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. By using knowledge of place value to separate a larger number into its parts–ones, tens, and hundreds–a large number becomes much more manageable.I’m going to assume you know the lattice algorithm for multidigit multiplication. You multiply in parts and then add to get your final answer. Often parents don’t feel qualified to help their child with a specific subject, but with the great resources available to parents online it can take only a few minutes to familiarize yourself with these alternative methods, including partial products and lattice multiplication:įirst, the partial products method, which works based on the same premise as partial sums and differences.

These algorithms are helpful for parents to know and be able to use to help their children. To compliment a previous article on Alternative Methods in Elementary Math: Partials Sums and Differences, we wanted to present information for upper elementary students learning multiplication through alternative algorithms that include partial products and lattice multiplication.

Lattice multiplication history