Posted on 12/15/2004 5:46:49 AM PST by Republicanprofessor
William H. Schmidt, Michigan State University Papers and Presentations, Mathematics and Science Initiative
Today the President addresses a serious issue in American education—How well we as a nation do in educating our children in mathematics. Dr. Loveless has addressed this issue using data from our nation's report card—NAEP. I will address the same issue but from an international point of view.
The data are clear. Recent results from the Third International Mathematics and Science Study (TIMSS) show that US eighth and twelfth graders do not do well by international standards—ranking below average in both grades and, in fact, near the bottom of the international rankings on a mathematics literacy test at the end of high school. Even our best students in mathematics taking an advanced mathematics test do not fare well against their counterparts in the other countries. Those results were obtained in 1995 but even a re-testing four years later in 1999 produced the same disappointing results. Put simply—there is no evidence to suggest that we as a nation are doing better, at least relative to other countries. New international results will soon become available as a third re-testing will occur this spring, but I fear there is little reason to expect major improvement.
Why do I feel this way? When you add the fourth grade results where our students were above average to the picture, a pattern emerges of a steady decline in our international ranking from fourth to twelfth grade. This suggests that our students do not start out behind but increasingly fall behind during the middle and high school years. This suggests that the problem lies not with our children, but that it is the education system that is failing them. This, I believe, strongly supports the need for a major national initiative in mathematics education.
Make no mistake—the problems in mathematics education have implications that are real and not just academic. The implications are for individual children as they seek employment in an increasingly technological economy where, given the lowering of trade barriers, they are competing not only with each other, but with children from around the world. The TIMSS data suggest they will not fare well in such a competition. This has implications for our nation as a whole, as well. It is not clear how long we can make up for deficiencies in our own educational system by importing the needed talent from other countries. Such a brain chase has become more competitive as other nations also compete for the same individuals. As the New York Times recently reported, the nation may soon regret not being concerned with the proper education of its own native born.
To stop here only restates what many already know—we, as adults, are failing our own children. What else have we learned from the international studies that might help us to respond to this serious situation. Other nations' representatives often ask me why does our student achievement not improve especially given that we are constantly reforming mathematics education in the US. The short answer is that we often engage in reform that is not based on scientific evidence but rather on opinion and someone's ideology. TIMSS offers us a good opportunity to use scientifically collected data on some 50 countries to find a more promising answer to the question of what we should do to improve the mathematics education of all children so that we truly do not leave any of them behind.
TIMSS results suggest that the top achieving countries have coherent, focused and demanding mathematics curricula. What would a coherent curriculum look like? A coherent curriculum leads students through a sequence of topics and performances over the grades that reflects the logical and sequential nature of knowledge in mathematics. Such a curriculum helps students to move from particular knowledge and skills toward an understanding of deeper structures, more complex ideas and mathematical reasoning including problem solving. For example, students should be expected to master the basic concept of number and basic computational skills in the early grades before they tackle more difficult mathematics.
What does the US curriculum look like? The US curriculum as reflected in many of the states' standards and in our nation's textbooks tends to reflect an arbitrariness where topics appear somewhat haphazardly throughout the grades. For example, teachers are expected to introduce relatively advanced mathematics in the earliest grades before students have had an opportunity to master basic concepts and computational skills. Secondly, the curriculum continues to focus on basic computational skills through grade eight and perhaps beyond. I would argue that if the logic of mathematics is not transparent to students, then it becomes difficult for them to develop a deep understanding that would lead to higher achievement.
What does a focused and rigorous curriculum look like in the top achieving countries? The number of topics that children are expected to learn at a given grade level is relatively small, permitting a thorough and deep coverage of each topic. For example, nine topics are the average number intended in the second grade. The US by contrast expects second grade teachers to cover twice as many mathematics topics. The result is a characterization of the US curriculum as a mile wide and an inch deep.
Coherent standards move from the simple to the complex. By the middle grades the top achieving countries do not intend that children should continue to study basic computation skills but rather that they begin the transition to the study of algebra, including linear equations and functions, geometry and even in some cases, basic trigonometry. By the end of eighth grade in these countries children have mostly completed US high school courses in algebra I and geometry. By contrast, most US students are destined to mostly continue the study of arithmetic. In fact, we estimate that at the end of eighth grade US students are some two or more years behind their counterparts around the world.
All of this is related to what students learn. That is why schools matter. The major policy implication of all of this is if we are serious about providing all students with a challenging mathematics curriculum it must be coherent, focused and demanding not by our own sense of what this might mean, but by international standards. We expect this of our companies, why would we expect less for our children's education. This implies we must secure the advice of the research mathematics community in this process together with those who understand children and how they learn mathematics.
