Well, the results are in: Half the students in my S5 math class do not know how to graph the equation y(x) = “constant” (i.e. y(x) = 4, y(x) = 8, y(x) = 12). Thirteen took the test on Monday, and six got a big-fat-zero on that particular problem. Damn.
But, in their defense, it is a strange equation. I mean, y(x) = 4? “y” is apparently a function of “x”, but where the hell is the “x”. I can hear their thought process: “Well, when y(x) = x+1, and Mr. Murphy asks for y(1), I just replace the x’s in the equation with 1… so y(1) = (1) + 1… but he gave me y(x) = 4… THERE ARE NO x’s TO REPLACE!! I HATE MR. MURPHY!!”
Here’s the rub (for you geeks that care but don’t already know)… the graph of y(x) = “constant” is nothing but a flat straight line that crosses the y-axis at a height of whatever constant value has been defined (if y = 4, it crosses the y-axis at 4). The slope of this flat line, m, is equal to zero. Therefore, given the equation of a line, y(x) = mx + q (where q is the y-intercept), the equation of my line, using the aforementioned y-intercept of 4, becomes: y(x) = 0*x + 4… which reduces to y(x) = 4, or generally as y(x) = “constant”.
The test… I was damn proud of it… to avoid the mastermind cheating that these kids are capable of, I assembled three different tests, sat them three to a table, and watched in amazement as a few still took long rest breaks by staring at their neighbors paper (or in one case one boy whispered the answer to a brutally hard multiplication problem, 8*7, to his buddy… “56” I hear as I approach, and “56” is quickly written…). I broke every problem down into pieces (a), (b), (c), etc… so instead of overwhelming them with one big question, they worked through each piece in a logical order. Furthermore, I had given a test review covering examples of every single problem in detail that I would cover (this was in addition to a set of notes with three more examples of every type of problem I would offer). Geez. Listen to me bitch and moan.
Test average: 42%
So I did what any teacher does when the average isn’t what was expected: I played with the numbers to see what was dragging it down.
Just as I thought… it was all those failing students.
While grading the tests, I realized that I was dealing with two groups of students; the kids who try, and the kids who don’t. Those who try, about half the class, attempt the homework, they come to recitation two times a week, and they ask questions. The kids who don’t try, well, they do the opposite.
The proof is in the numbers: The kids that failed (which by Ugandan Ministry of Education standards means they scored lower than a 35%, did so gloriously. Their scores are as follows: (0%, 2.1%, 4.2%, 12.5%, 21%, 24%). These kids don’t know a math function from a school function, and they had never “Excused My Dear Aunt Sally” even when asked “Please” (is this reference lost on anyone?... it represents the “Order of Operations”). In short, they lack even the fundamental concepts necessary to enter a math class where Calculus is being taught, and worse, they haven’t tried to correct these shortcomings in ANY way even though I have been extending them a hand for weeks now.
Back to it… When I removed those ghastly numbers from the pool, my average sky-rocketed to a, sad-by-American-standards but 1.2 points shy of a D2 distinction (that is, the second highest grade achievable in Uganda!), 68.8%.
So there it is: When I do my job and the students do theirs, the class average approaches an American “C”. That, I can deal with.
I had my second math class of the week today, and I had one of those “teacher moments”, one that makes you feel proud for what you are doing. You see some light at the end of the tunnel and that you are making a difference… I called the student that had scored a 2.1% to the board and asked her to find g(f(x)) when f(x) = 4 and g(x) = 2x + 2.
Before touching the chalk to the board, she turns around and says to me, “Master, I have failed you.”
“No. That’s not going to work this time. Write g(x).”
“Ok, now write g(1).”
“Remember, when I say g(1), it means you replace all the x’s in g(x) with a 1.”
g(1) = 2(1) + 2 = 4
“Now, write g(2).”
g(2) = 2(2) + 2 = 4
“Now write g(f(x)).”
To this she replies, “Master, I have failed.”
“No, you’re doing fine. Give me g(4).” I am trying to convey that regardless of what I put in to the parentheses next to g() I put THAT wherever there was an x. I’ve tried with problems, notes, speaking, everything I can think of, and I’m not getting anywhere. She needs to keep doing the problem until she sees the pattern.
We go through this with more numbers until finally, I say, “now write g(f)."
Reluctantly, she writes: g(f) = 2(f) + 2. And then quickly erases her work. With some goading, I get her to put it back on the board.
“Good! Now, write for me g(f(x)).”
The class and I sit there in silence. She traces over the 10 or so problems she has worked so far. Finally, she slowly writes:
g(f(x)) = 2(f(x)) + 2 = 2(4) + 2 = 10
I begin to clap for her. The class joins in. She goes to sit, her face an open book: I CAN LEARN THIS!
The period passes, and towards the end we find ourselves working through another problem missed with high frequency. h(x) = -x^2 + 10x. It is a simple enough parabolic curve, but if you don’t know your order of operations (you have to square whatever you put into x FIRST and THEN multiply by -1), you get extremely high numbers when you try to plot. I ask the class for a volunteer to plot the equation of the range [0, 5]. No one volunteers.
Just as I am about to call a random person, she raises her hand. 2.1% is, for the first time, asking to go to that board and try something that has stumped the entire class. I am thrilled.
“Of course! Come on up!”
She comes up, draws the table, and without hesitation cranks out every single answer in flawless form.
I begin to clap for her… the class joins in. I’m wearing a shit-eating grin as I return to the board. I say all that comes to mind, “that was brilliant work. This is my proudest moment as a teacher here in Uganda.”
There is work to be done, a lot of it. For the few that did poorly on the first test and decide they need help, seek it, and start trying, I think there is hope. For the few that think that the knowledge will come just by watching me write problems on the board, there will be trouble. And for those that have been working hard both in class and out, I see them blowing away the Ugandan standard. My goal for them is to pass the national tests next year with score that even an American student’s parents would be proud to display on the fridge.
Thanks for reading.
I love you all (but especially you, Michelle!)
P.S. If you want to give my test a go, download it here: http://filebox.vt.edu/users/demurphy/Work/Test%201%20Functions,%20Secants,%20Derivitives%2014-6-2010.pdf