Lattice Multiplication

[Cammie]

I was sitting and reviewing math with my son - just finished 3rd grade here in India.

 

We were doing two digit and three digit multiplication and he starts drawing boxes and doing "lattice multiplication."  I've never seen anything like it. 

 

I am NOT a math person.  I was just wondering what other people who know all about math curriculums think about lattice multiplication.  Does it have advantages over traditional multiplication?  Disadvantages?

 

Seeing this made me understand this idea of "new math!"  Was there really a need to change the way we do multiple digit multiplication??

 

Thanks!

[kiana]

Eh, it's not really any better or any worse than the traditional algorithm.

 

What matters most (imo) is that the student learn AT LEAST ONE method of multiplying and get really proficient at it.

[kiwik]

I tried to follow it once but it gave me a headache. I think people should know more than one way BUT at least one of the ways needs to be quick and efficient.

[Cammie]

What I really wonder is - WHY?  It looks so complicated to me!  He obviously understands it and can do it pretty fast.  I just don't know if my resistance is because I am a stuck in the mud or if there is a valid reason to resist it!

[Haiku]

Lattice multiplication relies on high visual acuity and visual discrimination skills and also risks more introduced errors with its physical format. I find it to me little more than a cute party trick.

 

I read and evaluated and searched for weeks for something to help my dyslexic son not get lost in long multiplication. In the end I decided the standard algorithm is the most efficient.

[Cammie]

All very interesting answers.  So now I am wondering why it is being taught in his school.  He is in a very alternative school - no tests until 5th grade so they are not "teaching to the test" in that regard.  What I need to find out is if it is a component of the IB curriculum that they are following (the primary years version of it.)  I never really thought there were different ways to teach math basics...like I said I'm not too mathy!

[wapiti]

All very interesting answers. So now I am wondering why it is being taught in his school. He is in a very alternative school - no tests until 5th grade so they are not "teaching to the test" in that regard. What I need to find out is if it is a component of the IB curriculum that they are following (the primary years version of it.) I never really thought there were different ways to teach math basics...like I said I'm not too mathy!

It has long been a feature of the Everyday Math program. I don't know about other fuzzy math programs.

[Alessandra]

Op, you have my sympathy.

 

Here is a funny video about Everyday Math and lattice multiplication.

 

 

 

[Mom2OandE]

My daughter finds it much easier. She can multiply millions in minutes versus struggling with the traditional methods.

[MinivanMom]

Lattice is taught in our local schools (urban, affluent, highly educated area). There is universal disdain for lattice (and other fuzzy, alternative algorithms). Parents of struggling students say that their children have trouble remembering all the steps and/or mix up the steps between lattice and traditional. Parents of bright students seem to be less opposed to it, because their children do better at juggling multiple methods and keeping them straight. Everyone complains about homework assignments where students are required to use lattice, and problems (with the correct answer) are marked wrong if the traditional algorithm is used.

 

Apparently the middle & high school math teachers request that students use the traditional algorithm, because it is simpler and quicker so there is also a widespread feeling among parents that all those years of lattice worksheets were a waste of time. I tend to agree. What is the point of learning lattice multiplication if:

a) it doesn't make the underlying concepts clearer

b ) it doesn't require the student to have an understanding of place value

c) it's going to be dropped down the road in favor of the traditional algorithm anyway

 

 

[EndOfOrdinary]

As a math teacher, I find nothing wrong with it. It is a visual representation of the standard algorithm. The standard algorithm is being pulled away from by some schools because kids have NO idea what it means. They are merely performing without understanding. Many lattice kids are doing the same thing, by some feel it is more difficult because they physically have to cross and see the repetitions of the multiplication. One is visual, one is linear. Same thing. The algorithm we use as the standard was only implemented during the Cold War to produce citizens of a work force who could quickly churn out answers with no need of understanding. Grunt labor to beat the Russians.

 

As for the IB program, it doesn't matter. The only thing that matters is if your son understands what he is doing when he is multiplying multi-digit numbers. He is using the distributive property. If he does not understand that, then none of the methodology matters. He will not be able to apply it late in algebra or pre algebra.