But, this will not be enough. It is necessary to change our curricular expectations, but it is not sufficient to increase the achievement of all of our students. Recent research involving the top achieving countries suggests that the preparation of middle school teachers in mathematics includes a demanding level of preparation in theoretical mathematics as well as preparation in topic specific pedagogy, i.e., how to teach particular mathematics topics to children of a certain age. The level of formal mathematics training is very demanding in these countries. This required level of knowledge for eighth grade teachers gives some insight as to how such a demanding curriculum can be required in other countries and not just for their elite, but for all children—a goal we only seek, but one that is realized in many European and Asian countries.
Secretary Paige and his department have identified the national problem that many mathematics teachers do not have a major or even a minor in mathematics. The problem, however, is even more severe. Data collected from a group of districts that are in many ways similar to the US indicate the severity of the problem. Over half of the sixth through eighth grade mathematics teachers have neither a major or a minor in mathematics. For those teachers only one-fourth feel, by their own assessment, well prepared academically to teach a basic set of topics—most dealing with arithmetic only. We must address this issue of teacher quality and one important way is to begin by including mathematical knowledge as a key component in the definition of teacher quality.
We, in this nation, have set a goal to provide all children with a demanding mathematics curriculum that leads to greater learning. The goal is right, but the road there is demanding. Curriculum must be rigorous and coherent by international standards. It must be focused. It must require our middle schools to expect more of our students. It must be taught by teachers well prepared in mathematics and in instructional approaches that themselves are steeped in mathematics as well as cognitive theories of how children learn. And, it must be for all children.
Excellence in mathematics must be our highest national priority if we are to fulfill the true promise of America for all of our children. To do otherwise is unconscionable.
A long read but worthwhile. I could not find a date for when this article was posted, but it popped up immediately when I did a google search for this professor at Michigan State and I thought it worthwhile.
This is not necessarily news, but I think we can infer a few solutions from the article.
Agreed. The writer nailed it. My son's currently in 8th grade pre-algebra, and all they're doing is revising stuff they did years ago: arithmetic of fractions, etc.. Needless to say, he's bored, and he usually likes math.
All you can do is make sure to teach 'em yourself.
We made the mistake of assuming our son's teachers were doing math facts with him. At the end of 5th grade, he was STILL having trouble. It was a large reason that we decided to homeschool him. He just returned to school this year; he's a freshman in high school doing Alg. 1. He's doing much better now that he had a few years one on one with Dad doing Math.
This suggests that the problem lies not with our children, but that it is the education system that is failing them. This, I believe, strongly supports the need for a major national initiative in mathematics education.
I can hear the lib response now: Whats needed is more money! If we only had 13 billion dollars more, well then, we would have what we need for the children!
/em sighs softly...
I see the results of this rot daily when the students hit the university. The problem is we've given a monopoly on teacher preparation to Colleges of Education where the curriculum is vacuous--ed majors are the major of last resort for weak college students--and where an egalitarian 'lowest common denominator' approach to everything prevails.
No Child Left Behind tried to address this, but the states (who granted these monopolies) have balked at the 'highly qualified teacher' requirements.
The solution lies in breaking the teachers college monopolies--indeed requiring a major in a subject to teach it at the junior high or high school level and increasing teacher pay to get decent majors in other subjects (esp. in this case mathematics) to take up school teaching as a profession. (If you can finish a major in mathematics or any of the natural sciences, I think you're smart enough to figure out how to make a lesson plan, record grades, write on a blackboard without standing in front of what you wrote, and all the other things teachers need to do without specialized courses--TA's tossed into university classrooms just out of undergrad majors do it routinely.)
Education colleges were a part of Dewey's plan to ruin American education. GEt rid of all of 'em.
Ah, but that's another problem: in most states of the union, 8th grade is completely vacuous--all review in all subjects except for science where it's something lite like 'Earth Science' or 'Ecology' (and I used the commercialized misspelling advisedly) and maybe health where it's time for sex ed. Ever since I went through it, I've advocated abolishing it. A year of community service would be more edifying than 8th grade.
I've also hear that there is a serious demographic split in the testing of AMerican students. Whites and Asians still score high (in the top 10) but when African American and Hispanic students from the inner city are included, the average drops like a rock. The U.S. is producing bright, educated kids and ones that haven't learned a thing in school. Very little in the middle.
You can thank Prentice-Hall, and others publishers, for producing the most abysmal textbooks ever.
My daughter is in an AP program, and her math book is HORRIBLE -- it just sorta tosses in new ideas with no real explanation of why it's there, how it works, or how it's used. The authors of the book spend a lot of time tossing in various linear algebra concepts, and they try to do it without having actually explain why linear algebra exists in the first place.
Matrix multiplication was actually introduced for the first time in the middle of a chapter on signed numbers!!! F***ing ridiculous.
The excuse given by the authors is that it's part of the "spiral learning model." I suppose such a model is helpful if a kid is first given some f***ing background in the subject matter, but this particular book doesn't bother to do that.
I can walk her through it, since I use most of the math in real life and understand it. But my daughter is just doing the mechanics -- and I suspect the other kids in her class are, too. The book does not teach for understanding, and the teacher hasn't got time to do it....
Sigh.
