Lattice Multiplication

Discussion in 'Debate & Marathon Threads Archive' started by Aliceacc, Sep 19, 2013.

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  1. mmswm

    mmswm Moderator

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    Like I said, believe what you will.
     
  2. ecteach

    ecteach Devotee

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    Did you see my question?
     
  3. Jeky

    Jeky Comrade

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    The biggest problem I have with the lattice method is that doesn't reinforce place value.
    I find that the partial products method is much more effective for students struggling with the traditional algorithm (at least for 2x2 problems anyways).
     
  4. mmswm

    mmswm Moderator

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    I apologize. No, I did not. Thank you for re-asking. It's not an ignorant question.

    Numbers, as we commonly know them, are really just polynomials in base ten. The traditional algorithms were derived using base n (where n is any random base). They will always work whether you're multiplying two "regular" numbers, complex numbers, polynomials etc. Lattice only works in base 10. I tried to type out an example, but it was just too confusing without a good equation editor, so I deleted the post. At any rate, if a student were taught the real reason why the traditional algorithm works, they'd be able to abstract it out and apply it to higher level topics such as the ones listed above. Not only that, but they'd get more from the topics, since they would be doing more than just repeating a series of steps. This is where many students fail. Since they were never taught WHY, or they were taught something that was incorrect (which is frighteningly common in elementary school classrooms), then they hit a wall where they can't draw from prior knowledge or the concept directly contradicts what they thought they knew. How is the student supposed to understand algebra with a wall like that up in their brains?

    ETA: I stand partially corrected. Lattice will work in other numerical bases so long as regrouping in those bases is understood as well. The problem lies when using a non-numerical base. This still gets me to my point that it's useless as prior knowledge to draw from when the students hit high school algebra and have to multiply polynomials.
     
    Last edited: Sep 19, 2013
  5. ecteach

    ecteach Devotee

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    Thank you mmswm. I will admit I had to read that 5 times, but I understand what you are saying.

    This kinda reminds me of the whole alligator mouth being used for greater than or less than. I was IN COLLEGE before I truly knew what those signs stood for. I was always told that the alligator ate the bigger number. When I realized that they stood for greater than and less than, it made so much more sense to me. Teach kids the right vocabulary. Sometimes they can handle it. ha ha.
     
  6. mmswm

    mmswm Moderator

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    I'm not exactly explaining myself well either. Between the hour and something in my personal life that has me extremely stressed out, my communication skills are suffering.

    At the end of the day, I feel it would be a better use of time to really explore number theory with struggling students instead of teaching alternate methods that can't drawn from down the line to learn higher level topics. There are hundreds of ways to explore the theory that still allows the student to set themselves up for later success, and I believe that is what we should be spending our time doing.
     
  7. DrivingPigeon

    DrivingPigeon Phenom

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    I do not teach multiplication, but any little "tricks" like that drive me nuts. Some of my new students (who came from other schools) use touch math to add, and I HATE it. They do not seem to understand what is really going on-that they are taking 4 objects and adding 2 more. Instead, they are just counting imaginary dots. Drives me crazy.
     
  8. problemsolver

    problemsolver Rookie

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    IsLattice still an issue for a lot of teachers
     
  9. Aliceacc

    Aliceacc Multitudinous

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    It's apparently an issue for some kids, since at least one of my 180 or so kids tried, unsuccessfully, to use it on Tuesday's test. It's not really an issue for me, per se, except that it sabotaged one of my students. And it's going to be a huge problem down the road if that kid doesn't know traditional multiplication.

    When my daughter was taught lattice, I taught it to myself so that I could help her with what her teacher said she needed to know.

    Then I made d*** sure she learned the traditional algorithm, since that's the way numbers are multiplied. That's what she'll need to know in the future. That's the method that makes sense in light of place value, and if you don't understand place value you will not understand math.

    Saying you don't care what upper level teachers think of what you're teaching kids isn't exactly acting in their best interests. It's setting them up for failure, keeping your eye on what's easier for you in the short term regardless of what it does to those kids. It's not about what I think, it's about what my kids-- and your kids-- need to know in order to succeed.

