Greater Depth

(Deeper not Higher)

(NOTE: Since writing this article, the ‘Greater Depth in Primary Mathematics’ book has been published. You can buy a PDF from this site, or you can get it on the Kindle store, or if you prefer, you can get the actual physical book.)

For the past few months I have been asked a lot about what greater depth actually means in terms of classroom practice.

There is a clear tension between the perceived need to push faster graspers onwards and upwards, and the perceived need to ‘keep everyone together’ as some people seem to have misinterpreted Mastery.

Do we extend or enrich, and what is the difference? I propose to write a short book on this subject in the coming months, such has been the interest from teachers. But for now, here are six quick suggestions.

Think how you could help children link a question to another topic. For example, if you draw it out, bus stop division looks an awful lot like the area of a rectangle with the two dimensions as factors.

Ask children to create similar questions to the ones they have answered. And then switch their question with someone else’s.

Instead of giving a calculation and requesting the answer, give part of the question and the answer to encourage children to think about deeper understanding of inverse operations. E.g. Instead of 23 x 7 = ?, ask them to think about ? x 7 = 161. Same question, different depth of thought required.

Ask children to convince first themself of the correctness of something they have worked out, then a friend, and finally a skeptic. Thanks to George Polya (c.1953) for this one.

Find open-ended investigations to help children apply the ‘factual’ learning. For example, after doing subtraction, ask children to find pairs of numbers with a particular difference, and to spot patterns in their answers. This works particularly well with Numicon shapes or Cuisenaire Rods. Thanks to Pete Griffin who first made me think about this. Another linked idea might be to ask children to start at say, 313, and repeatedly subtract 7. Get them to predict whether or not they will land on a specific number such a 54, and to explain why.

Never allow answers that do not contain the word ‘because’. Top tip from the wonderfully wise Hamsa Venkat.