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 A to Z Teacher Stuff Forums Lattice mulitiplication Vs. Traditional multiplication algorithm

#11
06-04-2008, 06:26 PM
 knitter63 Groupie Join Date: Jun 2007 Posts: 1,461 Ohio
I had to teach lattice multiplication and partial product multiplication to 3rd graders during my student teaching. I hated it. The traditional algorithms are so much simpler and efficient. Lattice and some of the other "reformed" math techniques are better at helping kids see why they are doing what they're doing to solve a problem, but can you seriously see an adult in a business meeting drawing a lattice table to solve a problem??

Yes, I can see adults using this method-I do. We use Everyday Math, and we teach the lattice method. It is not difficult to teach, especially if you give it time, and provide lots of practice. My 5th graders have dramatically improved their multiplication skills because of this method. I am not the least bit embarrassed by using the lattice method myself. In fact, when I have in front of other non-teaching adults, most tell me they wish they had learned that when they were in school!

#12
06-05-2008, 04:01 AM
 MrsC Multitudinous Join Date: Aug 2005 Posts: 11,403 Ontario, Canada Grade 7
Quote:
 Originally Posted by mdith4him can you seriously see an adult in a business meeting drawing a lattice table to solve a problem??
Actually, they would be most likely to whip out a calculator!
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It does not matter how slowly you go so long as you do not stop
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#13
06-05-2008, 07:04 AM
 MissFroggy Aficionado Join Date: Aug 2006 Posts: 3,901
The idea of these methods is to begin to understand how the problem works... I NEVER thought about the fact that you are actually multiplying ones, tens, and hundreds and multiplying each by each in a three-digit problem until I was an adult.

In the upcoming years of business, technology, etc. we don't have any idea WHAT people will be doing, calculator or otherwise... the old ways of memorizing and knowing rote facts may not be as useful as they were in the days of assembly line business and technology. We need to create a generation of people who can understand the WHY and HOW of things (not just math) because they will be the innovators. It's too easy to just use a calculator or go online.

I do teach the algorithm eventually to all my students, and I do have kids memorize their math facts, but in general, understanding WHY we do an algorithm the way we do is how we will continue to have inventors and engineers, etc. However, I will say, I was having this conversation with my grandpa who is a genius, graduated HS at 14 has about 5 degrees and is a nuclear engineer. He seemed puzzled about how anyone could NOT understand how multiplication works. He was shocked that I never thought about nor completely understood it until I became a teacher. I do think SOME people (and not just geniuses) get the traditional algorithm and what it really is without all the lattice and partial products and base ten blocks and all that. But for the people who don't get it, I think it's important.

For example, I was always told that you put the zeros in the second row of the multiplication problem because it's a "place holder". No one ever TOLD me that zero is actually there because you are multiplying by 50, not 5 and if I understood place value I MAY have understood this, but no one even told me. I couldn't multiply in my head, not even simple problems like 15 x 4. Now that I understand partial products, I can multiply in my head. I love to show off to the kids and have one with a calculator and one give me problems and I will solve three digit problems in a few seconds. I'm no genius, and I'm not even great at it, but I never could have done that before.

Ok, enough of my railing and raving!
#14
06-05-2008, 08:24 AM
 MrsC Multitudinous Join Date: Aug 2005 Posts: 11,403 Ontario, Canada Grade 7
Excellent points, MissFroggy. I think that when focussing only on being able to use the algorithm we are not ensuring that our students understand what they are doing. I was great at memorizing formulas and algorithms, but, like you, didn't have a deep understanding of what I was doing (for me, that understanding developed when I began teaching the concepts).
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It does not matter how slowly you go so long as you do not stop
Confucius

#15
06-05-2008, 08:41 AM
 Green_eyed_gal Comrade Join Date: Sep 2007 Posts: 262
Quote:
 Originally Posted by MissFroggy The idea of these methods is to begin to understand how the problem works... I NEVER thought about the fact that you are actually multiplying ones, tens, and hundreds and multiplying each by each in a three-digit problem until I was an adult. In the upcoming years of business, technology, etc. we don't have any idea WHAT people will be doing, calculator or otherwise... the old ways of memorizing and knowing rote facts may not be as useful as they were in the days of assembly line business and technology. We need to create a generation of people who can understand the WHY and HOW of things (not just math) because they will be the innovators. It's too easy to just use a calculator or go online. I do teach the algorithm eventually to all my students, and I do have kids memorize their math facts, but in general, understanding WHY we do an algorithm the way we do is how we will continue to have inventors and engineers, etc. However, I will say, I was having this conversation with my grandpa who is a genius, graduated HS at 14 has about 5 degrees and is a nuclear engineer. He seemed puzzled about how anyone could NOT understand how multiplication works. He was shocked that I never thought about nor completely understood it until I became a teacher. I do think SOME people (and not just geniuses) get the traditional algorithm and what it really is without all the lattice and partial products and base ten blocks and all that. But for the people who don't get it, I think it's important. For example, I was always told that you put the zeros in the second row of the multiplication problem because it's a "place holder". No one ever TOLD me that zero is actually there because you are multiplying by 50, not 5 and if I understood place value I MAY have understood this, but no one even told me. I couldn't multiply in my head, not even simple problems like 15 x 4. Now that I understand partial products, I can multiply in my head. I love to show off to the kids and have one with a calculator and one give me problems and I will solve three digit problems in a few seconds. I'm no genius, and I'm not even great at it, but I never could have done that before. Ok, enough of my railing and raving!
I cannot tell you how many ah-ha moments I had while going through my education program.. During math classes I was constantly saying..."Oh, that's why you do that". I was taught to memorize algorithms and never knew "why" behind them and that's why I struggled with math. I don't want my kiddos to struggle!!
#16
06-05-2008, 05:25 PM
 TeacherGroupie Multitudinous Join Date: May 2005 Posts: 26,867 Calif.
(climbing laboriously up onto the soapbox)

It's hard to make that kind of useful and eye-opening connection without someone modeling the process.

