## Long division? What could possibly go wrong?

To say that long division is difficult is an understatement. The teachers who have the onerous task of teaching it know how to do it but the problem then is recognising all those tiny facets that are so internalised as to be invisible. Of course a teacher needs to know how to do it but they also need to know how NOT to do it. This is where problems are identified and children learn faster. Too often children are just taught a routine and some learners just don’t ‘get it’. This is a big routine!

So what understanding is going on (or not) under the surface? Here’s one:

After lots of short division we need to understand that it is unnecessary to ask how many 27s in 3. A two digit number is never going to go into a single digit. And what if it doesn’t go into the first two digits? Why do some children write a zero? No need for a place holder. (Concept: Place value)

Why do we have to subtract? The concept that a remainder is the result of a subtraction is unspoken in short division. The difference is often seen rather than calculated. (Concept: Remainder)

So there it is. What now? Bring down the 5? Why? We have to unlearn the putting the remainder in front of the 5 like we would in short division, possibly because when the remainder is double digit it would be crowded. However, too often there is an incantation of ‘bring down the 5’ because it’s the next step to be remembered rather than for a reason of maths. (Concept: Place value)

And so the process repeats either by rote or by understanding.

But look at the next part. How many 27s in 217? Has the learner practised situations like this as a one off? (Concept: Estimation)

I thought 7 but there are issues about whether another 27 can be found, shades of chunking. Is it OK if it’s a bit more than 217 rather than way under? In the end it was 8. If I take my eye off the ball to work this out without an understanding of the process I might end up re-entering the algorithm at the wrong point. (Concept: Multiplication, Inverse, Division as whole shares)

So there we are, 128 remainder 1. No good? 128 1/27? You want a decimal? (Concept: Equivalent fractions)

Where did that .0 come from? We didn’t have unnecessary zeros at the start so why now? (Concept: Decimals)

How many 27s in 10? Am I allowed a zero here or do I just stick another one on to make it 100?

And so it goes on. When to stop? Do we know anything about rounding to a certain number of decimal places? (Concept: Rounding)

The whole process is a minefield of potential misconception not to mention differences of process from the already learned short algorithm.

This will not be well learned by a rhythmic repetition of different stages but by understanding of concepts from earlier learning not all of which gets a mention in the National Curriculum in earlier years.

leave a comment