This is only the 2nd year I've taught algebra 1 as a one-year course (in New Jersey we had a slower paced 2 year course of which 1 taught the 1st year). Recently, some interesting things have come to my attention that I'll be aware of the next time I teach it.
We've just started "baby graphing" ... I give them an equation, and x values, and then they find the y values and plot the points. They're still at the stage where they don't know if they should connect the points or not. When I prompted them on a linear graph as to whether they should connect them or not, I got "yes because they go up at a constant rate" or "yes, they follow a pattern". We'll fix that later. But here are some more immediate things that I need to address.
On the 2nd day we were doing this, I then did NOT give them x values. Oh HOLD THE PHONE! What should we do???? Oh no!!! We got that straightened out with the "rule of thumb" (then I had to tell them the origin of that phrase). Then here's the problem, sometimes I had given them a preset grid, and OH NO, the points they chose did not fit. They didn't figure out that they could change the scale, or NOT plot that particular point. So ... new buggaboos that I'm learning to address in the course of this unit.
Then, here's the more interesting one. I saw with alarming frequency that apparently, 10 divided by 20 is 2. I know. Who knew?! Then I realized, they did not know that if they saw "10 div 20" (where the div is the division sign) that that was the same as 10/20 or 20 into 10 (under the long division symbol). They didn't know what went where.
And finally, I'll have to come up with a clever way to make stick that if you're given: y = -x^2, and you plug in x=3, then that's NOT (-3)(-3). or similarly, if you plug in x=-5, then that's not (--5)^2 or 25. I'm thinking "x box": put a box around the x physically and follow PEMDAS. ... Another teacher today said that a student of hers suggested, "oh! y=-x^2 can just be written as y = 0 - x^2". Then they would follow PEMDAS more easily. Maybe I should try that.
Good luck. I've been following your blog for some time. I like your energy and commitment. I'd suggest trying to help some of your students' former teachers eliminate the fraction/division mistake. Long term, kids can't keep rising to classes inadequately prepared.
ReplyDeleteI actually have the same problem, but at a transfer school, there are no colleagues to conspire with. You might also be interested in checking out how some of your students use the words front, back, behind, etc... I found my kids were eccentric in their usage
Hmmmm, well, that's something I hadn't thought of ... "front, back, behind". Is your thought that they confuse positioning? That'll be interesting to test out. Thanks for the heads up.
ReplyDeleteMs. Cookie
It's interesting, because I encounter every single one of these issues with at least 90% of my Algebra 2 students.
ReplyDeleteAnd every year, we see a significant jump in Algebra 1 (and all) math scores, yet when they reach Algebra 2, they still don't really understand the process or meaning behind the mathematics--ESPECIALLY when it comes to graphing. And when they get to Algebra 2, it's so difficult to break their way of thinking because they cry, "But this is HOW I LEARNED IT!"
As for the y = -x^2, aside from writing it as y = 0 - x^2, you can also try having them think of the missing coefficient, y = -1x^2. Then again, using PEMDAS, exponents come before multiplication.
JT,
ReplyDeleteOh my GOODNESS with the "great state-test-scores" and "poor real knowledge". That bothers me, too.
Today I tried the y=-1x^2 in addition to the "x box" method ... where I put a box around JUST the x and said anything you plug in JUST goes to the x .... hopefully, if we keep plugging away at it, it'll gel.
Ms. Cookie