The Online Teacher Resource
#11




double division
It sounds like the math curriculum at this school was not planned out as well as it should have been, and your niece suffered for it  that's unfortunate. I'm glad she got the hang of it in the end.
The fact is that long division is built into most math curriculums and that fact is not going to change any time soon. The question is whether double division (or "1248 Division") can help in teaching long division by reinforcing the principles of division and giving students success with a less frustrating alternative. My only goal is to make it available for people to consider, and so far the feedback has been mostly positive  but not all positive. Jeff http://doubledivision.org 
#12




Depends on what you mean by "positive." Does positive mean, "They agree that this is the way to go?" or does it mean, "It was constructive"?
My opinion is quite simple: It is a clever approach that could be used to supplement long division, but it is no substitute for long division. Is that positive? 
#13




not a replacement
Yes, by "positive" I mean constructive. No one has thought that this method should replace long division.
Given that long division is built so strongly into our system, the question is whether this method has a place at all? I don't really know. I've seen that people teach this method without doing the doubling at the beginning  the goal being to show that division is subtracting off multiples of the divisor. Doubling the divisor in the beginning makes it into a more practical method  that is also instructive. If it's done right, I could image kids learning double division first and then learning long division as a faster way  and in the end understanding long division better. Jeff double division  long division teaching aid 
#14




I think we can agree.

#15




Division
I have been teaching a similar method for 6 years now and it really is quick to understand and learn. I will try this double, double "Tim Horton's Coffee" method tomorrow! (Ah Canada)
Division is, really in our lives, the act of taking groups out of a pile and spreading it around. As in..... I have 5 678 candies to share with 7 people.(lucky them!). I want to deal with friendly numbers that end in zeros because they give me 'zero' problems to subtract. If I know my multiplication facts, I know that 7X8= 56, so I could take out 5600 candies and give each person 800. 7X800=5600. I have taught the students to multiply 7X800 to be "56 and 2 zeros". Who ever says the full mane when calculating anyway! If I do not know my facts then I could take out any lesser multiple that I do know! Teaching multiplication before division MUST cover the Multiples of 10, 100, 1000 first! Then 5600 is a snap to subtract FROM 5678 and find there are only 78 remaining candies to divide up! Well 7X10 is 70,,, so take those out and give each person 10. This leaves only 8 candies so I give each person 1 more. The remaining one candy is a problem for fairness, so I eat it!!! How many candies did each person get? Well, I gave each person 800 and then 10 and then 1. Must be 811 each! So simple you can do it in your head. And of course double digit division is the same. Just nibble away at the pile and subtract 'zero' numbers. (multiples) The student does not need to know his/her facts as well as in the long division method. But they will see that if they learn their basics, they can do the questions faster! The long division method seems to teach rules but this other way seems to teach understanding! Just my thoughts! 
#16




Tim Horton Coffee
(I could go for a Tim Horton double double right now.)
Here is a paper on teaching long division that you may find interesting. http://www.math.technion.ac.il/~ra/englongdivision.doc Let me know how it goes doubling the divisor. What age children are you teaching? Jeff (I finally registered) double division 
#17




Division
Our school just adopted the EVERYDAY MATH series. It is published through the University of Chicago.
The series teaches this method as an alternative way to divide (called partial quotient division). They also teach partial sum addition, partial difference subtraction and partial product multiplication. Basically, it gives children the option to use this method or the traditional method.....I get mixed reviews from my students, but I stress that either way is acceptable. 
#18




But again, teachers in the future may require that students know long division.
We need to keep this in mind. 
#19




From what I've seen of the UofChicago partialquotient division methodit serves to help understanding but sadly it is not helpful in a practical sense (higher levels of mathematics). Some students who are taught this method and prefer it over standard division are totally incapable of doing "regular" division and continue to revert back to partialquotient, simply because they have not been taught to estimate with large numbers. Similar to the lattice method in multiplication, this method serves to delay learning of fundamental operations.

#20




Well done  much simpler and definitely logical
I teach numeracy and literacy in an Internet exchange centre, one of the stipulations is that we pass the very test that we are teaching. Your practical solution to long division is fantastic. It makes so much sense. A number of my learners have complained that there must be a logical technique to long division that does not involve the random multiplication guesswork.
This technique is a God send Quote:

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