# Chunking division. Why?

Discussion in 'Mathematics' started by existentialtyke, Jan 30, 2012.

1. ### existentialtyke

Why do primary schools, in particular, persist with 'chunking' division when 'bus stop' is so much more straightforward? I have known many children who have found division impenetrable due to chunking, only to pick it up quickly once the bus stop method is used.

2. ### PaulDGOccasional commenter

It's a mental method that works.

I mean, no one does "bus shelter" in their heads, do they?

(I think the real difficulty is the ordering here - we should start with "sharing out"; actual physical sharing out of counters, cups or whatever is in the resources cupboard from the last fad.

Then move on to obvious integer division from recognition of multiples in the times tables

Then move on to long division

Then bring in the two short cut tricks - "chunking" for mental maths and "reality checks" and "bus shelter" for pen and paper division where the numbers are small.

3. ### AnonymousNew commenter

I am not sure that it woeks as a mental method for a problem such as 24334/ 78 does it? Would that not be better solved with a paper method? Chunking that on paper produces a very long and cumbersome answer!

4. ### florapost

chunking that on paper is plain daft
i'm not saying no one does it, 'cos folk are plain daft, but as an objection - well, you might as well object to hand sewing because anyone with a king size sheet to hem will use a machine
you'd still hand sew the hem you caught on the way to school
mind you - bus stopping 24334/78 seems pretty pointless to me too - surely that's why god invented calculators
and the skill should be - knowing when to chunk, when to bus stop, when to use a calulator, and for that matter, when to use a spreadsheet instead
florapost, sick of checking other teachers' admin stats cos they haven't had the sense to create a spreadsheet in the first place

5. ### Polecat

I'm delighted to say that I haven't a clue what you are talking about.
However, I'm interested in polynomial division, and I wonder what 'clunking' and 'bus stopping' become in that scenario.

We use chunking because it is the next logical step after division as repeated subtraction on a number line. Chunking follows the same procedure , just in a written rather than a diagramatic way. So the children can see WHY they chunk. The same can't always be said of the bus stop, they don't understand what they are doing, subtracting from the left rather than the right is counterintuitive for them and, whilst you can teach them to follow the methd, if they don't understand WHY they find it difficult to spot mistakes in their method ( whilst with chunking they make mistakes but they find it easier to spot where they have gone wrong!)

That's the theory anyway!

7. ### PaulDGOccasional commenter

I'm not sure if chunking and factor theorem are connected, that's something I ought to work through one day.

But "bus shelter" is short division - which is long division but with all the working out done mentally or in the margin.

It's efficient for 2/3 digit numbers but the lack of a structured way to manage the working out means it leads to more errors than long division.

As you may have noticed, and certainly exam boards have, A level candidates tend not to be able to do polynomial division these days. Unless they were educated in countries that actually do some work in their equivalent of KS1-4, of course.

8. ### DMNew commenter

Hasn't polynomial division been largely replaced by synthetic division now?
I once read a nice piece of research that suggested that C grade A Level students could be taught synthetic division and polynomial division equally easily but, when tested a few weeks later, had much greater retention of the synthetic method. There was no measurable difference for A grade students.

9. ### Polecat

'Hasn't polynomial division been largely replaced by synthetic division now?'
OK DM, I know that the kids can't be expected to divide by anything other than a linear factor, but then you just look and see. I don't understand why we have to be burdened by fancy names. Perhaps 'synthetic division' is what I have been doing all of my life without realising it.

10. ### DMNew commenter

From the OCR Core 4 specification:
"Candidates should be able to d<font size="3" face="Times New Roman">ivide a polynomial, of degree not exceeding 4, by a linear or quadratic polynomial, and identify the quotient and remainder (which may be zero)"</font>
<font size="3" face="Times New Roman"></font>

11. ### Polecat

So they do have to know about polynomial long division. Good.

12. ### DMNew commenter

No - as I said before they can always use synthetic division.

13. ### florapost

oh you secondary school teachers!!!!!

14. ### Polecat

<table cellpadding="0" cellspacing="0"><tr><td class="post">'No - as I said before they can always use synthetic division.'
But I have just read that synthetic division, whatever that means, only applies to division by a linear factor. Just shows, one shouldn't believe everything one reads.
</td></tr></table>

15. ### DMNew commenter

Find the
quotient and remainder when
2x4 + 3x2 - x + 3 is divided by
x2 + 2x + 3
Quotient is
of degree 2 and remainder of degree 1 so:
2x4
+ 3x2 - x + 3 = (x2 + 2x + 3)(Ax2 + Bx + C) +
Dx + E
Expand
brackets and equate coefficients. Job done.

16. ### AnonymousNew commenter

Chunking - makes the concept easy to understand
e.g 246 / 3
Well we know 80 x 3 = 240
So that leaves us with 6
2 x 3 = 6
So we have 82 x 3 = 246
Bus stop - easy to learn. Although I have seen some great mistakes, usually involving the remainders although last week someone insisted on putting the divisor on the top.
However - it's the usual debate about understanding or learning a method.
Chunking does lead to a good mental method to calculate the answer. In theory.

17. ### Anna-Luise

In all my years tutoring A level maths students from plenty of different schools and colleges I haven't met one who was taught synthetic division. It doesn't appear in any A level textbook I own either.

Where has it replaced polynomial division?

18. ### DMNew commenter

I can understand your confusion. It seems synthetic division is now almost exclusively used to describe that algorithm I don't particularly like and the method of equating coefficients now has a variety of different names.

19. ### Polecat

'Expand brackets and equate coefficients. Job done.'
Yes, well, I have seen what others have told me is synthetic division, and it doesn't look anything like that. I'm coming around to the view that any method, other than long division, is called synthetic division for want of a better term. Of course, the method you describe is in exact one-to-one correspondence with long division, so there really isn't any difference.

20. ### DMNew commenter

Funny that. It is the preferred method in every textbook I own that was published this century and the only people I know who still teach the traditional long division algorithm are even older than me. Traditional long division of polynomials was poopooed on my teacher training course 10 years ago. I haven't personally carried out any sort of traditional long division of numbers or polynomials for 25 years. Horses for courses I suppose.