Monday, October 06, 2014
Describing a 7th or 8th grade basic algebra class as mathematics is quite a stretch, let alone one that includes teaching fractions. I am sure that one reason "some college" (like an AA or AS degree) is required for many jobs is it is the only way to be sure the job applicants are not innumerate.
One "college level" math class at my CC teaches how to use (not memorize) the compound interest formula to understand compounding of both debt and investments. I would not eliminate that math requirement. (Apropos the NYTimes story linked above, posted on my Fb page last weekend by a friend who got an MBA after starting at a CC, the course I just described does not include the 9th grade topic of solving a quadratic equation mentioned in that article.)
IMO, the problem would vanish in 5 years if ALL grade 3-7 teachers knew enough elementary math to teach it all with confidence and throw out the bad curricula being used in many schools.
Speaking as someone who is both good at math (as a college senior, I shared the highest score at my college that year on the Putnam Competition, among other math nerd things) and who has taught math in all grades 6-12, I think you really misunderstand the k-12 system if you place all of this on the teachers.
Don't forget that the concept of "prerequisites" doesn't exist in grades 3-7. At least in my experience, if you fail 3rd grade math, you're still a 4th grader in the fall and will take 4th grade math. Repeat throughout your academic career. I once had a high school sophomore in a geometry class who told me he hadn't passed a math class since second grade. (He didn't pass geometry either.)
I've taught at a high school where the counselor didn't believe in prerequisites either (she kept putting kids in the next math class in sequence whether or not they'd passed, with the idea that they'd make up the failed class with a computer based "credit recovery" program), but I prefer to believe she's a fluke. (I was math department head, and I spent a LOT of time trying to get her to stop doing this, but to no avail. She'd just tell me they couldn't graduate on time if they fell behind in math, and they couldn't use the (easier) credit recovery program until they'd failed the class, so it was important to fail them on through each year.)
If students aren't held to the idea that they have to learn the subject to move on, and no plan is in place to remediate previous missed content over the summer so they're ready for fall, no amount of the teacher knowledge or confidence will fix late elementary and early middle school math.
Also, at your college, where do the just-off-the-plane, haven't-been-in-school-in-10-years refugee students who speak almost no English start the math sequence? In k-12, the answer is "in the same math class as everyone else their age". I had high school students from Somalia who hadn't been in school in over a decade taking algebra I. This wasn't fair to either them or the rest of the class since they hadn't had any previous math about basic arithmetic (if that), but that's how old they were, so that's what school they went to, so that's what math class they were in. (In my state, you can't receive high school credit for any class below algebra I, so that's generally the lowest class offered.)
In a rural district I'd taught in previously, I also once had a Made in America problem in a similar situation. I had a kid who's parents had pulled him out in early elementary to "homeschool" him on their ranch. He probably learned a lot about ranching, but no particular math or other academic subjects until they handed him back off to the school system in 7th grade.
Anyway, I agree that it would help if all elementary school and middle school teachers were both competent and confident at math, but if you think that's all we need to fix this you're missing a lot about the overall dysfunction of the k-12 math system.
On another note, It would also help if they'd quit changing the k-12 math standards every few years and re-arranging which grades things are taught in. Because little Timmy is now retroactively supposed to have learned x skill in 5th grade, we don't have time to teach it in 6th grade since it won't be on the 6th grade standardized test (which has no impact on little Timmy's advancing to 7th grade no matter how badly he does, but can cause the school to be labeled as failing and get the staff in trouble if he doesn't do well). Never mind that last year in 5th grade it was was 6th grade skill, so that teacher didn't have time to teach it because it wasn't on the 5th grade standardized test that year. Having these yearly tests with specific skills being all you're evaluated on as a school encourages short-term thinking in terms of what and how you teach, but that's a whole different rant.
You raise some valid points, but many of them indicate to me that your students would be better off if people like you were making all of the decisions, and better yet if you were teaching 4th or 5th grade. Teachers who hate math and hate fractions should not be teaching either one. Decisions should not be made by principals who used to be just as bad.
In my state, students who fail the 3rd grade math test are held back unless they can pass it after a summer of remediation. Ditto for 5th grade. This does push the dropout decision into earlier grades, but the problem remains that so many fail those tests. There are good reasons (data) to believe that this is due as much to curriculum/book choice as teachers, at least at the lowest grades. Data concern a poor demographic school outperforming a middle demographic school.
Our standards have been pretty stable and common core will reinforce that stability, but I would urge you to look at the books more than the standards. You might be appalled.
This was, of course, several years ago. But we do continue to get our share of refugees of all sorts. We place them where they belong in ESOL and math once they come to us from HS or fresh off the plane, and they only advance if they actually make progress. I don't know if they are socially promoted in language arts, but I do know that students cannot move on to the next math class unless they actually pass the prerequisite course.