What do you think?
Lattice Multiplication
The only difference is that I like to add up at the end stepwise:
01
005
0006
00015
000003

Double division

Last Edited on 16-Jun-2008 2:12 PM

Through the years, we have seen a plethora of "new" approaches to math and grammar in the classroom, all supposedly designed to make learning math or grammar easier. With few or no exceptions, these approaches have utterly confused students. Eventually, they have been abandoned. Unfortunately, every generation of educationists endorses yet another way to complicate a perfectly functional and simple approach.
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Rich Turner (The Curmudgeon Himself)

Last Edited on 18-Jun-2008 7:49 PM

Now both you, Mudge, and Pogo are Americans so it might be that you were taught different methods to me.

Briefly, I was taught to do a long multiplication as follows:

To calculate 258 × 167:
Line up the numbers with the biggest number on top:
258
167

First multiply the 8 by 7 = 56. Put down the 6 and carry the 5. Multiply the 5 by 7 = 35 add the 5 = 40. Put down the 0 and carry the 4. Multiply the 2 by the 7 = 14 add the 4 = 18 put that down.

Add a 0 under the last number and repeat the same process using the 5 on finishing add two zeros and do the same for the 1. add the answers up to get the answer.

The advantages of lattice multiplication only kick in when you try to multiply really large numbers. Try multiplying a six figure number by a five or six figure number (not ones ending with lots of zeros) with both approaches and you will probably find lattice multiplication easier.

More on long division when I figure out how to write the post clearly.

Last Edited on 19-Jun-2008 4:29 AM

If I was doing the example given, I would have done it by cancellation but where that cannot be done, you are forced to do long division. Personally, I find double division much easier now that I've tried it.

What method do you use?

Seriously, tho, my mother taught grammar school for 25 years and during her career, the "new math" reared its ugly head. I think it was in the mid-60's.

The teachers learned it, under protest, claiming it had no advantage to the tried and true traditional method, but who listens to teachers when there are "educators' in the room?

As all the world knows, the "new math" is nothing but a distant memory, but the "educators" are still with us.

link

Here is one succinct comment re same from that article: "The New Math produced students who had heard of the commutative law, but did not know the multiplication tables".

New Math was the dream of some educrat who had apparently never taught anything himself. My own grade school began using it in 1965, when I, a senior in high school studying calculus, was asked to help the first-grader next door with his arithmetic homework. I was told he was learning addition. His homework was to fill in the blanks:

 9
+ 
14

Two years later, that grade school had ditched New Math and gone back to the old techniques, what the critics call "Drill and Kill."

Three or four years after that, the Houston Independent School District started boasting that it had changed all the grade school math to that wonderful new way called New Math! I was horrified.

The basics must be learned first. Then you can play around with it. Really. Like Doug, who used to do his calculus homework in ten minutes every night, then spend two hours figuring out other ways to get the same answer.

One of the things that article mentioned was new maths teaching set theory at a very early age. Now set theory does indeed underpin the fundamentals of the foundations of mathematics but it would not be ignorant to say so what?

The study of mathematical foundations is very important at a high level but is not necessary to learn to calculate. We should not aim only to teach mere calculation but that is the basis of all that is to follow. (Don't get basics and fundamentals mixed up here).

One insidious thing about it is that if you then switch back to traditional mathematics, you are unable to apply the set theory that you have used until much later when you have forgotten what it was about.

Last Edited on 25-Jun-2008 1:59 PM

"That's the way I multiply."

What is?