Holier than thou 

I try to avoid polemics, or being divisive. The topic below is one where, I suspect, opinion is already sharply divided and each side views the other with suspicion and some incredulity. 

1) It really gets my goat when a teacher reserves an efficient strategy or rule-of-thumb for themselves, yet insists that pupils may only have access to a complex and more confusing version (i.e. The revered “correct” version). What happens in practice is that bright sparks quickly see the underlying pattern, check it for reliability, and then adopt the rule of thumb unimpeded by the teacher’s beliefs. The rest remain confused, experience low success rates in their work and thus low confidence and motivation. 

2) If someone uses or shares a heuristic or strategy that isn’t technically accurate, but is efficient and reliable, it is bizarre to assume that they must be an ignorant teacher. Maybe they are. But maybe they’ve made a strategic calculation about how best to teach their pupils. 

I have never met a maths teacher who doesn’t know that “the decimal point doesn’t move, the digits do.” 

I get the impression most pupils have been told it too, especially in primary. 

Low accuracy in this topic is one of the most common hallmarks of pupils who struggle in maths generally. 

If a teacher teaches the strategy of “move the decimal point,” it is unlikely to be due to ignorance on their part. The cry “the point doesn’t move!” felt like a tired phrase before I’d even finished my PGCE year. It’s the “not all men” of the maths teaching world. 

When multiplying or dividing by a power of 10, the crucial change is the relative position of the digits and the place value columns. Moving the digits, or moving the columns (i.e. the decimal point) will both get you there. 

Overwhelmingly, numerate adults use the “rule” of “add a 0 to the end” when they are multiplying integers by 10. Overwhelmingly, numerate adults move the decimal point to multiply or divide by a power of 10. I don’t understand why we would block pupils’ access to this widely used approach, or than to be sanctimonious, to think “I’m not interested in them getting to the right answer, I’m interested in how they think, and in building deep understanding.” 

Any decent maths teacher is interested in how pupils think and in building deep understanding. But is simplistic and arguably harmful to insist that learning only takes the form of “deepening understanding.” We learn to speak with (relative) grammatical accuracy long before we learn what it means to conjugate. I suspect most British people can’t parse their speech and writing. I also suspect that, if we’d forced them to learn to parce as the sole method of learning to speak and write, they would be terrible at it, and most would hate it. 

We enjoy things we feel we are good at, and getting better at. Deep thought can only take place in the context of a rich landscape of examples, exceptions and intellectual self-confidence. Teaching a rule and building fluency creates the context for the surprisingly deep and difficult thought that underpins place value.


Filed under Interesting or Fun

12 responses to “Holier than thou 

  1. I’m guessing you read my comment on Hin-Tai Ting’s post. (If not I’m being paranoid). I’ve added to it now, it was a hastily-written comment when I was busy, its purpose wasn’t to negate anything I’d read. I work with lots of non-specialists teaching maths who have never thought about what happens when you multiply or divide by powers of 10, so that was at the forefront of my mind when I commented.

    As for using something like moving the decimal point, of course we all do it, it’s much easier mentally provided you know all the implicit ideas Hin-Tai said,l, and I am not necessarily an advocate of “deeper understanding”. I actually think lots of the deeper understanding we as teachers have many students cannot yet achieve because they are not fluent enough in procedures. I certainly fall on the side of procedure first in many cases.

    Last night I was simply reading a (very interesting) post and hastily wrote something based on my frequent experience. Sorry if I got your goat.

  2. Pingback: Teaching mathematical grammar | mathagogy

  3. Matt

    Do you think there is ever an argument for teaching “swap sides swap sign”? It’s another one I’m sure that most teachers do mentally and it makes rearranging and solving much easier in many cases. If pupils understand that they are really adding/subtracting to both sides then I don’t see the harm!

    • That’s one I think is harmful, actually! It doesn’t generalise to any of the other operations (e.g. Square root, dividing, etc) so leads to them needing to learn multiple rules instead of seeing that there is one simple rule governing the whole thing. That’s an interesting question though, making me think about when it is and isn’t the right call.

  4. Pingback: Simultaneous Equations, refining the procedure | mho maths

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