Sunday, March 25, 2012
Grades
Read this rant about the pointlessness of grades.
The author is a recently retired physics teacher who says that grades have replaced learning as the primary objective in grade schools, and that they are not a good reflection of mastery. The author makes a lot of good points, but in the end I can't fully agree. My main reasons for not hating grades are:
1) Students are actually motivated by them. Grades are a way to transmit the necessity of learning. In the end, we don't just learn because it is fun but because it is useful. Students are not really in a position to know what skills will be useful so we have to tell them somehow.
2) Students are not very good at achieving mastery goals, so giving them credit for behavioral goals (which the author calls "completion credit") is a way to motivate them to take the small steps necessary to master necessary skills. One interesting study in this regard involved making small payments to students. When students were payed for long term, abstract objectives they were motivated but didn't really know what to do. When students were payed for more concrete inputs (like the number of books they read) they knew exactly what to do.
So, I agree that right now grades are pretty arbitrary. Students and parents get stressed out about them and try to influence teachers. They aren't that great at reflecting mastery. But what would we have without them? How could we indicate to students that learning is actually important?
Of course, this contradicts my view that a lot of things taught in school actually aren't important. Maybe we should be more selective about the things we choose to grade.
Next item: The Algebra Project.
The premise of this project is that everyone needs to have access to algebra because it is the gateway to more advanced math and science classes, and ultimately, college. It is run like a grass roots organizations, trying to get struggling communities to pull together to support algebra in the way they came together during the civil rights era.
I don't think everyone needs to know algebra. I don't think everyone needs to go to college. Pulling a community together in support of math is a great idea, but it is also a utopian one. The fact is that our economy doesn't really need people with basic algebra skills. The economy needs people who actually really like math and science and can motivate themselves all the way through a graduate degree in engineering because on some level they think it is all very interesting.
Organizing a community to teach 8th graders algebra will have positive results, I am sure. Hopefully a few of the students gain enough confidence to keep going with math and science. And organizing a community seems like a better idea to me than passing a law like No Child Left Behind. It seems more organic and less of a top down institutional solution.
But programs like this mostly just remind me of how messed up our system is at the very foundations. We try to force kids against their will through a factory/day care system with an endless series of curricular goals with little evidence that these goals are actually useful. Why? Because this is what people need to get into college. And why do colleges take high school so seriously? Because if they just had placement tests they would have to admit a bunch of 12 year olds (honestly, a motivated 12 year old could easily surpass a typical high school graduate). This would interfere with our idea of college as a coming-of-age party.
So why do we care about college? Because employers take college seriously. Again, why? Employers are perfectly happy to let people waste 4 years in college because 25 year olds (especially ones that have been jumping through educational hoops for 20 years) are a lot easier to manage than 15 year olds.
Anyway, the point is that for most jobs you don't really need to know algebra, or anything else that is taught in high school or the vast majority of college courses. High school and college just give us time to grow up. I personally am not too upset at having spent the majority of my life in mostly useless educational settings because I actually enjoy learning. But lets not be too idealistic about the impact of teaching kids algebra.
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Interesting point of view. I have often discussed with people about elementary school grades being mostly based on completion and college grades being mostly based on competence, with middle and high school somewhere in between. And that is important. First we try to teach kids how to learn -- develop those skills which will make them better learners -- all while helping them learn basic skills. Then by the time they get to college, they are more ready to focus on research and subject mastery. Making everyone take algebra is more of the same idea. The practice in using logic, definitions, and problem solving are important in about every job, while at the same time solidifying the more basic math skills that are used in almost every profession. I really don't think most 9th or 10th graders have solidified what they want to do for their careers, and learning algebra keeps future opportunities open, while not taking algebra closes a huge number of doors.
ReplyDeleteI agree with your sentiment, but I don't think that missing out on algebra in 8th grade necessarily closes doors. People could easily learn algebra later on, when they are 20 or 25 and realize that they need to know algebra to get a job. But in our current system it closes doors because students are expected to go through a very regimented educational path.
ReplyDeleteSure, algebra is a great way to exercise the kinds of logic that people need in some jobs. But employers who think that algebra is important should require their employees to take an algebra test. The fact is that most employers don't seem to care because they keep hiring high school and college who don't have a very good grasp of algebra or any other kind of logic.
Actually, I've tutored people who had to take algebra tests for their employment. Firefighters, forest rangers, police officers, etc. all need to pass tests that include algebra. But people don't know about it until they try to get the jobs. I've taught pre-nursing students who didn't pay attention in high school -- not realizing how important that class would be to a nursing career. And because their algebra was so weak, they weren't able to enter the nursing program for an extra year as they took remedial math to get ready for algebra.
DeleteGiven enough time, anyone can learn algebra, but the later you start, the harder it is to learn. Some students never got the job they wanted because they slacked so badly in secondary school algebra they didn't have enough time to bolster their understanding to the necessary level.
Interesting. I wonder whether those careers actually require people t use algebra, or if they use it to measure general intelligence. In my experience, a pilot has to be pretty dang good at arithmetic, but there really isn't much algebra involved.
ReplyDeleteSo you think algebra is like a language in that the brain can adapt to it more easily at a young age? Here is an article that supports that view: http://www.pnas.org/content/101/15/5686.long
Can someone be too young to learn algebra? I remember when I was first introduced to variables I thought it was so much easier than the complicated arithmetic they made us learn in 6th grade.
Actually, I think people use algebra all the time. As long as they fool themselves into thinking it's not algebra, they are pretty good at it. But as soon as they think they have to do algebra, they suddenly can't do it any more.
ReplyDeleteConsider renting something that costs $20 to initiate the rental and $13 per day of use. The cost is a linear function of the time. It's a degree one polynomial. Most people have no trouble figuring it out. But if you then asked them about a line with y-intercept 20 and slope 13, they panic and can't do it, even though it is an identical problem. I think we need to require algebra, but we have to get away from the overly formal and formulaic way it is taught.
This is partially an issue of how we define algebra. I definitely agree that people are able to solve many problems such as the one you described, but should we call it algebra if they don't model the situation in some abstract way (using an equation or graph or something)?
ReplyDeleteFor most people, up to a certain level of complexity problems are easier without the abstraction. It is the abstraction that is difficult. But after a certain point problems become unmanageable unless you abstract them. I guess my feeling is that in a typical person's workday they don't deal with problems on a very abstract level.
I guess my main point is that we should focus on bid ideas, like modeling with abstraction rather than accumulating a lot of very specific tools without ever understanding or applying them to interesting situations.