![]() So your implication that somehow lack of place value understanding is grounded in use of the lattice method simply doesn’t make sense. It is introduced with addition and subtraction. Nothing like having a sense of history no longer than your own you have data or just impressions for your claim? Because place value isn’t something that gets taught just a multiplication algorithms are introduced. It pisses me off royally to read some of the incredible lies and insinuations about this approach that have popped up thanks to the Math Wars. And I expect that you know some of the history behind lattice (or “gelosia”) multiplication, how far back it goes, why it fell into disuse, etc. In any event, if someone can’t multiply two single-digit numbers, the lattice approach isn’t any more magical than the algorithm most people my age were taught. Have you had any students state the an advantage of lattice is that it does a better job of organizing the numerals and thus cutting down on computational mistakes due to misalignment? While I’ve never had an elementary student put it that way, I know that many prefer this method and claim it’s “easier,” but explaining WHY it’s easier from their perspective is not so easy for them to articulate. I do like what you chose to do to challenge the beliefs of your students and make them confront their baseless assumptions/claims about place-value. The result is often that the teacher teaches these algorithms as unrelated to one another, much as I’ve seen teachers teach fractions, decimals, and percents as if they were at best marginally related. ![]() In curricular materials where the lattice method is one of those offered, it’s rare in my (somewhat limited) experience to find a teacher who understands either how lattice multiplication actually works or how it relates to the other algorithms offered in the text. I think a task worth giving is to ask teachers to explain the similarities and differences among several algorithms for the same task (in this case, multiplication). Is it any wonder this country produces very few non-mathematicians who have the slightest clue what mathematics actually is? And therein, of course, lies the danger: mindless teachers teaching mindless algorithms mindlessly to kids as if THAT was what MATHEMATICS was about. I will say that it’s appalling that future teachers think that the purpose of algorithms is to get you to think: just the opposite is the case – they hide the thinking that went into creating the algorithm and minimize thinking necessary on the part of the user. I have a lot to say on the subject of lattice multiplication, but probably don’t have time to get to it until at least Sunday. If the premise is that the lattice helps us to learn place value, then we should know enough about place value to make a commitment to the meaning of a tens digit.Ĭan you guess which of the answers below is the more popular in my classroom? No follow-up or clarification questions allowed. When you are done, use a marker to highlight each and every tens digit in the lattice. So here’s the task: Perform the lattice algorithm to multiply 7,343 by 1,568. So if it teaches place value, they should be able to ace any place value task involving the lattice, right? Well, they have been analyzing the algorithm they have written papers about it. If these future teachers thought the lattice algorithm exposes important ideas of place value, then what task could I give them to demonstrate that it does not? Last semester I decided to put that claim to the test. And I suspect most children are not either. I am absolutely NOT thinking about the values of those digits. As I work the lattice, I am going digit-by-digit. I could not disagree with this claim more strongly. The lattice algorithm is very good for teaching place value because you have to pay attention to the places as you work with it. ![]() And then they write about it, using the ideas of the course to analyze the algorithm.Īfter a number of semesters of this, I became tired of reading in their work some variant of the following claim, We learn the steps in class, they go off and practice it. I have used the lattice algorithm for years with my future elementary teachers. This post isn’t really about the lattice algorithm, but it’s the context for what I’m really trying to say, which is this: It is worth the time to craft classroom tasks carefully. If you do not, and if you would like a primer, here is one. I’m going to assume you know the lattice algorithm for multidigit multiplication.
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