Questioning Questioning

A thing I get asked about is the difference between focusing questions and funneling questions.

You may have already noticed that there’s something off with what I just said.

That’s because when we’re talking about focusing and funneling in the context of mathematics teaching, questions cannot be divided neatly between focusing and funneling. Focusing and funneling is about the pattern of questions used, not the individual questions themselves. And like most things worth discussing, funneling versus focusing is more of a continuum than absolute categories.

The key difference between the two, and thus the learning outcomes, rests on the teacher’s ability to draw on the context of the learning to empower the student to use what they already know, rather than merely corral them to the answer. Getting one answer is great, but taking the time and care now to best position a student to get all future answers to similar questions is better.

A Funneling Pattern of Questioning

A pattern of questioning on the far end of the funneling side of the spectrum might go something like this:

“What is the question asking for?”

“Where is that formula on your fact sheet?”

“What is the radius?”

“What is that number cubed?”

“What is that number multiplied by Pi?”

“What is that number multiplied by four thirds?”

Notice those questions are less questions and more a sequence of instructions worded as questions. Also notice that there’s nothing student specific here, nothing to ground the student in what they do understand about the situation. I frequently find that teachers who use funneling patterns of questions will use the exact same pattern for every student. While certainly straightforward, this approach cannot take advantage of anything the student already has going for them.

In a world where mathematics is a series of steps to be memorized, this makes an amount of sense. If a student is stuck, they must not remember the next step. So the teacher asks a question intended to prompt the student to find that next exact step. This is where endless, time draining math drills come from. It’s all about steps that must be memorized.

Consider how inefficient this is. After days of drills, perhaps a majority of the students have this sequence memorized (for now, more drilling will be required later as much of this will be forgotten by the time the high stakes test rolls around)

But it never is just ‘use the radius to find the volume’, is it? No, we have to add ‘find the volume using circumference’. ‘Find the radius given the volume.’ ‘Find the volume of a sphere with twice the radius of this other sphere.’

Every single one of those questions now requires their own sequence of memorized steps. And so the funneling teacher changes their pattern of questioning to match the new sequence for the  new problem.

Note how fast the number of required memorized sequences grows. Note how similar so many of them are. I’d tell you to note how easily students get the steps confused even if they manage to remember them all, but you don’t need me to tell you that.

Question funnels are simple and straightforward, but so is filling a swimming pool with a teaspoon. Simplicity does not equal desirability.

A Focusing Pattern of Questioning

Patterns of questioning on the focusing end of the spectrum are very different. Rather than the context of the questioning beginning and ending with the wording of the problem, a focusing teacher considers the breadth of everything they know about this specific student and landscape of learning surrounding the problem. They consider what comes next and what came before in the content. They evaluate all the connections that need to be made and the different ways they are related.

Frequently the first question in a focusing pattern might be some derivation of “What is this problem about?” But notice how if the teacher is taking into account the student and the content, their next question will always be different between students, because the students will respond with different answers to that first question. “Oh, this question is about finding the volume? What does that mean?” or “Oh, this is about finding the surface area? Is that what you said this kind of thing was about yesterday during our bowling ball exercise?”

The premise here is that the student has some prior understanding to build off of, they just haven’t connected enough of the dots to make the leap with this particular problem yet. So you help them remember what they already know, and then, if necessary, nudge them towards applying it. You are making the jump easier, but you are not making it for them.

I want to touch on a culture of learning problem teachers might run into as they transition to a more focusing approach to questioning.

Frequently students who have only ever been funneled will be resistant to patterns of questioning that want them to actually think about their reasoning. They are expecting their teacher to spoon feed them the steps via orders worded as questions. Creating a classroom culture of learning out of an atmosphere of mimicking is its own whole thing, but be aware that changing expectations is a process that takes time and is best accomplished with patience and understanding. It begins by holding true that math is FigureOutAble.

Want more? Check out my podcast episode on the same subject here.