Wednesday, March 07, 2007

12th Grade NAEP Math Scores

The regular release of scores from the National Assessment of Educational Progress ("the nation's report card") is always a sobering experience. I don't like to be alarmist, but inevitably, it's a cause for some national self-flagellation.

The 2005 12th grade math scores are no exception. While tests given to 4th and 8th graders suffer from a certain reality that pretty much everyone attends these grades, by 12th grade, many people who have no interest in learning have removed themselves from school. Those remaining should skew toward the reasonably advanced. Indeed, the majority of high school graduates intend to go on to additional education.

Unfortunately, they don't seem to be learning the basic math skills that further education should require. Check out the sample 12th grade NAEP math questions here. The first is a very simple multiple choice geometry question; 73% of students got it right. The second is a simple algebra question that requires you to cough up an answer; only 23% of students got it right. Many students take algebra before geometry, so it seems odd at first glance that the geometry question was easier for people than the algebra one. But I think there's an unfortunate dynamic going on here that doesn't indicate good things for the rigor of most kids' curriculum.

The first geometry answer could likely be deduced through some real world observations (answer A isn't right since the second angle looks bigger than the first angle... and if you've ever doodled shapes inside a protractor in class, you might know a straight line totals 180 degrees). Children see streets in real life, too, so there's less of an eyes-glazed-over response to the question. Plus, it's multiple choice. You might give it a shot. The second question, though, with its f(x) and f(g(x)) language, doesn't feature a lot of real world reference points. Answering it requires a confidence gleaned from having taken and understood algebra. It is a pure content question, measuring content mastery. And unfortunately, three-quarters of high school seniors seem to lack that.

It goes without saying that children who can't do algebra will have an awfully hard time succeeding in college-level math. And a great number of jobs -- particularly fast-growing, high-paying ones -- will require some college-level math. U.S. schools do not seem to be preparing the majority of high school seniors for these career paths. But hey, at least the kids' grades are good. A report on high school transcripts, released about the same time as the NAEP scores, shows that students now average a 2.98 GPA in high school, higher than in previous years. Too bad their NAEP scores don't show a similar rise.


Royce Wells said...

So then who is a fault her?. Since there is obviously a problem here, what steps are being taken to solve it if any?

If the majority of the students taking this test are of a reasonably advanced level, and they are still preforming below average on the tests, then I would reason that there is some problem in the school system.

However, I am loath to rely completely on tests. Often they present a skewed view of the student population. Though it remains to be seen whether the test was skewed in a good way or a bad way.

SteveH said...

"However, I am loath to rely completely on tests."

This is a common cry from those in education, but the question is what other information is so important that it makes flunking these simples tests OK?

There is another problem here too. Our state tests are designed and calibrated by the same people who push the fuzzy math in schools. Often, these tests are filled with fuzzy, real-world problems that don't test for mastery of the basic of content and skills required for college math. In spite of their control over the curricula and tests, the questions are really not difficult by any standard. So, here we have an educational system that defines math the way it wants (some say they hijacked math), creates the tests, and defines the proficiency cut-offs, and they still can't get the job done.

Many argue about how lower school math programs teach things like the lattice method for multiplication and avoid the traditional long division technique. This is only a symptom of the problem. You begin to see the real problem when kids are supposed to be learning about manipulating fractions. Everyday Math tells teachers (in fifth grade) that learning how to divide fractions is not so important because it is rarely used by adults. Of course, this attitude virtually guarantees that the kids will not need it as adults.

The reason 12th graders are so bad in math starts back in Kindergarten. By the time kids get to high school, the die has been cast. They are put on either the honors or AP math track of real math (only there because they are really smart and/or they get help outside the school) or they get put into the real world check-book math classes. They don't get real math at a slower pace, they get pretend math.

It's a philosophical problem. In the lower grades, they are not big on mastery of content and skills. Everything is about the process of learning, which usually involves a lot of mixed-ability group learning. This is very wasteful of time with little emphasis on mastery of content and skills. I naively told my son's first grade teacher that he loved geography, knew all of the state capitals, and could find any country in the world, even East Timor. She said that "Yes, he has a lot of superficial knowledge." I call it foundational knowledge. Ironically, later that year, my son had to show the student teacher where Kuwait was on the map during a thematic unit on Sands From Around the World. So much for thematic learning.

Many problems in education surface in high school, but the problems (philosophical and competence) start in Kindergarten.

Anonymous said...

"They are put on either the honors or AP math track of real math (only there because they are really smart and/or they get help outside the school) or they get put into the real world check-book math classes. They don't get real math at a slower pace, they get pretend math."

Having taught physics at one of our nation's premier universities, I can assure you that most get "pretend math" irrespective of what track they find themselves on. I've lost count of the times I've been floored by students' general lack of knowledge of basic geometry, algebra, trigonometry, even the concept of imaginary number. And this wasn't even "physics for the numeracy challenged," but rather calculus-based (hah!) courses for future scientists and engineers.

The last time I taught, in my first lecture I gave a spot quiz on basic mathematics required for the course. I said "if you don't ace this, you don't belong here." Needless to say, over half failed. I quit teaching after that quarter, tenure be damned. Talk about a waste of my time.

I agree it's a philosophical problem, but not in the same sense as the prior poster. The problem is that we cannot bear to fail a student, so we lower standards of "success" to the point where every student succeeds. And every other student makes the honor roll. And every student is happy, right up until they become adults and have to face their own inadequacies stemming from marking time in 13 years of pep rallies and popularity contests, classrooms taught by burned out "woulda-never-beens". Heaven knows it's better to guard chidren's precious self esteem than to give them honest feedback on how good they really are doing to maybe motivate one or two to higher levels of discipline and competency. Or even worry their parents that little marginally literate Johny won't get through a 4-yr. college. No wonder democratic process is failing in the U.S.

Your child's teacher should be fired for gross incompetence. In a heartbeat I'd vote to increase taxes to, say, double teacher and administrator salaries while instituting genuine certification requirements for same, not the watered down diploma in touchy-feeliness that passes for an education degree. Engineers, lawyers, physicians, they all require hard-nosed testing. Real professions with competency standards beyond 4-yr certificate of attendance at a local teaching school. Why not do the same for those who purport to educate our youth?