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Economist Walter Williams weighs in on the academic atrocity also known as 'fuzzy math':
American education will never be improved until we address one of the problems seen as too delicate to discuss. That problem is the overall quality of people teaching our children. Students who have chosen education as their major have the lowest SAT scores of any other major. Students who have graduated with an education degree earn lower scores than any other major on graduate school admissions tests such as the GRE, MCAT or LSAT. Schools of education, either graduate or undergraduate, represent the academic slums of most any university. As such, they are home to the least able students and professors with the lowest academic respect. Were we serious about efforts to improve public education, one of the first things we would do is eliminate schools of education.
The inability to think critically makes educationists fall easy easy prey to harebrained schemes, and what's worse, they don't have the intelligence to recognize that the harebrained scheme isn't working. Just one of many examples is the use of fuzzy math teaching techniques found in "Rethinking Mathematics: Teaching Social Justice by the Numbers." Among its topics: "Sweatshop Accounting," "Chicanos Have Math in Their Blood," "Multicultural Math," and "Home Buying While Brown or Black." The latter contains discussions on racial profiling, the war in Iraq, corporate control of the media, and environmental racism.
If you have a fifth-grader, his textbook might be "Everyday Math." Among its study questions are: If math were a color, it would be —, (blank) because —. (blank). If it were a food, it would be —, (blank) because —. (blank). If it were weather, it would be —, (blank) because —. (blank). All of this is sheer nonsense, and what's worse is that the National Council of Teachers of Mathematics sponsors and supports much of this nonsense.
Mathematics, more than any other subject, is culturally neutral. The square root of 16 is 4 whether you're an Asian, European, or African, or even a Plutonian or Martian. While math and science literacy among white 15-year-olds is nothing to write home about, that among black 15-year-olds is nothing less than a disaster.
Few people appreciate the implications of poor math preparation. Mathematics, more than anything else, teaches one how to think logically. As such, it is an important intellectual tool. If one graduates from high school with little or no preparation in algebra, geometry and a bit of trigonometry, he is likely to find whole areas of academic study, as well as the highest paying jobs, hermetically sealed off from him for his entire life.
You can read the entire article here. For those interested, Williams has a number of syndicated columns over the past few years that are quite critical of the declining 'educational' departments in American universities.
7 comments:
"If math were a color, it would be —, (blank) because —. ..."
I don't remember that in fifth grade EM. It's probably there, but it's easily skipped. You can open EM almost anywhere and see proper math problems. That's not the problem.
The biggest problem with EM is that it is designed around no requirement for mastery at any one time. That's why schools buy it. It takes the pressure off of the students and the teacher. It's OK to let kids defer mastery. The Math Boxes in later grades will allow kids to catch up at their own speed. It goes along with the idea that kids will learn when they are ready. They think that if you force kids to learn things in "lock step", then they won't learn and they will grow to hate math. Our school likes EM because it fits their full-inclusion, differentiated instuction model.
This is all nice in theory, but it doesn't work in practice. Enough kids will figure it out on the first pass (or will get help at home) that the school won't see that there is a big problem.
Open up EM anywhere and you will see proper math problems. However, it's all in a jumble. Right in the middle of learning new material you have Math Boxes that give you problems that you haven't seen in a long time. This might be nice for those who have mastered the material the first time around, but it is of little help if you haven't. The Math Boxes don't focus on any one topic. They jump all over the place. If a student has trouble with one type of problem in a Math Box, there is no support or way to finally master the problem. There is no way for either the student or teacher to fix the problem. The student has many more problems to do and has to move on, and the teacher can't deal with 20 different problems that could pop up. My son's teacher didn't even collect the Home Links. She had the kids do self grading.
So how does EM work in practice? It introduces new material in class. My son's teacher gave short introductions and set the kids off to work on their own or in groups. The teacher sat at her desk and works on the computer. (My son says that all of the teachers do this.) If the kids don't understand how to do a problem, then they can ask the teacher. My son said that the kids never did that. You really can't put that kind of onus on the kids when they might be afraid of the teacher or really can't explain what it is that they don't know. When the class is done, the kids get a page to do in their Home Links workbook.
I remember one time in fourth grade when my son had to do his EM homework. He was fooling around and not getting to work. I came back after 5 minutes and told him to get to work. He said that he finished it. I looked at the homework and it was a tear-out worksheet with 6 simple questions on it. The goal was obviously not mastery. That's the whole point. They think that if they do this enough times, then kids will learn by osmosis.
