This is an informal essay I had to write for my class. I know, I know…it’s school crap, but I love you.
Part of the reason I decided to keep up this blog is to practicing writing stuff that other people might actually want to read. Luckily, this class I’m in has the same goal. So I’m just test-driving essay, if you will. And if you won’t.
So if you wanna be a dear (a nice person, not the animal…you can’t be the animal), then read this. If you actually made it to end without dying of boredom, let me know in the comments. I’ll also be accepting constructive criticism and flattery.
1. Eww, I hate math
When you’re in college, most introductions begin with the question “What is your major?”. Apart from the obvious majors, like accounting, this is typically followed by “And what do you want to do with that?”. As a math major, this conversation usually* plays out like this:
Potential Friend (PF): “So, what are you majoring in?”
Me: “Oh, I’m a math major”
The PF cringes and/or looks confused, both responses triggered by bad memories of high school math.
PF: “Eww, I hate math. But cool…what do you want to do with that?”
Me: “I want to be a teacher.”
PF: “Like a professor?”
Me: “No, either middle school or high school.”
PF: “Hmm…well, good luck with that. I hear they need good math teachers”
However, my decision to major in mathematics is not because of the “job security” (which is debatable). It simply comes from my love of math. And the reason I emphasized in education is because I want others to love math, too. Realistically, I can settle for helping others to not hate it.
2. It’s kind of like a puzzle
It is the reason that preschoolers are drawn to jig-saw puzzles, that eighth graders try to figure out the best “first move” in tic-tac-toe, and that your grandma plays sudoku. Our brains enjoy the challenge of using logic to arrive at an answer.
It has rules to follow and boundaries to work within, but math also requires your creativity. You have to study the problem, figure out what it is asking and choose how to solve it. There are many roads you can take, but as long as you play by the rules, they all arrive at one destination. It’s kind of like a puzzle.
3. Plug and Chug
“There are two ways to write an equation for a line. Copy them down and we’ll do some examples.” Kenny and Francisco are sleeping. Zaydrian is using a bent-out paperclip to pick at the lint caught in his comb. Dulce is decorating a note she wrote to her friend with a pink highlighter, and Manny is practicing the art of one-handed concealed text-messaging. The other twenty students are either talking or staring into space, eyes glazed over and minds elsewhere. The teacher’s monotone voice and frequent glances at the clock suggest that even she is bored with the lesson.
Somewhere between fifth grade and eighth grade, math is reduced to algorithms and memorization. “Do each problem the way it is done in the book. Just plug in different numbers.”
This is the math that people hate. It doesn’t make sense and it’s boring. Students have become disengaged and detached from the process of learning.
4. Dimes and Quarters
One way to keep the process of learning alive is to take advantage of the natural curiosity to solve. It’s about posing a problem that makes a student say: “Hmmm” and then actually think. This is called “intellectual necessitation”.
At its worst, “necessitating” gets the student to use their natural mathematical intuition. At its best, it creates an intrinsic desire to connect this intuition with formal mathematics.
For example, I might tell you that I have $1.55. It’s made of eleven different coins, but they are only dimes and quarters. Can you figure out how many of each I have?
You may start coming up with different combinations of quarters and dimes, testing them out until you find that I must have three quarters and eight dimes***. Okay, great. But then some rich dude comes along. He may just be bragging, but he says he has 30 bills in his wallet, totaling $255. And they are all Lincolns and Jacksons. How many of each does he have?
This problem is harder and the combinations will take you much longer. Plus, this guy is big and intimidating. You need a better, or more efficient, way to solve this problem.
Let’s call the number of five dollar bills “x” and the number of twenties “y”.
We know “x + y = 30” because that’s the total number of bills. And we also know that “5 times x” is how much cash he has in five dollar bills, and “20 times y” is how much he has in twenties.
Put them together, and we know that “5x + 20y =255”.
Boom. We have a system of equations. With a little bit of help from Mr. Algebra or Mrs. Geometry****, we can easily solve for x and y . And maybe the rich guy will be so impressed, he’ll give us some money. (This would be called “extrinsic motivation” and it is sometimes necessary. I like to use candy and/or baked goods.)
5. Math is a tool..in a good way
Everybody has a mathematical intuition. You can conceive of problems involving multiple variables and constraints whether or not you can write a system of equations. The numbers and symbols that have come to represent math are simply tools for communicating this intuition. These tools allow us to be efficient in our daily lives and the study of the world.
Effective math education means engaging this intuition first, and then generously providing students with the tools they need to express and deepen their knowledge. And with luck, become a mathlete (math + athlete).
* By “usually”, I mean about 85% of the time, according to my calculations**.
** By calculations, I mean “guesstimate”. I don’t go around calculating things.
*** This is called the “brute force” method, and it’s possible when you are dealing with relatively small numbers. However, the purpose of formal mathematics is to provide you with the tools to bypass this hard labor. It’s the equivalent of cutting your lawn with safety scissors when you could be using a riding lawn mover with a built-in stereo and a cup-holder for your ice tea.
****This “story” about money, combined with a geometric interpretation (solving for “y”, graphing these two equations and finding where they intersect) and an algebraic interpretation (solving for x and y using multiplication/division and addition/subtraction of the equations) is an example of using the “Physical, Geometric and Algebraic (PGA)” method of teaching math.
P.S. Anybody else catch this on Glee last week?