Lattice mulitiplication Vs. Traditional multiplication algorithm

Discussion in 'Elementary Education' started by Green_eyed_gal, May 31, 2008.

  1. Green_eyed_gal

    Green_eyed_gal Comrade

    Joined:
    Sep 3, 2007
    Messages:
    255
    Likes Received:
    0

    May 31, 2008

    I've been doing some research on lattice multiplication... I thought it was a cool way of doing multiplication, but I was trying to find more information about it... I didn't want to teach my kids something that I wasn't informed about.

    Well, while looking through Youtube I came across this video http://youtube.com/watch?v=Tr1qee-bTZI&feature=related

    I'm a new teacher and I want to do what is best for the kids.. Our school uses Scott Foresman Mathematics and we have TERC as supplemental material. I've never used TERC so I brought home some stuff to look over during the summer.

    I was excited about finding lattice multiplication because double digit multiplication is a tough concept for a lot of kids. Well, after viewing the video above I'm not so sure anymore. I think that teaching the traditional algorithm is the only way to go even if I have to spend more time having the kids practice.

    I'm just curious about other teacher's views on this.. Would it still be ok to teach the lattice method after the kids have mastered the traditional algorithm?
     
  2.  
  3. buck8teacher

    buck8teacher Devotee

    Joined:
    Jan 23, 2007
    Messages:
    1,087
    Likes Received:
    0

    May 31, 2008

    Lattice is kinda hard for me to follow. I tried it a few times with some of my struggling 4th graders when I student taught last year. I use Investigations (TERC) math as my main math program. Therefore, I'm all about letting the kids use the strategies that are best for them.

    For two digit multplication, a lot of my kids perfer repeated addition. A lot of them like to break it up, for example:
    32x6
    We break up 32 into 30 and 2. Then they multiply 30 x 6 and 2 x6.
    30x6=180
    2x6=12
    180+12=192
    so 32x6=192.

    Some of my kiddos like the traditional algorithm, while some don't. I think it's because we teach addition with regrouping (up and down) in the middle of the year, and they can't use it as a strategy until it's introduced. Therefore, a lot of my kids forget to add in the tens that they carried. They like breaking it down because it's more like how they are used to doing math.

    Of course, I teach third and we don't double digit multplication. I did in 4th and they did it the same way, breaking it down.

    I hope this helps!
     
  4. EMonkey

    EMonkey Connoisseur

    Joined:
    May 10, 2008
    Messages:
    1,597
    Likes Received:
    0

    May 31, 2008

    The video appeared to be saying lattice and cluster are effective teaching tools but the everyday math and the other text book are lacking in the way multiplication and division are being taught. Basicly the video is cutting down the text books and incouraging teachers if you are useing the lattice method or the cluster method not to leave out the more common algorythm which those text books do.

    I have used all of the methods in my class (when I taught fifth). the cluster method assists children in conceptual understanding. the lattice and the breaking the numbers up help children who feel stumped by the normal algorythm. They all help children who are doing well in math see the multitude of ways one can do a single problem.
     
  5. Miss Kirby

    Miss Kirby Fanatic

    Joined:
    Oct 7, 2004
    Messages:
    2,699
    Likes Received:
    0

    May 31, 2008

    When I took a math class in undergrad she said to teach the traditional algorithm first. Then, when most of them have it, teach the other algorithms.
     
  6. mdith4him

    mdith4him Companion

    Joined:
    Apr 23, 2008
    Messages:
    195
    Likes Received:
    0

    May 31, 2008

    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??

    I say if it's not broken, don't fix it! Lattice and some of the other methods might be best saved to introduce to individual students who have trouble figuring out the traditional algorithm.
     
  7. MrsC

    MrsC Multitudinous

    Joined:
    Aug 8, 2005
    Messages:
    12,101
    Likes Received:
    72

    May 31, 2008

    I like to introduce my students to a variety of methods and have them be able to use what works best for them. When introducing a concept (e.g. multiplication), I present a problem and have them come up with a variety of strategies to come up with a solution. Other methods are more awkward for us, because that isn't they way we are used to, but they are just as valid; many of the "reformed" methods are actually very old and are common in other cultures.
     
  8. MissFroggy

    MissFroggy Aficionado

    Joined:
    Aug 26, 2006
    Messages:
    3,729
    Likes Received:
    0

    May 31, 2008

    I don't teach the lattice because it takes too long to make the thing if they are not premade for the kids, and anyone with any spatial difficulties is incredibly confused by this. It's just sort of a trick.

    Instead, I teach partial products like buck8. We also use investigations. I have adapted it a bit though.

