Struggling in Algebra

The Washington Post Jan 16, 2006 Page B01

Lagging Freshmen Reassigned Before Test;
Pr. George's Creates 2-Year Algebra Class:
Author(s): Nick Anderson

At least 2,500 ninth-graders in Prince George's County will abruptly
move this week from a standard one-year algebra course into a two-year
program, shielding the struggling students from a state graduation test
this spring that officials said they were likely to fail.

Bob LeChevalier...

Fairfax County VA has had a 2-year version of algebra for a few years
pretty much for the same purpose, although the kids sign up for it at
the beginning of the year, rather than being switched mid-year. The
result is that a significantly higher percentage of the kids pass the
state test.

hrubin...

The important ideas of algebra can be taught MUCH more
quickly, if one tries to teach the understanding. Those
IDEAS belong in the primary grades; by the time they
approach high school, great damage has already been done.

Seveigny...

We have the same course in our district, called Fundamentals of Algebra.
Kids are slotted into the class based on their middle school math courses
and teacher recommendations. While its useful for kids with disabilities

hrubin...

The important parts of algebra do not in any way depend
on arithmetic prowess. In fact, I would not consider
teaching fractions without having algebraic understanding.

While its useful for kids with disabilities

it's really a dead end course since after a student finishes it, they really
aren't prepared to go on to Geometry. The course does help them pass the

hrubin...

Why is algebra needed for geometry? None of Euclid's students
knew algebra, as it had not yet been invented. Viete, the one
who is responsible for modern algebraic notation, deplored that
al-mukaballah and al-jabr were not in the category of the proofs
of Euclidean geometry.

toto...

Because the geometry course has *expanded* and includes much
more than Euclidean proof.

I know you think Euclidean proofs are not included in geometry in
high school, but my kids certainly had them. One of the things that
has been done is to connect algebra to geometry in ways that were
not done when I was in school. Also, in the schools my kids went
to, coordinate geometry was integrated throughout the course.

Btw, for anyone here interested in Euclid's Elements, I found this
website that applies modern technology to the theorems.

The course does help them pass the

toto...

I don't understand why a two year algebra course that covers
the same thing a one year algebra course covers, but at a
slower pace for kids who need more time to absorb the concepts
would not prepare them to go on to a geometry course. And

hrubin...

The present algebra courses rarely even discuss the concepts.
The concepts can be learned fairly easily, but not by teaching
computations first. I doubt that as many as 5% of the
elementary school teachers have any grasp of the important
mathematical concepts which should be taught to all in
elementary school, and which exceed what is now taught in
high school.

Teaching people how to compute solutions of standard problems
does not help develop concepts.

And

why shouldn't there be a two year geometry course then for these
kids (they would miss out on algbra II and trig, but some of the
topics of those courses might be covered in a two year geometry
class).

hrubin...

Get the computations of areas, etc., out of the geometry
course, and go back to the concepts. As for trigonometry,
it is at most one day of concepts, a week or so of
development, and the rest is all computation.

That does not mean that they should NOT be taught to compute.
But putting in a time schedule based on it is a major error.

high school exit exam but they don't do well on the state Algebra test
because the state test covers information that they haven't learned.

Bob LeChevalier...

Here, the two year course covers the exact same curriculum as the 1
year algebra course, leading to the same end-of-course state test.
Either is accepted as a prerequisite for geometry.

Seveigny...

Our course doesn't cover the exact same curriculum as the 1 year Algebra
test and doesnt't lead to meeting the prerequisites for Geometry.

hrubin...

If properly taught, there are no prerequisites for geometry.

According to the fantasy standards, kids should learn Algebra in 8th grade.
While some kids are developmentally ready to work with abstractions at that
age, many are not. Furthermore, many kids get lost early on and come to

hrubin...

I doubt that anyone is ready later who is not still ready by
then. Abstract ideas are understandable early. The process
of abstraction is not understandable without this, which the
schools and teachers do not comprehend and are continually
undermining.

