There are some dangerous myths that endure in the world of mathematics: "two minuses equal a plus" and "one is a prime number" always bring me out in a cold sweat. But the one that's potentially more deadly than all the others is that open questions are better than closed ones.
As a result of this myth, I have seen teachers of all ages and experience speaking to pupils with palpable apprehension - apparently petrified of any question that can be answered in a single sentence and after less than 10 minutes of thinking time. Would this brand their lesson as inadequate? Would they be barred from setting foot in a classroom again? And so I witness teachers forcing themselves not to ask: "What is two-thirds of #163;24?" and instead scrambling around for something along the lines of: "Fractions are better than decimals, discuss."
Open-ended, unstructured questions are important in order to let pupils' mathematical imaginations flourish. But so-called "closed" questions have a crucial role to play in the classroom. They are necessary to ascertain pupils' understanding quickly. They are an essential Assessment for Learning tool.
Whether a question is open or closed does not determine whether it is good or bad. The quality of a question is determined solely by how much it makes the pupils think and how greatly it tests their misconceptions. So I try to make my questions as probing as possible. For example: "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 pupils thinking? Of course 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 pupils get it right, they understand it, so move on. If not, get them to discuss their reasoning, intervene if necessary and try another example.
So, forget closed and open questions and start to think about "probing". Everyone will be a winner.
Craig Barton is an AST from Thornleigh Salesian College, Bolton. He is also the creator of www.mrbartonmaths.com and TES secondary maths adviser. He can be found on Twitter using @TESMaths
IN THE FORUMS
There is some honest feedback in the TES Resources maths forum about what it is really like being a maths teacher. Would it put you off?
Find all links and resources at www.tes.co.ukresources042
Test pupils' ability to write numbers in expanded form with a handy worksheet from Jinky Dabon.
For differentiated place value tasks check out SQUIDLEY's presentation.