Yesterday, I taught a Year 11 maths revision lesson. As a revision lesson, the plan was to ask students to complete a series of questions and intervene as necessary, not for me to demonstrate worked examples. The first question was a relatively simple calculator problem. For those who are interested, it relied upon the ‘remainder theorem’ and required students to find an unknown term in a polynomial given the remainder was 17 when divided by the linear factor x + 1.
I asked them to write the answer on their mini whiteboards but I soon detected that nothing much was being written. I gave them a hint. Looking around, I said, ‘You don’t know what to do, do you?’ and about half the class shook their heads. So I taught the question instead as a worked example and then found another one for them to do on their own.
A few years back, I would have taken a different approach. Instead of teaching it as a worked example, I would have picked a student and started posing questions: Which theorem are we going to use here? What do we know? What are we trying to find? Which CAS calculator function could we use? And so on. However, I’ve moved away from this. I don’t think Katharine Birbalsingh invented the term, but following a conversation with her a few years ago, I would now call this approach, ‘Guess What’s In My Head’, and I no longer see its value.
Guess What’s In My Head sucks all of the pace out of a lesson. It’s inefficient, with five or even 10 minutes lost, gradually trying to pull out of a student something you could have explained to them in two or three. Yet teachers feel drawn to it, possibly as a result of our training and the misguided notion that students will understand something better if you can somehow get them to come up with it themselves.
Nevertheless any injunction against Guess What’s In My Head poses a problem. Rosenshine’s Principles, based upon the process-product research of the 1960s, suggest teachers should ask lots of questions during instruction. So when is a question worth asking and when does it become a game of Guess What’s In My Head?
Although I am going to attempt to draw a distinction, I am not going to pretend this is a clearcut distinction. Teaching is a messy and indefinite business and however I attempt to capture the difference, there will be borderline cases.
Firstly, I think you know when you are venturing into Guess What’s In My Head when you notice you’re going to have to ask a series of leading questions. These are indicators because another characteristic is that you are not really retrieving something the students already know. Instead, you are constructing the concept with them.
Yes, my students had used the relevant calculator strategy before — it was revision — but shorn of the context of a lesson explicitly about the remainder theorem, they were missing what they needed to diagnose the nature of the problem. By asking them questions at this point, it would have been new knowledge to construct.
Questions are worthwhile when there is something in long-term memory for the students to retrieve. In a sense, that’s a circular argument because you only know if something is in long-term memory by asking questions. However, in my maths class, I started with a question and rapidly worked out that the knowledge was not there to retrieve, so I ceased further attempts and moved on. I cut my losses.
And the mini whiteboards helped, because I could see it was a shared lack of knowledge.
I always liked it when there were math problems that involved puzzling out an answer. It of course took much more time than simply being told how to do it, but it was much more interesting to derive a formula or discover some principle. I think this sort of experience may contribute to the number of mathematics teachers that aren't fans of direct instruction (and the number of people who speak about fostering "discovery" and things like that). They enjoyed the puzzling over problems more than the simple knowledge. It feels smart to figure something out.
Looking back at my primary/secondary math experience though, if I'd done less puzzling and more straight up learning, I would maybe have learned a lot more allowing me to puzzle over more interesting problems.
It seems to me that knowing when to ask questions, and what questions to ask, is one of the most difficult things about teaching. And it doesn't seem like teachers get much or any training in the art of asking questions.
The title of this post reminds me of a professor I had in law school who tried to use the so-called Socratic method, which is traditional in American law schools. But of course, law school professors also don't get training in how to do it, and I always thought this professor's version was like: I'm thinking of a number between 1 and 64,000 ... One day he asked the class, "What do we call poor people?" This led to several minutes of people trying to guess what word or phrase he was thinking of ("welfare recipients?"). He finally revealed that the word he wanted was "judgment-proof."