During my time as a high school math teacher, I was often asked the dreaded question: “when am I ever going to use this?” At the time, my response was always to find some practical use for whatever math they were asking about. Recently, however, a conversation with a coworker sent me down a rabbit hole, and I realized that dreaded question reveals something of a divide in the way we think about education in this country. Without further ado, I will now take you on a journey through the layers of the rabbit hole in which I recently found myself.
Let’s start with something like FOIL. For those of you who don’t remember your high school algebra, FOIL stands for First Outer Inner Last, and it is basically a shortcut for multiplying two binomials, for example: (x+1)(x-3) (it’s coming back to you now, isn’t it?). Here, we ask a simple question to get us started: should FOIL be taught in schools?
At first, you might think to yourself something like, “of course we should teach FOIL, why wouldn’t we?” Well, this may surprise you, but FOIL isn’t actually a thing. FOIL is really just one specific case of the distributive property. The distributive property is much more versatile, since it can be used in place of FOIL, and can also be used to multiply much more complicated expressions. So now you’re probably thinking, “wow, the distributive property seems pretty cool, why don’t we just teach that and forget about this FOIL stuff?” And from a strictly practical point of view, you’re correct. Unfortunately, it isn’t that simple.
As teachers, it is our responsibility to prepare students for the future. That means college, careers, and unfortunately, standardized tests. Many of these tests prominently feature situations where FOIL is helpful, and many of these tests (such as the SAT and ACT) are timed. As teachers, we recognize that to send students into standardized tests without every possible tool is to send them into the future unprepared. So we teach FOIL. And we should teach the distributive property as well. But isn’t that redundant?
It is redundant, and here’s why. There are essentially two schools of thought with regard to how we think about education in America, and those schools are now butting heads. The first school believes the purpose of education is to teach students what they need to know. There’s certainly merit to this; there are obviously some things that most, if not all, students need to know. But beyond the obvious, who decides what students actually need to know? Do they really need this? Or that? Who can say? Then there are the Standardized Tests, and the idea that what students need to know is essentially defined by what some company puts on a test. Personally, I believe this to be dangerous, but perhaps since it is the only concrete way to define what a student needs to know, it’s the system that we currently have.
Then there’s a newer school of thought, one that is harder to define. I once heard someone say, “education is not about filling cups, it’s about lighting fires.” This is the essence of the newer school of thought, and I couldn’t possibly agree more. We live in an age where most human knowledge is unprecedentedly accessible. There is essentially no point in shoving information into the heads of children; there is no point to rote, uninspired memorization. Instead, this newer school of thought believes that the role of a teacher is to inspire students to find the information on their own, to spark student interest, and to show students the door to the future and encourage them to walk through it.
So should we teach FOIL or not? Well, there’s one factor we haven’t touched on: FOIL is boring. No child has ever been inspired to be a mathematician because they just love multiplying binomials. FOIL (and the distributive property in general) are mostly stepping stones to bigger and better things, and we tend to treat them as if they’re an entire concept all to themselves. The reality is that mathematics is beautiful, mysterious, and huge, as is the rest of the world, and rather than give students a glimpse of what the universe is really like, we pick and choose a few snippets and we say, “you need to know this, it’s going to be on a test.”
The world has changed, and education needs to change with it. The old methods, tried and true as they may be, will not prepare students for the careers, challenges, and lives of tomorrow. Yes, there are some things across all disciplines that basically every student needs to know. But how can a student be excited about learning if they can’t catch a glimpse of anything beyond the next big test? I believe we owe it to our students to at least give them a sneak peek of what is really out there.
As for FOIL vs. the distributive property? Teach what you want. But at the end of every day, ask yourself this: did you light any fires today?