I will often hear students say that they are solving problems without doing any math. An example: I put an equation on the board and asked my students to make a table of points that solve the equation:
2x + y = 12 was the equation.
Some points that solve the equations are (0, 12), (1, 10), (2, 8), (3, 6), (4, 4), etc. There are an infinite number of points that solve the equation.
When I ask my students how they got the points, a lot of them well say something (sheepishly) like "well, I didn't use any math, I could just look at the equation and see it."
When they say "I didn't use any math," what they mean is they didn't write stuff down and do adding/subtracting multiplying/dividing. Like, at no point did they plug in a 5 for x:
2x + y = 12
2(5) + y = 12
10 + y = 12
-10 -10
y = 2
so the point (5, 2) also solves the equation.
The above work they call "math."
I try to stress that "doing math" isn't actually math. It's arithmetic. The adding/subtracting multiplying/dividing of numbers is simply arithmetic which is just a part of math.
But mathematics is really just logic. It's logic applied to a very precise, well defined system. Looking at the equations 2x + y = 10 and just "seeing" points is really an application of logic, and that's math.
Similarly, some students find more points in the equation above by noticing the pattern (every time the x-value increases by 1, the y-value decreases by two in the (x, y) points). They seem to feel that noticing and using a pattern isn't "math." No, it's not "arithmetic," because math is nothing if not lazy people noticing patterns to make their lives easier.
I feel like this must be a result of poor teaching, from a young age. We call arithmetic "math" and never really teach straight, plain logic. It's frustrating, and something that CS Lewis mentions often throughout his writings. Teaching logic is challenging, and arithmetic can be easily grasped at a young age, so i understand its emphasis, but this is a huge disservice to our children.
2x + y = 12 was the equation.
Some points that solve the equations are (0, 12), (1, 10), (2, 8), (3, 6), (4, 4), etc. There are an infinite number of points that solve the equation.
When I ask my students how they got the points, a lot of them well say something (sheepishly) like "well, I didn't use any math, I could just look at the equation and see it."
When they say "I didn't use any math," what they mean is they didn't write stuff down and do adding/subtracting multiplying/dividing. Like, at no point did they plug in a 5 for x:
2x + y = 12
2(5) + y = 12
10 + y = 12
-10 -10
y = 2
so the point (5, 2) also solves the equation.
The above work they call "math."
I try to stress that "doing math" isn't actually math. It's arithmetic. The adding/subtracting multiplying/dividing of numbers is simply arithmetic which is just a part of math.
But mathematics is really just logic. It's logic applied to a very precise, well defined system. Looking at the equations 2x + y = 10 and just "seeing" points is really an application of logic, and that's math.
Similarly, some students find more points in the equation above by noticing the pattern (every time the x-value increases by 1, the y-value decreases by two in the (x, y) points). They seem to feel that noticing and using a pattern isn't "math." No, it's not "arithmetic," because math is nothing if not lazy people noticing patterns to make their lives easier.
I feel like this must be a result of poor teaching, from a young age. We call arithmetic "math" and never really teach straight, plain logic. It's frustrating, and something that CS Lewis mentions often throughout his writings. Teaching logic is challenging, and arithmetic can be easily grasped at a young age, so i understand its emphasis, but this is a huge disservice to our children.
No comments:
Post a Comment