There are some dangerous myths that perpetrate the world of mathematics: “two minuses equal a plus” and “one is a prime number” always bring me out in cold sweats. However, one that has been gaining ground over the last few years, and is potentially more deadly than all others is this: open questions are better than closed ones.
As a result of this myth, I have seen many lessons were teachers of all ages and experience have spoken to students with a palpable apprehension, seemingly petrified that if they dare utter a question that could be answered in a single sentence (and after less than 10 minutes of thinking time), their lesson would be immediately deemed inadequate and they would be barred from ever setting foot into a classroom again. And so I witness teachers forcing themselves not to ask “what is two-thirds of £24?” and instead scrambling around for something along the lines of: “fractions are better than decimals, discuss”.
So-called “closed” questions have a crucial role to play in the classroom. They are needed to quickly ascertain students’ understanding, perhaps coupled with mini-whiteboards or True/False cards, and as such are an essential Assessment for Learning (AfL) tool. Likewise, open-ended, unstructured questions are also important in order to let students’ mathematical imagination flourish.
Whether a question is open or closed does not determine whether it is good or bad. In my opinion, the quality of a question is determined solely by how much it makes the students think and how much it tests their misconceptions. So I try to make my questions as probing as possible.
“Which number is the biggest: 0.8, 0.715, 0.87, 0.8099”
This is certainly a closed question – there is only one correct answer. But does it get the students thinking? I feel it does. If they have misconceptions about place value, this question will weed them out. A quick whole-class vote between the four options will immediately inform you where to take your teaching next. If the students get it right, they understand it, so move on. If not, get them to discuss their reasoning, intervene if needed and try another example.
So, forget closed and open and start thinking probing!