    Say the problem is 27 x 34.

    we do 27 x 4, and 27 x 3(0).. they solve for 27 x 3, and tack on the zero. Then they add the two products together.

    The coolest thing with the partial products is after awhile, the kids automatically start to line them up the way we do the traditional algorithm because they get tired of writing the numbers over and over. I saw a kid doing this and asked him if his parents showed him how to line the numbers up that way. He said, "no, I just saw it was a shortcut so I didn't have to write the numbers so much." I was pretty darn impressed!

    When I introduced the larger problems we spent time together trying to figure out the best way. They were initially confused by the traditional algorithm and we tried a few different ways. The kids were drawn to the partial products. I only have 7 kids in my 4th grade math group though, so we can do things like that together.

    For my third graders, when we just multiply by 1 digit, I just taught the traditional algorithm.
     
  9. loves3rdgrade

    loves3rdgrade Rookie

    Joined:
    Feb 22, 2008
    Messages:
    7
    Likes Received:
    0

    Jun 3, 2008

    I currently teach the lattice method and it is great how the low kids GET IT! Our district has a lot of cool stuff on our website. Check out this website. It has a powerpoint explaining lattice. We actually did it for one of our first lessons on the smartboard! I hope it helps! http://www.cdschools.org/5422101251...5141221820/9.9_EDM_Lattice_Multiplication.ppt

    If that doesn't go right through... go to this website:
    http://www.cdschools.org/542210125141221820/cwp/view.asp?A=3&Q=298196&C=58088
    and then scroll down to Unit 9 and click on 9.9 Lattice powerpoint lesson

    Also check out our website for a lot of good ideas!
     
  10. Lives4Math

    Lives4Math Comrade

    Joined:
    Apr 8, 2008
    Messages:
    343
    Likes Received:
    0

    Jun 4, 2008

    I looooove lattice method! I wish they would have shown me that when I was in school!! I learned it in college and showed my 5th graders both ways. I tell them that I don't care which way way they do it as long as they get the right answer. I don't care if it takes them longer....as long as they're getting the right answer...their state tests are NOT timed so i'd rather teach them a way that they understand and can get the right answer than teach them something that they don't understand and won't be able to get the right answer.
     
  11. 3Sons

    3Sons Connoisseur

    Joined:
    Aug 30, 2007
    Messages:
    1,813
    Likes Received:
    13

    Jun 4, 2008

    The lattice method seems to leave an incredible amount of room for careless error, and I'm not convinced it does anything to actually aid understanding.

    I think every elementary teacher should at least investigate Singapore math. It successfully does what constructivist theorists are hoping to do but do not accomplish.
     
  12. knitter63

    knitter63 Groupie

    Joined:
    Jun 26, 2007
    Messages:
    1,402
    Likes Received:
    0

    Jun 4, 2008

    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!
     
  13. MrsC

    MrsC Multitudinous

    Joined:
    Aug 8, 2005
    Messages:
    12,101
    Likes Received:
    72

    Jun 5, 2008

    Actually, they would be most likely to whip out a calculator! :lol:
     
  14. MissFroggy

    MissFroggy Aficionado

    Joined:
    Aug 26, 2006
    Messages:
    3,729
    Likes Received:
    0

    Jun 5, 2008

    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!
     
  15. MrsC

    MrsC Multitudinous

    Joined:
    Aug 8, 2005
    Messages:
    12,101
    Likes Received:
    72

    Jun 5, 2008

    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).
     
  16. Green_eyed_gal

    Green_eyed_gal Comrade

    Joined:
    Sep 3, 2007
    Messages:
    255
    Likes Received:
    0

    Jun 5, 2008

    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!!
     
  17. TeacherGroupie

    TeacherGroupie Multitudinous

    Joined:
    May 13, 2005
    Messages:
    26,893
    Likes Received:
    89

    Jun 5, 2008

    (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.
     
  18. MrsC

    MrsC Multitudinous

    Joined:
    Aug 8, 2005
    Messages:
    12,101
    Likes Received:
    72

    Jun 5, 2008

    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!"
     
  19. TeacherGroupie

    TeacherGroupie Multitudinous

    Joined:
    May 13, 2005
    Messages:
    26,893
    Likes Received:
    89

    Jun 5, 2008

    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.
     
  20. MrsC

    MrsC Multitudinous

    Joined:
    Aug 8, 2005
    Messages:
    12,101
    Likes Received:
    72

    Jun 5, 2008

    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.
     
  21. pwhatley

    pwhatley Maven

    Joined:
    Apr 14, 2007
    Messages:
    5,282
    Likes Received:
    0

    Jun 5, 2008


    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.
    • 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.
      • 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.
     

Share This Page

test