    It's what Common Core is supposed to be all about: determining a body of knowledge that all our kids need to know in order to establish a basis for success. The traditional algorithm is part of that body of knowlege. Neglecting to teach it means that there's an important chunk of math that a group of students won't know, and it's going to hurt them down the road.
     
  10. MissCeliaB

    MissCeliaB Aficionado

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    I was teaching 3rd grade at the height of the lattice craze, and it was a nightmare. Not only did they have no clue conceptually what was going on, but they could not draw the lines straight at all. I find lattice to be terribly developmentally inappropriate for the age when we teach these skills. They don't have the fine motor skills, and it doesn't lend itself well to representation with manipulatives. I always preferred to start with base-10 blocks and partial products. That helped many of my students see conceptually what was happening. Then when I taught the traditional algorithm, they could see where the algorithm fit in with the partial products, and it made sense to them given their firm base in understanding place value.

    I honestly only ever used lattice as enrichment, and with higher-level students, often as early finisher work. Or, I'd show it to the whole class for fun on a rainy day. I'm actually teaching one of the students I taught in 3rd grade now as a high school junior, and he was just telling me the other day how much that confused him when I explained it. (I had a chart out on my desk that looked like a lattice chart...)
     
  11. Aliceacc

    Aliceacc Multitudinous

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    I'm with you on both counts.

    I don't do box either. Last year, when I had to cover a colleague's class for trimester review, they had to teach me the box method; I had seen it before but never really learned it.

    And sometimes the kids just don't think. Last night my son used the "AC" method for a trinomial with a GCF of 2. He simply didn't stop and look at the whole problem.
     
  12. ChristyF

    ChristyF Moderator

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    I don't get the lattice multiplication. I had a student try to teach me, but he couldn't. I do show the scaffolding method, though. I try and show them a couple of different ways to approach 2 by 2 or beyond. 90% grasp the concept and move on to the traditional way. I'm fine with those that don't, because scaffolding, to me, works just as well. It's about them understanding the numbers they are multiplying. It still goes in the same order, it just stretches it out to show what they are multiplying.

    [​IMG]
     
  13. TeacherNY

    TeacherNY Maven

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    I had to look this up since I have always heard of it but never knew what it was. I can see where students can make errors even if they have been taught it properly. If they try it out on the first test of the school year (after not doing any math all summer) I can totally see where they would think they are doing it the right way but might make a mistake. I think it's "cool" anyhow but I'm just glad I don't have to teach any math beyond 1+1 :lol:
     
  14. smalltowngal

    smalltowngal Multitudinous

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    DP~those counting imaginary dots drives me crazy. I have tested a few jr/high school kids that when I was testing their fluency were still having to count on their fingers!
     
  15. SpecialPreskoo

    SpecialPreskoo Moderator

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  16. SpecialPreskoo

    SpecialPreskoo Moderator

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    Cool. I figured it out. I think I'd still do it the old fashioned way if I had to work a problem out.
     
  17. TeacherGroupie

    TeacherGroupie Moderator

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    As it turns out, lattice multiplication was the (or "a") standard algorithm for multiplication for some centuries. I do like its slightly more transparent handling of "carry" numbers, and I could see its use as a steppingstone for a handful of students. But it was supplanted by what is now the standard algorithm for several reasons: its setup indisputably requires more steps; the intermediate sums in the diagonals are somewhat less obviously connected to place values; worst (as mmswm has pointed out, though in different language), it can't be generalized straightforwardly to multiplication with unlike variables, whereas the standard algorithm can, which means that students have to learn a whole different way to multiply rather than being able to employ a familiar tool.

    (mm, I did figure out, thanks to your observation about bases, how to generalize lattice multiplication to multiplication with one like variable - that is, (2x + 3)(4x + 1). It does work - but it also requires the user to know already what she's doing, and it's cumbersome. If you're interested, I'll explain.)
     
  18. JustMe

    JustMe Virtuoso

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    I count on my fingers. All the time. Hey, whatever gets me to the answer.
     
  19. Upstream

    Upstream Rookie

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    I totally agree! I taught resource math for five years for grades 5 and 6. The biggest problem in teaching multi-digit multiplication was that my students never memorized basic multiplication facts AND didn't understand re-grouping in addition and subtraction. Learning does take effort on the part of the student, period.

