Can someone please tell me why division is taught in such a confusing way in year 3?

[Divideandrule]

I have been polite in saying confusing, I really mean bloody stupidly. DD has come home confused as they have to use number lines and do repeated subtraction or something? She was trying to explain it to me and I didn't get it. (This is the child who enjoys and is good at maths, totally gets place value etc, in high group).

So, I showed her the bus-stop method for the same calculations. Eureka moment and a big smile on her face.

Do I have a word with her teacher about this? I get the need for some methods working for some children and different ones working for others. Surely if she understands the way I showed her - incidentally we had remainders with numbers so had to carry - she should go with that?

Anyone?

or harder one
775 / 31
know this is going to be more than 20
31 x 20 = 620
775-620 = 155
31 x 5 (get this as 15 = 3x5) = 155
so answer is 20+5 = 25

Division isn't necessarily repeated subtraction, is it?

That's only an interpretation of the process. It's simultaneous subtraction. In simple division you take all the portions away from the initial figure at the same time. Conceptually it's a different proposition from subtraction, because with subtraction you calculate how many you have remaining after one diminution. But with division you do all of the diminutions at the same time and then calculate the remainder, (unless you're doing long division.)

That is my beef too. Whilst repeated subtraction often ends in the same result it is not the same thing as division. The four bits of arithmetic are adding subtracting multiplying and division. Multiplying and division are not just extensions of adding and subtracting - they are more fundamental than that. And I don't think the number line, chunking etc really gets that across.

The point is to understand what division is and then know the methods to reliably work it out. There is nothing wrong with the "bus stop method" (why is it called that ?!) - the problem is many people were taught the method and never the explanation. It is the way it was taught that was the problem. You need to understanding division is sharing into equal portions and why the method does that. Once you know that you can forget why and just know it does.

Most maths at higher level does not rely on you working it out from first principles. You do that when you are learning it and then accept the fast method and use that to do whatever it is you wanted to do.

All the primary school methods are just tools along the way - we get far too hung up on which particular method you should use. If you have a method that you understand and it reliably gives the right answer that use it. If one method confuses try another - if that makes sense - great - use it.

44 x 5 is 220 :) but close.

juniper904 - I think your directions illustration is telling. Some people prefer landmark directions (your method 1) and others prefer to work out a route on a map (method 2). One is not universally a superior method for all people (very far from it).

Agree very much with throckenholt's post.

Could someone tell me what the bus stop method is?

I have never thought of division as repeated subtraction and I managed an A* at GCSE. I learnt methods which, when applied to the numbers, achieved the correct answers. Job done as far as I'm concerned. I have never had much interest in maths, except for when it is useful in real life situations, and in a real life situation, what you need is the correct answer, not necessarily an in depth knowledge of how or why that is the case.

I've never thought of division as repeated subtraction and I don't think it is. I explained division to DD using slices of cake and fractions - she didn't have any trouble with the concept once she had visualised it.

The bus-stop or bus-shelter method is so called because the way you write the division sign looks like a bus shelter (a roof with a wall only on one side.)

Well, for those of you who only want to learn day-to-day, useful maths, and maths for passing unchallenging and boring exams, just go with the bus stop method and ignore other explanations and ways of looking at a problem. On that basis, I presume you consider most of school to be a complete waste of time, since most of what you learn is irrelevant to how you go about your daily life. I mean, why on earth did I waste my time learning about the properties of lithium and potassium; or what happened in 1066? Why bother to write about what a book means or what themes it contains? Who cares what it's supposed to mean to anyone else? Either you enjoy it or you don't. It's all just for passing pointless exams, so why not cut the crap and just do the bits we all HAVE to know to get things out of the way quickly. We could all get through school and out the other end by the time we were 10, then, and go out to work (if there were any jobs available).

OK, thanks choccyp1g .

Have you seen this?

www.mumsnet.com/learning/maths/what-chunking-means-in-maths

There is a whole section on current methods used to teach maths

www.mumsnet.com/learning/maths/maths-introduction-section-one

bonsoir,

here is someone using the bus shelter
www.mathsisfun.com/long_division.html

I've never thought of division as repeated subtraction and I don't think it is.

Start with 18 chocolate buttons and share between three people. What happens?

Division is the inverse of multiplication, grouping or sharing - repeated subtraction is one of several ways of solving it - but in actual fact if you are making groups or sharing something out it can actually be confusing to some children by presenting it as repeated subtraction - it isn't taking away or subtracting it's rearranging - nothing is subtracted, it's all still there. Not to mention repeated subtraction doesn't transfer well into fractional division later on - i know it's a long way from year 3 but if we are laying the ground for 'unlearning ' later on it can cause problems for children at a later stage.
But since the NC requires children to be able to do it that way...........

Sorry feenie - in answer to your chocolate question - the children eat the chocolate and in that case it is repeated subtraction

Feenie - "start with 18 chocolate buttons and share between 3 people. What happens?"

The 18 chocolate buttons are divided into 3 equal amounts = 6 each. That's not subtracting, its sharing.

But how would you do it? If you share 3 out each time, you are subtracting three from the pile that you started with, no?

@ clutteredup

No. I would split the 18 into 3 equal groups of 6 buttons.

I am not in my mind subtracting anything from anything else, I am re-grouping.

But a child learning division and doing it practically would share them out, one by one and three at a time. The total diminishes by 3 every time until there are none left to share equally.

That's cos you know how to divide and what you are doing, Iamnotinterested.

But the OP's dd sounds like she has a good grasp of what division is and does not need to follow the steps that you describe.

Child today to me in class (sound of lightbulb going on) 'so you share out some of it [we were doing division problems using money], say 10p or 5p at a time because that's easy and doing it in 1ps would take too long, and then use subtraction to find out how much money you have left to share out?'

Bingo

IANI, for your example, I too visualise 3 equal groups of 6. But when it comes to bigger numbers (say 459 divided by 7) I can't visualise the size of each group 'all at once'. instead I share it out bit by bit - say 50 into each group first, think about what's left, share the next bit out 10 at a time, then 5, then the remainder is left. It is, as my pupil said, sharing out equally using subtraction to find out how much is left each time.

True - but I agree with whoever said that it's another way of understanding that an able mathematician should be able to understand.