more similar ‘problems’ to go on and attempt to solve successfully. In this instance, ‘inducing cognitive conflict’ simply wasn’t necessary; it would have added nothing, yet come at a cost.
I noted above that I opt for this approach the vast majority of the time; there are still times that I will sit with a student and I ask them a series of questions until we arrive at the answer. It’s difficult for me to pin down when I make this choice, since as I say, I haven’t really spent much time thinking about it, but broadly speaking I’d suggest there were two main times when I might do so. The first is simply when time allows. If it’s an after school session with one student, we have an abundance of time and they have 100% of my attention, so I may opt to lead them with questions. Even here though, I won’t always; it’s just not always the most time-efficient choice, and doesn’t automatically yield gain over simple ‘telling’. When I’m perhaps more inclined to feel questions are essential is when I get the sense that there is no meaningful understanding going on at all, despite a student having seen a topic many times now, and so perhaps it’s time go back to the beginning to help elicit such understanding. There’s still a time cost, but it’s now essential that it be spent. So do I conclude that questions necessarily lead to better understanding? Not sure yet.
Does asking questions necessarily lead to better understanding?
There are lots of other times I use questions. I’ve started many lessons with a round of ‘literacy questions.’ I ask students to respond to questions in full sentences, they are selected at random, and the nature of the questions is often rooted in knowledge recall rather than calculation e.g. how do we find the area of a triangle? I use these in part to keep old topics alive in students’ minds. I’ve used assessments that have lots of questions on them to assess who has can do what. I’ve used exit tickets with a single question on them to grasp who can do what by the end of a particular lesson, and more importantly, who can’t.
What else? Well in my observations I was praised for a number of things that are apparently good. One was to insist on specificity; when a student answered that you ‘add the two sides,’ I asked ‘which two sides?’ Another was that I would sometimes take it further, so given a response I might then ask a related question, or ask ‘why’, or ask for the technical word in place of a colloquial one that a student used. I might pose such questions to the same student, or another student. I might ask another student to repeat what the first said – the purpose now being to set an expectation: all must be listening. If a student couldn’t answer I would go to another, and then another until we have one who can answer… and then go back to the first two students for a repetition of their correct answer. I’m sure many of these things are simply internalised from Lemov’s ‘Teach Like a Champion.’ – certainly ‘100% Right’ and ‘No Opt Out’ are in there at least.
Anything more? Well when I taught expanding brackets, I didn’t start by showing them 4(2x + 5) and then explaining the need to multiply both terms inside the bracket by what was outside, instead I showed them that 4(2x + 5) = 8x + 20 and asked students if they could spot what I’d done. Even in a low ability Year 7 group, they could all see how I arrived at ‘the answer.’ Although I reiterated the process afterwards, asking that question was probably more effective than simply telling them what to do. But why? In this instance I suspect it’s because the connection is so simple to make, even if the rationale is not yet understood. By comparison actually understanding what is meant by ‘multiply both terms inside the bracket by whatever is outside the bracket,’ is comparably complex! In my mind, it’s a bit like trying to teach someone what a triangle is. You don’t tell them that it’s a three sided shape with three angles that sum to 180 degrees, you simply show them examples and non-examples of triangles, which is easier for the brain to conceptualise. You of course then come to the technical definitions or properties of triangles once students are comfortable and familiar with what they are.
Additionally, I wonder if this approach overcomes a particular mental block. If you show some students how to expand brackets, they will react with a puzzled sense of ‘What are you doing? Why? I don’t get it!’ *cue head on desk* Ironically these same students demanding ‘why’ may be no more ready for the explanation as to the distributive property; attempts to explain the ‘why’ risking their being even more confused. By posing this question of ‘What have I done?’ or ‘How did I do this?’ it seems to grant a feeling to the student that they ‘get it,’ they’re sated in having resolved a question, they see what you’ve done, and they’re happy now replicating it.
Herein ends the outpouring of my mind; analyses and conclusions to come on Wednesday, along with a fantastic contribution by @Redorgreenpen. In the meantime please feel free to comment on any of these experiences, whether you recognise them, agree with them, or would like to challenge them.