 

There are six different ways to explain adding. Schools in the US usually only discuss maybe two. The others are just as valid, but require students to understand the concept not just perform a process. That is virtually impossible with more than five kids to a teacher. This is exactly the same thing.

[kiana]

The algorithm we use as the standard was only implemented during the Cold War to produce citizens of a work force who could quickly churn out answers with no need of understanding. 

 

what?

 

This algorithm is taught as the standard in, for example, Ray's Practical Arithmetic (1877). Here's a link -- http://tinyurl.com/m2x78fc -- and it's on pages 42-49. 

[EndOfOrdinary]

Yes. It was taught then, but not as the only way to and place value is openly explained along with the applications using the Distributive property. It was not a complete and go again style of education. That was what happened in the late 1940's and began replacing the entire math approach by the late 1950's. It happened in the same way Latin was removed from schools as standard ed so more focus could be placed on "practical subjects."

[EndOfOrdinary]

People now cannot even explain why the use the algorithm. They just do it. That is what happened.

[OneStepAtATime]

Cammie, I cannot say whether lattice method is a good or bad thing or even just another way to look at math for your child.  But I know that for mine it opened doors that had been closed before.  But my child is dyslexic and highly visual.  Math has been a struggle for her.  I am grateful for the lattice method.

 

2 years ago we had DD attend a summer program at a specialized school for kids who are intelligent but learn differently.  Her math teacher was trying to help her with the standard algorithm normally taught in the States but she was still struggling mightily and hated every minute of it.  Her math teacher was the most knowledgeable, highly gifted math teacher I have ever met.  We had a meeting and she walked through several issues that were potentially causing difficulties for DD and said she was going to try different approaches to find the ways that fit best for DD for helping her understand math concepts and to be able to complete the math problems with a better understanding of what she was being asked to do.  Lattice was one of those "different approaches" and suddenly multiplication made sense to DD.  She loved it.  She could finally "see" multiplication in a way that made perfect sense to her.  I remember vividly the day that she learned lattice she came home grinning from ear to ear and told me how much fun she had had in math class and how multiplication finally made sense....for the very first time in her entire life.  She was heading into 6th grade that summer.

 

Her teacher that summer made it very clear to me that there are many ways to approach math and if one way doesn't work, try another.  Everyone thinks differently.  It opened up a whole new world for us.  I had no idea there were multiple ways to approach math.   Lattice doesn't make sense to me.  But it does to my daughter.  And she loves it.  No more tears and confusion when doing multiplication.  This isn't "fuzzy" math to her.  It is a concrete way of visualizing the process that finally makes sense in her brain.  Is this something that everyone should have to do?  Well, no, that was the point the math teacher was trying to make. We all think differently.  The most effective student is one that recognizes when one approach isn't working and can find other ways to approach the material so that it makes sense to them.  If one way isn't working, try another way.  Once I started applying that philosophy in other subjects, too, a lot of things started making sense to DD.

 

Since your child is sort of stuck doing whatever the school is teaching as the required method I realize this may be very frustrating for you, though, and I sympathize.  Lattice would have driven me crazy as a child.  But I am not highly visually oriented.  As long as he is also understanding place value, and perhaps you can get him familiar with the other method, too, just so he has exposure to both, lattice, IMHO, isn't going to ruin him for life.  It is just another way to approach multiplication.

 

Best wishes.

[Cammie]

Wow - amazing answers!  Thank you all so much!  Luckily my son is mathy and for him doing it both ways is possible.  I think I have some sort of math related disability...I can DO the math but I don't feel I ever understand the RELATIONSHIP of the numbers.  This has been a burden my whole life!  I have no...instinct for the numbers.

 

Funny story - I went to Law School because there was no math on the LSAT - then I became a divorce lawyer which was ALL ABOUT THE MATH!  DS and I are working through Khan Academy Fourth Grade materials now and it is a learning experience for me.  My daughter is doing Trigonometry in 8th grade (I don't remember EVER doing Trig at all).  Luckily I married a very mathy guy!