And this, ladies and gentlemen, is why even kindergarten teachers need to KNOW math. And English. And history. And science. And PE. And the fine arts. And... you get the idea.

Froggy, MrsC, and Green-eyed, I wish for you many decades of connection-making aha! moments you just haven't gotten around to yet.

Remember: it's not the facts that you know but what you can understand with 'em that makes a real education.

(climbing laboriously down from the soapbox)

And, oh yeah: the play of ideas is the best play ever.
#17
06-05-2008, 05:48 PM
 MrsC Multitudinous Join Date: Aug 2005 Posts: 11,403 Ontario, Canada Grade 7
Quote:
 Originally Posted by TeacherGroupie Froggy, MrsC, and Green-eyed, I wish for you many decades of connection-making aha! moments you just haven't gotten around to yet.
And I hope that my students don't have to wait until they are as old as I am before they have those moments!

I like to present a math problem and have the students work in groups to come up with as many ways of solving the problem as they can. We then spend time analyzing the wide variety of strategies that can be used to arrive at the same end. Almost invariably, I hear, "I never thought of doing it that way. I'm going to try it!"
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It does not matter how slowly you go so long as you do not stop
Confucius

#18
06-05-2008, 06:00 PM
 TeacherGroupie Multitudinous Join Date: May 2005 Posts: 26,867 Calif.
I trust, MrsC, that what you mean is not hoping that they're not having them at your age, but hoping that they don't wait till they're your age (whatever your age is) to start.

The age past which it's improper to have aha! moments doesn't exist.

Fortunately for me.
#19
06-05-2008, 06:44 PM
 MrsC Multitudinous Join Date: Aug 2005 Posts: 11,403 Ontario, Canada Grade 7
Quote:
 Originally Posted by TeacherGroupie I trust, MrsC, that what you mean is not hoping that they're not having them at your age, but hoping that they don't wait till they're your age (whatever your age is) to start. The age past which it's improper to have aha! moments doesn't exist. Fortunately for me.
Exactly what I meant to say, TG. Providing my students with opportunities to have those "aha" moments is the whole purpose in what I do.
__________________
It does not matter how slowly you go so long as you do not stop
Confucius

#20
06-05-2008, 10:58 PM
 pwhatley Maven Join Date: Apr 2007 Posts: 5,102 USA 3rd Grade Teacher

I may be wrong, but here is the point that I think was being made by the woman in the video: The math curricula about which she was speaking only teach the lattice, partial product/quotient type of methods. They completely leave out the traditional algorithm, and totally dismiss the idea of SKILL MASTERY.

Here is what I think (for what it's worth, lol):
• There are traditional algorithms in mathematics for valid reasons -- they work. We use them to teach addition, subtraction, etc., so why not multiplication and division?
• The traditional algorithm should be taught first (IMHO). However, as part of teaching that method, students must be taught aspects of math such as place value, carrying, etc.
• The lattice method and others should be taught as secondary methods that will improve student understanding of how and why the traditional algorithm works.
• The same goes for division. More about that below.

Before anyone gets mad, here are my thoughts as to why I think this way. [LIST][*]I was NOT a math whiz in school. I was reading books by age three, but hit a brick wall when I was introduced to division in 4th grade. It took months of tutoring for me to understand the basics. If my (wonderful and creative) math teacher had put any of these "nonstandard" or "nontraditional" methods in front of me, I would never have understood division at all.[LIST][*]I tutored in two different university learning centers for a number of years. While I did not tutor math (I did English, SS, Humanities, Psych, Sociology, etc.), I had a front page seat to see the problems being encountered by the incoming students. They could not do simple multiplication and division problems without calculators! It was like breaking an addiction to get them to do the problems with pencil and paper.
• Despite my life-long love of learning (and possibly because of my efforts to instill such a love in her), my daughter did not complete high school. In fact, she attended a youth boot camp program of her own volition. A huge part of her problems in school was her mouth - she's a social butterfly who would rather talk than eat.
• However, probably the most serious problem began in 5th grade, when she began having problems in math. Prior to that, most things came easy to her. I tried everything that I could think of to help her (so did my husband). I honestly think if we could have afforded to take her to Sylvan or something it might have helped (mainly because it would have been SOMEONE ELSE tutoring her).
• Anyway, she is now fighting her way through studying for her GED. She has tested for it twice, and both times she missed passing it by 2 points on the math portion.
• Had I known more about the methods of math she was learning in school, I might have been able to help her more. I was one of those parents who had no idea what the textbook/workbook was talking about! (Estimation threw me for a loop, too - I couldn't figure out why you would want to estimate, when you could just solve the problem, lol.) I DID stay in contact with her teachers, but I was working an hourly position & couldn't take off during the week unless someone was dying (I got one day off for a miscarriage).

Anyway, those are my thoughts on the matter. I didn't write them out of self-pity or anger. I'm just trying to give a different point of view. Sorry it was so long - I can't help it - I'm just wordy by nature, lol.

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 Tags algorithm, lattice, mulitiplication, multiplication, traditional

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