I would like to make
a few comments--- helpful ones I hope--- on your LSJ article.
I am a MSU Math
professor. While I am a research mathematician, I have been teaching courses
in Math Education, and have been closely following current developments
in Math education. Evaluating Math programs is a tricky business in the
current environment. There are major battles going on, and reports from
even trusted sources are usually tinged with the politics of these battles.
The AAAS report is
a case in point. It was not written by scientists. Rather, the AAAS has
lent its imprimatur, under the name `Project 2061' , to a group of EDUCATORS
who are not trained in mathematics or science. These educators have a specific
political agenda. They would like to see all education done in group settings
with the `discovery method' and with no instruction from the teacher. They
would like to see mathematics classes with long writing assignments,
no right and wrong answers, no practice problems, complete reliance on
calculators, and a minimization of algebra.
Accordingly, they
designed a set of criteria focusing not on WHAT and HOW mathematics is
covered by the program, but rather on the extent to which it conforms to
the above agenda. Take a close look at the Project 2061 website: "http://project2061.aaas.org/newsinfo/press/attach_a.pdf"
Your chart is Attachment A. Note that it is titled `quality of instruction'.
It is a ranking of the INSTRUCTIONAL PRACTICES used by the math program,
not a rankingof the overall quality of the program. Attachment B spells
out the criteria. The `Benchmarks' (made up by the 2061 people) describe
a dumbed-down middle school program. In other programs and in other countries
most of these topics are covered in grades 4-5. Some ("shapes can match
exactly or have the same shape in different sizes'') are kindergarten level,
and not even correct english! For each of these `benchmarks' the 2061 group
applied the `criteria of quality of instructional guidance' listed at the
bottom of Attachment B. Here you see the political agenda I described above.
Many of these phrases are educational jargon that require experience to
decode. For example, the three listed under Category VI all mean ``no tests,
quizzes or worksheets'' and the two in Category III mean ``group work with
manipulatives''. The last one, `supporting all students' means `dumbed
down'.
None of these criteria
assess what specific mathematics is covered. Thus the Connected Mathematics
Project (CMP) can be the highest rated, even though the topics it covers
in grade 8 are covered in grade 7 in competing programs, and covered in
grade 6 in Japan, Korean, China, Singapore and Russia.
All that one should
conclude from the Project 2061 report is that their top-rated programs
are politically correct. I have looked over the CMP program carefully.
It definitely is politically correct.
What criteria should
be used? A good math program has several stages. Grades K-4 should throughly
cover the basics: addition, subtraction, multiplication, division,
fractions, and a little geometry. Grades 5--7 should be preparation for
the real math that starts with a solid grade 8 algebra course focusing
on quadratic equations and polynomials, and a grade 9 course in Euclidean
geometry, with proofs. (That is the plan followed by most countries, and
the one recommended by the U.S. Department of Education). Virtually all
students find these two courses very hard; many find them TOO hard and
drop out of math at that point. But these courses are not intrinsically
difficult. In other countries ALL students take them as a matter of routine
and, as the TIMSS study shows, master the material. The problem lies in
the US grade 5--7 programs. There our children spend their time going over
more arithmetic, instead of taking the first steps toward real algebra
and geometry with proofs.
This last sentence
exactly describes the problem with CMP and similar programs. The Project
2061 report does not reveal this fundamental deficiency because its criteria
do not include real algebra and geometry
with proofs.
For different ratings,
ones based on the actual mathematics covered and taught, see the website
"http://www.mathematicallycorrect.com/"
Click on the 5th line called ``Mathematics Program Reviews for Grades 2,
5, and 7 ''. ('Mathematically Correct' is an organization of parents and
scientists who are working to restore serious mathematics to schools. A
study of their website is essential for understanding the battle lines
in the current debate over mathematics education).
I have young children
in the Okemos schools. I am VERY concerned about the mathematics programs.
You should be very concerned also. If your daughter is taking 8th grade
CMP (rather than Honors Algebra I) then she is not on track to take calculus
in high school. Calculus is the basic entry point to majoring in science,
engineering and medicine. In Korea all students, including the children
of rice farmers, take calculus as juniors in high school. You should be
asking Okemos officials why it is that your daughter, who is apparently
a top student in a top school system, is two years behind the children
of Korean rice farmers.
Sincerely,
Tom Parker