The next day, EM moves on to another topic. If you don't master it the first time, then you have all sorts of wrong ideas and confusion in your head that will fester until the next time you see the material. That next time might be a month later.
Spiraling in EM doesn't mean that you build on top of previously mastered material. It means that you get a variation of the same material all over again. Some refer to it as circling. It's the same process. The teacher introduces the subject and then the kids are on their own. The teacher doesn't collect the homework so he/she won't know there is a problem until a test is given. Since EM jumps all around, the tests will jump all around. Since EM says that it's OK to delay mastery, and they will see the material again, the teacher is not too concerned about fixing mistakes. By the way, if the test is the first time the teacher gets feedback on individual mastery problems, it's too late.
How does EM propose to finally achieve mastery? Math Boxes. It's worst in 6th grade because it's their last chance. In the middle of a new unit on a subject, they get one or more pages of Math Boxes containing all sorts of problems. There is no way that a teacher can address all of the different issues that pop up, even if the kids bother to tell him/her. If teachers don't collect the homework, then they just don't care.
Everyday Math is repeated partial learning. Every day is the beginning of September. Their basic assumption is flawed. It says that teachers don't have to identify and fix misunderstandings at any one time. The problems will fix themselves.
It is amazing to me that any school can justify using a curriculum that encourages teachers NOT to teach!
I just couldn't do it! I would be overwhelmed with guilt!
I think that many teachers figure it out and do teach. However, if you look at the number of pages in the workbooks and divide it by the number of school days, then something has to give. The teacher is faced with the tradeoff of more understanding and mastery or more coverage. My son's fifth grade EM teacher opted for more understanding and failed to cover 35 percent of the course. She also held after-school sessions to fix mastery issues (7+8=?) from previous years. I think this is the better choice, but she just didn't get to a lot of needed material.
I went over the new sixth grade EM edition with my son last summer and it had topics that he would get this year in 7th grade pre-algebra. Many of the topics were perfectly fine, but curriculum evaluators don't realize that the only way to cover all of the material is on an extremely superficial basis.
By comparison, my son's current Glencoe Pre-Algebra textbook is a breath of fresh air. Topics are carefully developed and plenty of examples are given. The teacher teaches. My son gets homework assignments that can have 30 - 50 problems to do. Mastery is expected right then. The teacher doesn't collect the homework, but that's a separate issue.
I think many K-6 educators get into teaching because they like kids and want to be nurturing and caring. This can be at odds with setting high and specific expectations of knowledge and skills. In their perfect world, they want happy kids of all ability levels who are independent learners; no stress natural learning.
All I can say is that there is a lot that is unnatural about my son's learning. The school gets to live in La La Land, but parents have to make sure that learning gets done. I've mentioned before that our K-8 schools love the idea the they are a pump rather than a filter. They just never see the HUGE filter (when it's too late) when the kids hit high school.
Thank you for sharing your insight!
I think that all of us would agree that the "pump not a filter" idea is really at the heart of our concerns.
I've heard it from both sides for years...it's incredible how words can be twisted to mean absolutely nothing! (Yes, I learned that in ed school :D)
If a program does not prepare students for success at the next level, it is useless in my opinion.
The problem with EM is that many students aren't even prepared to enter the filter...they may have been pumped, alright, but to a different location!
Open up EM anywhere and you will see proper math problems. However, it's all in a jumble.
This is the essence of the middle school model and "interdisciplinarity," aka "integrated curriculum."
Everything is a jumble; no analytic categories are maintained. Coherence, sequential treatment, and depth disappear.
Before you get overly focused on the 'program', (EM or CMP or investigations or whatever) be sure you understand what/who is driving the publishers to this paradigm. In my state, Massachusetts, the spiral is built into the state standards. It's also intertwined with the ed schools.
I'm not sure what came first in this knot, ed schools, standards, or books. I just know it's a knot and not easily undone.
Paul, Your statements are SO TRUE!!!
We have the same situation in Missouri.
The University of Missouri Columbia Mathematics Department wrote a letter
http://www.math.missouri.edu/~jan/MOmath/
to the Department of Elementary and Secondary Education (DESE) and the Missouri Department of Higher Education (MDHE) with their concerns (and an urgent plea!)
Have any of the "powers that be" read the recommendations in this 2006 report which identifies four state policy dimensions for improving college readiness opportunities for all high school students:
http://www.stanford.edu/group/bridgeproject/Claim%20Comm%20Grnd%20Rpt%20FINAL%2003%2029%2006.pdf
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