On the other side of the coin, my daughter is actually doing the more advanced stuff, but it's so poorly presented -- no motivation of topics, no systematic buildup, etc. -- that she's utterly confused most of the time....
I agree. There is way too much pedagogy, which deadens the brains of the bright and doesn't contribute any real knowledge. But you would not believe the way the education professors circle their wagons when criticized. They won't allow for new ideas (although the need for brainstorming and change is dramatic).
the states (who granted these monopolies) have balked at the 'highly qualified teacher' requirements
Schools have a hard enough time finding teachers to teach at all, whether in their area or not, much less highly qualified ones. Yes, higher salaries may draw better teachers. But also less certification b.s. and more discipline in the classrooms. Who wants to waste their time with ill-disciplined brats who disrupt class and won't let you teach?
Parents and teachers also resist the mandated testing too. Makes Johnny look too dumb.
As I mentioned on the discussion of the recent PISA study, I think that it is mandatory that teachers understand mathematics in order to teach it. I will assert that a teacher who does understand mathematics cannot possibly teach or grade work in mathematics.
I agree with your post. I was an electrical engineer, turned high school teacher. Science major, math minor. I got to teach one class in science, (no openings in the department in ten years) and taught low level math as my seniority moved me up. Kids were poorly prepared when they came from poor areas. Well prepared when they came from wealthy areas. (My school had both feeder schools, the difference was that in the wealthy schools more was expected, and teachers gave 10 to 14 pages of supplementary homework per day. The teachers in the poor schools did not expect much and did not assign much, maybe one page a day.)
I lost my job because of a mass layoff based solely on senority. The union controls firing. I went back to my engineering job and began to teach new engineers as the company hired them. I was one of the highest ranked industry teachers, but the school could find no way to keep me. So I contend that it is not just a problem with the level of ability of the teachers, the union creates roadblocks to getting and keeping the best teachers.
Incidently, the text books we had were very good. Class size was large, and many teachers teaching math did not have math as a strength, but likewise there were many strong math teachers, particularly in the higher levels of math. My belief is that homework, and lots of it is the key to success in math. (And the homework must be looked over by the teacher.)
And if not all the way, supplement at home - be involved. As a single parent, it's not feasable for me to homeschool, but my son is also in 8th grade and education has always been supplemented at home. Not so much in a book-sense, but in life-sense.
The danger does come when the kids get bored. If their love for learning decreases, so will the results. My son was getting bored in science - talked with his teacher (seeing as he wants to major in life sciences, kind of important he stay interested) - though the curriculum can't be changed, he suggested that my son do extra research and work on subjects he's interested in and he'd be happy to give feedback. This also gives him the opportunity to see tangible applications for science.
Like I said, be involved. Public school will never be good enough on it's own. IMHO
The problem in mathematics teaching has been going on since the '30s or so. When I was in elementary school in the '50s, our principal was constantly fighting to keep using the old pre-WWII math books up through grade 4, which contained lots of rote learning and enough drill for anyone. Her view (and she had an MA in mathematics from UC Berkeley) was that there was simply no substitute for rote and drill below the age of 10. She wanted evey student who went through her school to know basic arithmetic cold. Our kids did better in junior high and high school than all the other schools in town, except the other school which also kept using the old books. The were only replaced in the mid-1960s when they literally wore out after 35 years of use.
For me, the rote was pure torture, but I'm an anomoly: theoretical mathematics comes very easily to me, but arithmetic is still painful. However, knowing the arithmetic made it possible for me to do real math later on.
I'm also convinced the teaching of the middle school subjects in mathematics -- elementary algebra and plain geometry -- need to be much more rigorous. In my daughters' middle school, there was only one good mathematics teacher out of a dozen. In their high school, there was a huge bifurcation. There were several good mathematics teachers, but they only taught the very top kids (the ones two grade levels ahead- calculus as juniors, AP calculus as seniors), the rest of the math faculty was so bad the kids who were struggling couldn't get the material, let alone ever catch up with the kids who were getting the best instruction.
Notice the problem in the article wasn't with the classes up to the age of 10, it's with what happens after. At 4th grade our kids do fine, between 4th and 12th, when they need more than rote and don't get it, we slip behind almost all other developed countries (last time I checked, only Canada was worse, but maybe that's changed one way or another).
When they start paying for Quality Math and Science Teachers we will get quality math and science programs. The reason that alot of middle school kids get stuck at this level is because the people expected to teach higher math and science don't know it themselvs.
Ain't it the truth. For some now forgotten reason, one of my kids was being asked to show the inverse image of an open set was open in a pre-calculus or calculus class a couple of years ago. They book had a clunky way to get at the problem, so I just got out my old copy of Rudin's Principles of Analysis and explained the proof to her, which she then used. The teacher marked it wrong!! (Straight out of RUDIN, for Gosh sakes!!) Turned out the teacher didn't understand the proof, and it took me an hour, with the book and another math teacher, to explain it to her.... Argh.
Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.