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?

Division IS repeated subtraction, in the same way as multiplication is repeated addition. It's a step on the way to bus stop division, which needs a very, very secure understanding of place value - your dd needs to know why it works, and how, as well as being able to perform it.

Feenie But she DOES have a very, very secure understanding of place value. Her teacher said so at parent's evening. Absolutely rock solid.

I believe it is called chunking and-it-confuses-me

I went in and the teacher showed me how they teach it - I was concerned that if I did it any differently when helping with homework,I would just cause confusion.I can now do it their way,and then they will progress to carrying numbers.

Then she'll no doubt learn the bus stop method sooner than most, OP. But she does need to understand that division is repeated subtraction., it's an important step.

My ds1 (year 3) told me today that he doesn't want me to look at his maths book at parent's evening, because he doesn't understand the bus stop method, and doesn't see why they just can't do chunking, because it's far easier.

going to have to look them up, because I haven't actually got a clue what he's talking about.

Times have changed. It doesn't mean the new methods are wrong.

I teach year 3, and our calculation policy also show division as being repeated subtraction. This is actually an important level descriptor for level 3 (in the assessment method my school uses).

Children need to have a really, really firm grasp of number to understand the bus stop method.

When I myself was in year 2, we did column addition for subtraction and addition. We could follow a method, but we had no real understanding of what we were doing or why. If we made mistakes, then we couldn't spot them as we didn't understand the relativity of the numbers.

If you're interested in the reasons why we don't teach column addition until the end of year 4 (and, even then, as extended columns) or the bus stop method until upper KS2, google 'relational and instrumental understanding of maths'.

I wrote an essay about this at uni, and the example we were given was the idea of giving directions to a house.

Method 1- instrumental. Tell someone to turn right after the postbox, take the second exit at the roundabout and the third turn. Great. But if you miss the post box, then what?

Method 2- relational. Show them a map. Then they understand the route to take. Even if they miss the postbox, they can follow the route back and apply the method again.

It's a simplistic model, but I think it works.

Incidentally, explaining our calculation policy to parents was the number 1 thing that came up at parents' evening.

They couldn't understand why we do things on number lines rather than the way they were taught.

If your dd understands how numbers work and what division really is, then what's difficult and confusing about repeated subtraction of the same number???? I can see it is a slow way of doing it, but not a difficult or confusing way of doing it.

rabbitstew Because she, and I, don't see the need for the way school are teaching it when she can quickly and accurately do the bus-stop method.

She has to understand what she is doing as well as follow a method. If she doesn't it will cause her problems later when the teacher assumes she has a secure understanding of the CONCEPT of division and all she knows is one method of dividing.

It's called chunking and was definitely invented by a non-mathematician who didn't understand maths at school.

My mil says it's great, because it, plus the grid method are earning her lots of money because she's inundated with children for tutoring who don't understand them. She does a couple of lessons with them and shows them the old methods and suddenly they understand and are happy. And it's not just because she is tutoring them. She started off by trying to teach them that method, then found they consistantly found the old methods quicker and easier to understand-in about half the number of lessons.

DeWe - I suspect that your MIL is teaching these pupils the 'old' methods so they can get an answer, their parents are happy, and noone worries too much about whether the children actually understand what it all means, as research shows that that is what happened with the old methods.

But hey, I'm glad it works for your MIL.

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.)

My DCs school holds regular workshops for parents to show us how and why they teach +, -, / and x they way they do. It did make the reasons behind it clearer although even with the help of some Y6 students, I failed to manage the methods on my white board (and I have Maths A level and a science degree ) I can understand why it's taught this way, although my DS is very good at maths - naturally sees the patterns and understands the concepts and it has been very frustrating for him to have to do things this way. He has been taught the old-fashioned methods for recent entrance exams because the new ways simply take too long to do.

I've got a bit of sympathy for long winded explanations of how to do calculations because it's common to find people who can get the right answer to an equation but can't explain why (my dad for example) and surely school is about teaching children not only how to do it but why they are doing it.

It's very unfortunate then if they can do it but only after a long time and can't pass exams because their calculations take too long. (But maybe that's something for exam boards to look into.)

Sorry, I still fail to understand why Divideandrule's clever dd found the method confusing. Yes, it is slow and unnecessary to do it that way, but not confusing if you understand the concept. Maths is about playing about with numbers. There are many ways of understanding the same thing and the more ways you understand it, the more flexible you can be in your thinking around a problem. What is enjoyable about maths is that there IS often more than one way to get to an answer. Obviously, if you are not naturally flexible in your thinking, you will get confused, because then division won't only mean one thing to you, it will mean too many things for you to get your head around. That seems like a fault in the way you think to me - you can't cope with more than one way of seeing things.

Some people can't cope with more than one way of doing things.

doesn't chunking also help with the idea that division is the inverse of multiplication?

I help my year3 dd to do both. She understands both methods. I let her chose which she uses and her teacher is fine with this. She usually uses chunking when the number is small but with larger numbers uses the bus stop method because it's quicker.

Her teacher seems happy with that because she can easily display the use of both. I think both methods have their advantages.

I can do the bus stop method (the old one with the numbers under the big square-root sign) but I have no idea how it actually works.

Chunking sounds really complicated written down but it's probably the way you do division in your head without thinking about it, at least, it's the way I do it.

Say, 104/16.

I don't know my times tables so nothing resonates with me for 104. (Although actually now I've thought about it it's twice 52 which does correlate to something, is that 8s? Anyway I'm getting distracted.)

So, I know that 15 goes into 105 7 times, just by counting. 15 (1) 30 (2) 60 (4) 90 (6) 105 (7)

So, it's likely to be somewhere around 7.

16 is 1 more than 5. So I have to add 1 to each of those 15s - which is plus 7 because there are 7 15s.

105 + 7 = 112. 112 is 7 x 16.

Let's go back one, by subtracting 16.

112 - 16 = 96. 96 is 6 x 16.

Either way you look at it, both of these numbers are 8 away from 104. Since 8 is half of 16, and we know that 6 x 16 = 96, + 8 = 104, so 104/16 is 6 and a half, 6.5.

That's as clear as I can get my mental process written out.

Does anyone else want to practice writing out their mental process? 264 / 44 ends up in an easy number (no long decimal places).

rabbitstew You have just said yourself that the method is slow and unnecessary. Why then should a child have to do it when another method is quicker and clearer FOR THEM. To clarify, she is really good with X tables, knows the inverses, knows what division means. It just seems to be with her that the process of the chunking method isn't the clearest way for her to do it.

isn't there a quick chunking method?
so 367 divided by 35
I know this is going to be more than 10 (10 x 35 = 350)
367 - 350 = 17
17

That's an easy example though because of the division being by 10.

Does it work for my 264/44 example?

44*5=222
264-222=42
42