The title for this post is related to my previous post about how science is everywhere… because, if science is everywhere, algebra is flat out pandemic.#forreals
Before you decide you want to kill me, please listen. This is my backstory.
I always did “well” in math. By well, I mean, I got mostly good grades, but my teachers said I was “good at” math.
You could have fooled me. Because I just didn’t get it. Now, I hate that phrase, but I think it applies here. With one notable exception, I got good or even better grades in math. I could “help” my peers. I even won the math award in my senior year.
But I didn’t understand the math. I understood how to solve an equation, or follow the steps and get an answer. And I could often show others how to do so. But – and here’s the thing – the math didn’t mean anything. It was all just the human version of stupid pet tricks. I knew it was supposed to mean something. And there was one very notable day when my calculus teacher kept trying to show me how one particular equation could be applied practically… with no success.
To be fair, I think the problem there, looking back, was that we had radically different ideas of what practical meant. He was trying to explain an equation I couldn’t relate to with a real-life example I couldn’t relate to.
Fast forward fifteen years. I was sitting between classes I was teaching, working out a lace pattern for a sweater I was planning to knit for a Christmas gift. I sorted out where to increase and decrease on each row of the repeating pattern. Within each row were other repeating patterns. I decide, um, uh-uh, I was not counting al those stitches across each row. I came up with a formula for the basic lace pattern, and then tacking increases/decreases at the sides for shaping. I came up with something like this…
shaping stitches on one side + (repeating lace pattern)*the amount needed for chest measurement + shaping stitches on the other side
Only it looked like this:
K3 +YO + P3 + (K3 YO P1 YO K3) x 36 + K3 + YO + P3
I sat there at my desk, dumbfounded. That was algebra. It took me until my mid-30’s to make the connection.
(Don’t try to knit that. It’s not the actual pattern I cam up with – I was spit balling for the post. The sweater in question is somewhere 2000 miles away, so I can’t look at it easily to write down what I actually knitted.)
And for those of you who are saying it is not algebra, yes, it is.
Normally, at this point, I’d quote a dictionary definition to support my case. I’m going to do so… but I apologize. It contains the sort of gobbeldy-gook that flummoxed me in school. 😐
a generalization of arithmetic in which letters representing numbers are combined according to the rules of arithmetic
any of various systems or branches of mathematics or logic concerned with the properties and relationships of abstract entities (as complex numbers, matrices, sets, vectors, groups, rings, or fields) manipulated in symbolic form under operations often analogous to those of arithmetic — compare boolean algebra
Okay, let’s deal with #1 today. Translated for those of us who speak plain American-English, Algebra is just math facts (arithmetic – addition, subtraction, multiplication, division) worked with letters, or rather, symbols that aren’t the numeric symbols we’re used to seeing. By this definition, way back in first grade, when faced with 1 + __ = 7, that was algebra. Okay, they used a lank instead of a letter, but still. I could sort out that 2 needed to go into the blank. Later, it might get ramped up a bit: 1 + (2 * __) = 7, and it was still very doable. But I don’t remember any in-between steps. If they happened, they didn’t make an impression on me. So by the time I got to algebra, it was like a series of fairly entertaining logic puzzles, with no connection to real life.
One of my favorite (that’s actually a little sarcasm, there) places where we use algebra all.the.time (Yes, maybe even you) is in cooking. When I once made a comment on a message board about algebra being used in adjusting recipes, I got a pretty nasty response demanding an example. Well, um, how about the distributive property of multiplication? I’m just going to make up this recipes.
I have a recipe that serves 4.
4 servings = 1 cup of milk, 4-1/4 cups of flour, 1 tablespoon of yeast, 2 teaspoons of salt, and 1 egg.
4S = 1CM + 4.25CF + 1TY + 2tS + 1E
(do not panic. All those letters just represent stuff you know what it is.
C = cup, M = milk, and so on)
What if I need 6 servings? To change 4 servings into 6 servings, I have to multiply by 1-1/2, or 1.5
1.5 * 4S = 1.5(1CM + 4.25CF + 1TY + 2tS + 1E)
1.5 * 4S = 1.5 * 1CM + 1.5 * 4.25CF + 1.5 * 1TY + 1.5 * 2tS + 1.5 * 1E
6S = 1.5CM + 6.375CF + 1.5TY + 3tS + 1.5E
Or, back in plain English…
6 servings = 1.5 cups of milk, 6-3/8 cups of flour, 1-12 tablespoons of yeast, 3 teaspoons of salt, and 1-1/2 eggs.
good luck with that 1-1/2 eggs, thing.
I almost (not always) do this in my head, although there is one recipe where I changed the servings so often I wrote the calculations into the cookbook.
Stanley Schmidt really underscored this concept for me in his very earliest level Life of Fred Books, where he starts having children not just memorize math facts, but memorize them with concrete applications.
3 + 4 = 7
3 trees + 4 tress = 7
3 apples + 4 apples = 7
3y + 4y = 7y
Yes. In early elementary math.
Although we don’t use Life of Fred books exclusively, I have found no other book that explains mathematical concepts (and not just to the kids, by the way) in a manner that makes them real, relevant, and recognizable in everyday life. And that’s so important. Dr. Schmidt masterfully and consistently shows how algebra is just a way to every day math.
The fact is, even if you don’t “get” algebra (or what you heard when you were being exposed as a student) we all use algebra every day. It’s just not the complex mess I remember being served up when I was in school.