Re: Algebra (was Re: Half Grades?)

[Victor Steinbok <Victor.Steinbok@VERIZON.NET>]

At 8:22 AM -0700 9/3/01, Kathie Humes wrote:
> Folks,
>
> I don't think we have figured out how to meet the needs of high
> school math students.  In general, there is one way only, so highly
> successful freshmen are in geometry class with seniors struggling to
> pass the class and graduate.  If kids fail algebra or geometry, they
> simply have the option of doing it all over again the exact same
> way.  Regardless of reading, language or learning differences, all
> kids are run through the same gristmill.
>
> The efforts to design alternatives, it seems to me, are well
> intentioned, if awkward in implementation.  I think the notion is
> that some kids simply need more time to master the material -- in
> theory, a good idea.  In our high schools, there are more parental
> complaints about math than any other subject.  Math instruction
> seems more resistant to change and innovation than other areas.  And
> until math is made relevant, there will not be public buy-in to
> "algebra for all."
>
> Kathie Humes
>
> (and for George:  I am a parent activist for education reform)

There have been several alternatives that began taking root since
1989 Standards came out. However, they have raised ire of certain
elements, particularly in California. George Cunningham can tell you
more about them and why they are so adamantly insisting on the
"standard" sequence that does not exist anywhere else in the world.

It is not the case that "integrated" mathematics is taught in the
rest of the world, however, it is not taught in the differentiated
and sequential manner it is presented here. My own experience is with
an undifferentiated sequence up to grade 5 (out of 10), followed by
algebra and plane geometry in 6-8, and analysis (that is precalc and
calc in our language) and solid geometry for grades 9-10. That is,
the algebra and geometry courses run IN PARALLEL and the curriculum
is closely correlated between these two courses, as well as chemistry
and physics courses in grades 7-10. [Note: since 1984 the school
system has been changed to include mandatory kindergarten, which was
re-labeled grade 1, so all the other grades shifted one up. Students
still graduate between 17 and 18 years old.]

Other countries do it differently, but, for the most part, the
courses are either integrated or closely correlated--topics in one
are introduced to correspond to prerequisite or follow-up topics in
another. For example, if coordinate geometry is taught in an algebra
class, vectors are being taught in geometry AT THE SAME TIME, not two
years later. The content is spread out over several years, allowing
better review and support for individual strands. One does not have
to jump from trying to figure out slope-intercept formulae one year,
to regurgitating pre-fab proofs the next, as in the "standard"
sequence, or to go from one topic to an unrelated one in a matter of
one or two weeks as is the case in some integrated courses. (IMP and
ARISE, for example, do a better job, but they are not free from
problems.)

Complaints about the sequential nature of American math education
have been brought since the formal educational system had taken hold,
i.e., last quarter of the nineteenth century. The first attempt to
revise the curriculum was interrupted by WWI, the second by the Great
Depression. After that, the focus shifted to outcome-based reforms,
largely because of the post-sputnik science scare. The reforms have
been effective in increasing the number of scientists/engineers,
despite the New Math fiasco, but were largely unsuccessful in
improving the education of the rest of the population.

There is, however, a caveat. When we assume that American secondary
math education fails our students, we do not compare apples to
apples. Secondary math education fails MOST students in every
country. Some do relatively better, some worse, but NOT ONE COUNTRY
educates ALL are nearly all student to similarly high levels in
mathematics. US may do worse than some, but there are other problems
in American schools (weapons and discipline, for example) that should
take priority in being addressed.

I believe American math education can and should be improved and I
changed my career path to join in the improvement effort. However,
this is not the cause for general alarm some right-wingers make it
out to be. The depth of the problem is not the same from school to
school, and even from teacher to teacher. Let's not assume that this
is a universal disaster and everything must be scrapped. The main
goal should be progress, not replacement.

"MATH" is not resistant to innovation--no more so than other school
disciplines. However, the content of school mathematics has not
changed significantly in two hundred years. In other subjects,
revisions are necessary nearly annually. There isn't as much ideology
attached to mathematics education as there is, for example, to
history and language teaching, but, certain people are trying to make
the math education debate ideological. If we can shift it back from
an ideological realm to psychological, we would all be better off.

       VS-)

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