Tad Watanabe wrote: Yes, the long division algorithm is (or can be) very conceptual. It is true that many people do not know why it works but that does not mean that the algorithm is not conceptual. It was rarely approached that way.
Suppse you have 458 div 3. Make 458 with base 10 blocks. Now, if you have constructed the understanding that division can be thought of as "sharing." Then you want to share the 4 flats, 5 longs, and 8 units. The natural place to start is flats [most people will come to this conclusion after trying to do it starting with units a couple of times]. You share 3 of the 4 flats, one to each of the three group, leaving the last one. 1 5 2 ------------- 3 ) 4 5 8 3 --- 1 5 1 5 ----- 8 6 ----- 2
Now, you can record your action - shared 1 flat among three groups, leaving one. The next step is to break the flat into longs and combining the longs you already had - giving you 15. Share 15 longs among 3, giving 5 in each group, leaving no long. Record the action. Now, share 8 units - 2 per group with 2 left over. Record the action. The long division algorithm is a neat way of recording the action that you perform.
Of course, there are other methods, but, my point was, the long division is much more conceptual in the sense that it reflects our action with objects much better than other three algorithms.
Tad Watanabe Towson State Univeristy Towson, Maryland `
On Thu, 23 Feb 1995, Wayne Murrah wrote:
> Do you REALLY think that long division is conceptual? Can children explain > WHY it works? How 'bout adults? For most of the population, I think that > the algorithm is a merely a 'black box'! > > WAYNE MURRAH > (firstname.lastname@example.org) > >