    P.S. love the cat photo and quote about light @ end of tunnel!
     
  20. kab164

    kab164 Companion

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    I disagree regarding Touch math. I have worked with struggling math students, some of them did end up in special ed. For them to touch the bigger number and count on to add works well. I have spent a lot of time teaching students how to memorize multiplication facts. In all the years I've been in schools, I had one boy who could NOT memorize facts. However, he could multiply using touch math faster than most of the other students could doing it the traditional way. The dots may be imaginary to those of us who don't need them, but are a great support for the students who do.
     
  21. Aliceacc

    Aliceacc Multitudinous

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    We were talking about this today at lunch. (OK, I admit, I started the conversation.)

    One of the new teachers showed us an entirely different method, dealing with counting boxes in a grid. We looked at it for a minute or two, and I realized it was a form of FOIL using place value.

    Pretty cool (like Lattice... as much as I hate it, I'm not denying the "pretty cool" factor.) But not something I would ever consider teaching.
     
  22. Upstream

    Upstream Rookie

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    Lattice multiplication, not TouchMath.

    Your reply is off-topic. The discussion was about the algorithm for multi-digit multiplication versus 'the lattice method'. It is accurate that some students benefit from a kinesthetic approach to memorizing facts, nonetheless, a student must apply effort, no matter the method of memorizing the facts. And using TouchMath is a method of memorization. The students understand the underlying concept of adding the same number multiple times whether using TouchMath or not. When a student uses TouchMath to recall multiplication facts, he or she has memorized skip counting for the digits 1-9. Research has demonstrated that thinking "multiplicatively" forms new thought pathways in the brain and a deeper understanding of the processes of math. A student must be able to recall multiplication facts AND understand re-grouping in order to successfully process multi-digit multiplication problems!
     
  23. Upstream

    Upstream Rookie

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    Yeah, I've seen that too and agree. Teach the concept, not a trick!
     
  24. Aliceacc

    Aliceacc Multitudinous

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    We tend to be OK with people being a bit off-topic here. I was discussing my frustrations with Lattice; like most people here, I'm entirely open to the conversation taking some turns.

    That's the way of most conversations. And most of us here are open to that reality.
     
  25. TeacherGroupie

    TeacherGroupie Moderator

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    I agree with Alice, Upstream: on A to Z as in life, discussions don't necessarily proceed strictly linearly. In any case, it wasn't kab164 who introduced the topic of TouchMath (on the value of which, actually, you and kab164 seem to agree), but an earlier poster to whose disparagement of TouchMath kab164 was responding.
     
  26. Upstream

    Upstream Rookie

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    I understand that most conversations take turns but there is usually
    a connection. i still see very little relation between my post and your response. You only mention TouchMath in relation to multiplication and addition and don't mention lattice method at all. When I went back and read some other posts I saw mention of TouchMath. It just wasn't apparent in your response. Not trying to be snarky, just didn't seem related.
     
  27. Upstream

    Upstream Rookie

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    Thanks, I see what you mean about responding to a different post. I really wasn't trying to be mean or a "B"! Yes, TouchMath works for many kids, maybe because it extends the transition from concrete to abstract. I do think very linearly and will remember that new posts don't necessarily respond to my entire previous post, but maybe just part of it, as Alice's did.

    And you probably picked up on my frustration with "methods" being taught in place of concepts. I think that concepts are what allow all learners to recall content that was learned previously but has not been used recently. And that is how we build on and apply knowledge throughout life.
     
  28. TeacherGroupie

    TeacherGroupie Moderator

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    No worries, Upstream: just trying to ensure that poor kab isn't smarting under discredit where discredit wasn't due.
     
  29. problemsolver

    problemsolver Rookie

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    Well my wife teaches Lattice and says that if her kids arent picking up lattice she teaches them the singapore method which is similar to lattice (as it teaches them to use the box). Lattice combined with Singapore should help.
     
  30. Aliceacc

    Aliceacc Multitudinous

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    I know nothing about Singapore.

    But I do know that the traditional algorithm prepares kids for upper level math.

    Does Singapore? Not being snarky; I honestly know nothing about it.
     
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