I could have easily declared the following as a math teacher, but I’m being more demonstrative now:
No. More. FOIL.
Anyone who’s followed these posting in the last couple of years knows that I’m all for finding efficient ways of remembering how one works through different elements of math. I’m also for remembering processes so long as, later on, there’s a stronger element of true understanding there. Yet, what inevitably ends up happening is one of three scenarios:
1. They confuse “First, Outside, Inside, Last” i.e. trying to combine the two terms right next to each other when they’re not like terms.
2. They can’t factor because the mnemonic wasn’t taught to them for backwards compatibility.
3. They move on to trinomial multiplication and run out of letters.
I’m of the opinion that the geometric method just works whichever way around. It gives a visual representation to my students of how any polynomial can be multiplied or factored for that matter. For my ELLs particularly, making the transition from concrete to abstract is that much more important. Furthermore, I find FOIL, like so many other gimmicks, limited to their scope. They almost impose limits on what our children can and need to know for their future maths.
In the younger grades, I can somewhat understand trying to focus on a certain set of cases for studying math. When developing number sense, children need a certain set of axioms by which to ground their understanding of our math system. However, by the time they get to 8th grade, some of these gimmicks rear their ugly head when integers get involved. (PEMDAS and Keep-Keep-Change come to mind here). Thus, they’re so stuck in how the “last” teacher taught them that unlearning the previous methods become difficult.
With my students in 8th grade, I have an obligation to leave these students in good shape for high school. Most of my alumni can tell you that my teaching got them at least through 1st semester of freshman year, if not through all of it. If we think of our teaching (and our students) as part of a continuous learning process and not an assessment driven segment that someone down the assembly line may (or may not) pick up down the line. Limiting the amount of gimmicks (or developing fresh and profound ones, whatever that means) increase the likelihood that our students can delve into these topics, no matter what level of math they’re in.
Because I’d rather my students be the ones foiling and not getting FOILed.
Mr. V, who got one thing he can tell you: you’ve gotta be free …
p.s. – JD provided the basis for this a year ago, but it’s definitely worth going over.