Thursday, December 4, 2003; Page PG04
Maryland has no specific certification for middle school teachers. A middle school principal may assign any teacher with a general K-8 certification to teach math, English, science and social studies.
But here comes the No Child Left Behind Act (NCLB), the 2001 national education law, to the attempted rescue. One of its many requirements is that states must set standards for "highly qualified" middle school teachers. So, this year, the Maryland State Board of Education has ruled that those middle school math teachers who have a general K-8 certification will need to earn an "endorsement" in middle school math in order to be deemed "highly qualified."
How to set standards which will not disqualify almost any math teacher? It is the absurdly low-level Praxis II Middle School Math Content Exam to the rescue of the Maryland State Department of Education, even though it is counterproductive for the students. Not only will highly qualified teachers pass this exam, but so will minimally qualified ones and even teachers whose knowledge of arithmetic is lower than that of a well-trained sixth-grade student. The Praxis II set of exams is used by many states as criteria for the certification of teachers.
Maryland appears to be setting the bar for middle school math teachers below the bar of Maryland's pretend algebra test (pretentiously named the Maryland High School Assessment on Functions, Algebra, Data Analysis and Probability test), which is largely a grade 6-level Math test. It is aimed at weak and poorly trained grade 9 students. This is because Maryland teachers may use the Praxis II Middle School Math Content Exam to earn the distinction of "highly qualified."
This year, only about half the students passed the Maryland algebra test. This includes only about two out of three white students. Absurd! It includes only about three of 10 minority students. Doubly absurd! Our children deserve better, and they deserve more effective instruction. All (not just some) middle school math teachers need to be truly qualified to teach the arithmetic and other middle school math that is the bulk of the Maryland algebra test.
I read all 12 multiple-choice items and the two "constructed response" items of the Praxis II Middle School math content exam (for teachers), available on the Web at ftp://ftp.ets.org/pub/tandl/0069.pdf). A well-trained grade 6 student should be able to do at least 11 of the 12 sample multiple-choice questions and the first of the two sample "constructed response" items. This would result in a score of 75 percent, likely to be a passing score in most states.
The 12 sample multiple-choice items for Praxis II "middle school math" content exam for teachers contains no item that requires a calculation as sophisticated as adding 1/3 + 2/5. A well-trained grade 6 student should be able to do arithmetic problems that are considerably more difficult than the 12 Praxis II "middle school math" content sample multiple-choice questions.
Two of the sample multiple-choice questions on the Praxis II Math content exam are simple ratio questions. None of the sample questions is an "advanced" ratio question such as the one below.
Praxis II Sample Question 7, a simple ratio problem: Suppose that 40 percent (by weight) of a county's trash is paper and 8 percent is plastic. If approximately 60 tons of the trash consists of paper, approximately how many tons of the trash consists of plastics?
Solution: The ratio of paper to plastic is 40 to 8, or 5 to 1. So the tonnage of plastics is one-fifth that of paper, or one-fifth of 60 tons: 12 tons.
The teachers may use a hand calculator when doing these divisions (40/8 and 60/5).
Problem 1, an advanced ratio problem: Suppose that 40 percent (by weight) of a county's trash is paper and 8 percent is plastic. If approximately 60 tons of the trash consists of paper and plastic, approximately how many tons of the trash consists of plastics?
Now one has to stop a minute to think about that problem, in contrast with the straightforward ratio calculation needed for the Praxis II Sample Question 7. (To some, there is little difference between these two ratio problems. But to middle school math teachers, the extra thought required of students is considered significant. Most likely, the Praxis II test writers purposely chose the simpler type of problem.) Solution: Together, paper and plastic compose 40 percent + 8 percent = 48 percent of a county's trash.
The ratio of paper and plastic to plastic is 48 to 8, or 6 to 1.
So the tonnage of plastics is one-sixth that of paper and plastic, or 60 to 6: 10 tons.
Item 15 on the sample Maryland High School Assessment on Functions, Algebra, Data Analysis and Probability, the Maryland algebra test, is an advanced ratio problem (on the Web at www.mdk12.org/mspp/high_school/look_like/algebra/v15.html). When Item 15 was field-tested in 2000, fewer than one third of the students had the correct answer, which is not much better than random guessing. Absurd!
Middle school teachers who are fluent in advanced ratio problems, such as Problem 1, will be able to provide useful instruction to their students, who will then be able to do Item 15 on the sample Maryland algebra test. This will not be true for teachers who can merely do simple ratio problems, such as Questions 7 and 10 from the sample Praxis II test.
Our children deserve better.
Jerome Dancis is an associate professor of mathematics at University of Maryland at College Park. His Web site is www.math.umd.edu/~jnd
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