So today I had a bit of a moment in my bottom set year 10 class.

It was our second lesson together, ever, and we were multiplying and dividing by powers of 10. Together, we constructed a place value grid on the board and worked out that if you divide by 100, the numbers move to the right, two columns. During the utterly thrilling session of Multiplying & Dividing by Powers of Ten Bingo, I noticed that some pupils were moving the numbers in the opposite direction to what we had decided on.

Why?

They were so used to moving the decimal point that, when we had discussed what direction they go in when you multiply or divide, they applied the direction to the decimal point instead.

At that moment I thought to myself “am I doing the right thing?”.

This class will always find maths a challenge. They will take their linear foundation GCSE at the end of year 10 in order to give them an early bash at it, followed by a re-sit in November of year 11 and then again in June of year 11. I have two years to help them get to grips with the subject and, here’s the crucial bit, I have the opportunity to help them attempt to get a C in Maths.

Should I teach them that the decimal point stays put and the numbers move? Or should I teach them to move the decimal point?

This throws up a massive question over the way I decide to teach these pupils for the next two years. I know that I could teach a ‘certain’ way in order to train them to answer exam questions, but this will be purely instrumental, tricks, rules, methods to follow.

My instinct was to teach relationally, especially as I have two years with them (for the past couple of years I have got yr11 bottom set when they arrived in yr11, so only had one year with them). However, when I realised they were so used to moving the decimal point, I wondered whether I wasn’t just making their life harder by insisting on drawing out the place value grid.

Or can I have a combination? Can I teach them about multiplication and division using a place value grid and then finish off with a “now you know how it works, here’s a quick trick to make your life easier”?

This decimal point dilemma has really got me thinking. What do I want? Pupils with a relational understanding, although this may take longer to achieve and therefore slow down the pace with which we cover content, or pupils who can follow methods and rules who may be able to answer exam questions through training and therefore be more likely to get a C and, thus, more likely to have choices in life. (I am torn, by the way, between ‘helping pupils to get a C in order to improve their opportunities in life’ and ‘not devaluing a C grade by training pupils to achieve it through following rules when they may not really understand it’. Some may say those pupils do not deserve to pass maths, but others may say it is those pupils who need our help more than anyone.)

It makes me uncomfortable and I’m not sure what I want. I know I want to do the best I can for them, so I’ll focus on building their confidence in maths and building trust and rapport with the class. I think I’ll have to work out what is right for them and what is right for us.

Reblogged this on The Echo Chamber.

Like you say, the question of moving the decimal point is one which is actually way deeper than it first seems. And also like you, my first instinct is to say that it is the digits that move AROUND the decimal point. With mine – Year 4s – I found it good to talk about THE IMMOVABLE DOT which sounds way more exciting than it is. Then we stuck a kid at the front of the class with a placard saying I AM THE IMMOVABLE DOT and we did the calculations around this stati child. Ridiculous humour is sometimes useful for the pedagogical dilemmas.

Honestly not sure what I’d do in your situation though – I’d like to take the moral highground but I’m not sure.

Yep, I did the same thing with year seven. Each had a whiteboard with a number and they moved around the person with the decimal point. I said the decimal point just sat in their throne and pointed at the others telling them to move. I know what you mean about the moral high ground, I believe in relational teaching and I know it’s got to be the way. Also, I worry that if we start picking and choosing when we teach relationally, we end up thinking that certain groups can’t handle it and the rich get richer.

Reblogged this on TickTock Maths and commented:

This is a really interesting post, and a great starting point for a debate.

Pingback: Should we move the decimal point? | TickTock Maths

I find your dilemma fascinating. At school in the olden days (1980s!) we all ‘moved the decimal point’ even at A level simply because it was much faster – and we understood the maths behind it perfectly well. I’m about to start a second career as a primary teacher and I’m a little uncomfortable about only teaching a slower method when there’s a much faster one available. Must confess I’ve taught my own son to move the decimal point! Love to hear what experienced teachers think.

Indeed, I’m sure I always moved the decimal point too – but I knew why. The trouble is, bottom set year 10 don’t necessarily know why we’re moving it, they just know that’s what you have to do, hence the discomfort in teaching them to do it. It’s a difficult one, because I want to teach them the way that will help them understand and will be best for them – but maybe there is a dichotomy there.

Sounds tricky! Can understanding ever follow the ‘doing’ in your experience? I’m probably not putting it very well but I wonder if the satisfaction of getting the correct answer and then being able to use the technique to solve more complex problems might then lead to some of them ‘getting it’ in the end?

Reblogged this on teachingwithcandy and commented:

Interesting blog entry well worth reading.

When multiplying 89.634 by 100, I just move the decimal point two places.

Of course, I could move the digits instead, but that is moving 5 things instead of one. Too much work for lazy old me.

Apparently, it is very important to understand the maths and learn that the decimal point always stays still.

The trouble is, I just don’t understand what it means to say ‘The decimal point stays still.’

I guess it means that when I look at the numbers 89.634 and 8963.4, I can tell children that the decimal point never moves and is in exactly the same place in both of those numbers.

But anybody can see for themselves that the decimal point is not in the same place in those two numbers.

When you look at a place value grid, though, the decimal point does not jump around, it always stays between the units and tenths column. It is fixed.

I haven’t tried this. If I ask primary school children, if the decimal point is in the same place in the numbers 89.634 and 8963,4, will they say yes it is in the same place, or no. it isn’t in the same place.

That would be an interesting experiment.

if they say the decimal point is in a different place in those two numbers, it will take a lot of explaining to convince them it is in the same place.

I think many teachers are worried that children will end up not knowing that 89.63 is a different number to 8.963, because nobody has taught children that moving the decimal point like that is the same as multiplying by 10.

If children don’t know that moving the decimal point will multiply a number by 10, that is definitely a gap in their conceptual understanding of decimals.

How can this gap in their conceptual understanding of decimals be remedied?