Furthermore, many kids get lost early on and come to

middle school without a true understanding of basic math and are unprepared.

hrubin...

This cannot come from arithmetic. Algebraic notation is really
language of a type the linguists deny, and this is the most
important part.

The whole question of math really pushes my buttons. Math classes in
elementary, middle and high school are a mile long and an inch deep. We
haven't accepted the lessons of the TIMMS study from the 90's. We should
teach fewer concepts, teach them well and then move on without the six weeks
of remediation/review that are offered at the start of each year. We should

hrubin...

NO concepts are being taught properly. One CAN teach them
with great difficulty without variables, but computational
facility has nothing to do with it.

Bob LeChevalier...

I agree for the most part. But the problem is that without that
review, the kids forget the stuff. I personally think our lousy
international test scores in high school are because a substantial
portion of high schoolers aren't taking ANY math in their last year,
or if they are, they are taking a math course that focuses on geometry
or advanced algebra, and they've totally forgotten how to do
arithmetic because they simply don't care to know.

Seveigny...

Oh yes, the review is necessary. Our lousy international scores are due to
the fact that most students take the minimum two years of math and then walk
away while other countries demand more from their students. I agree as well
that most "forget" arithmetic because they don't see it as either necessary
or important.
~Cate

hrubin...

This is looking at it the wrong way. The educationists found
that many students did not remember all the details of previous
courses, and mistakenly concluded from this that those courses
could not be applied without review, and introduced the idea
that therefore review is necessary. Concepts are not forgotten,
while details are.

If the arithmetic, which is not particularly important as far
as the manipulations go, is taught conceptually, students would
know what to do given the tables, or calculators. This is FAR
more important than memorizing anything.

Gary Schnabl...

Obviously, IMO. But I wouldn't restrict to the final year, but all years for
a large majority. If that weren't so, then why are states jumping on the
bandwagon and finally mandating more than the little math that is prescribed
now?

hrubin...

Concepts are not easily forgotten; facts and routine methods
are., But it is facts and routine methods which are easy to
examine, and which are essentially all that is taught.

use a variety of techniques to teach math including manipulatives in
elementary school and imbedding math in vocational classes. Many students
see math as useless information, especially kids who aren't on a track to
college. This year a friend of mine renovated his house. Many of the
workers who worked on his house were from Mexico and had very little formal
education. Yet they were able to grade his property, install pavers which
required high school mathematical skills because it was necessary for the
job. I've heard kids who couldn't pass geometry in shop classes talk about
how a window couldn't be installed in a house because the angle was wrong.
One of the problems that I see in high school is that it is expected all
students will go to college. This is fantasy land. It is neither realistic
nor useful for our society to expect all students to go to college. We need
more vocational paths which will prepare students to go to trade schools.
Unfortunately, those classes are the first to go in lean times and receive
less support in good times. Good vocational classes are expensive. At my
high school, the teachers are using out dated technology because they
haven't got the new machines and materials needed to keep up. My mechanic,
who keeps my vehicles running smoothly, needs to be able to read well in
order to understand the manuals so he can service my car. My students don't
see that connection. Reading "Huck Finn" isn't going to prepare them to
read a manual and work on a car or a computer.
Sorry....Rant off.

For special ed kids, they sometimes do the same for geometry as well,
taking two years to cover what is normally a single year curriculum.

The highly unusual shift comes midway through the school year in one of
Washington's largest suburban school systems and in some respects runs
counter to a regional trend of pushing students to take higher-level
mathematics as early as possible.

One-fifth of the county's students who began high school in August in
the bench-mark course Algebra 1 will be affected by the changes. The
students had missed several classes in the first half of the year and
received low grades.

Starting Tuesday, those students will move into a retooled class called
Algebraic Concepts. That will give them a one-year reprieve before
facing the state test and a fresh shot at learning what they need to
know about computations, graphs and word problems with variables X and
Y.

The county's action shows how Maryland's decision to impose high-
stakes graduation tests at the end of core academic classes is
beginning to reverberate through public high schools. The requirement
kicks in for the Class of 2009, this year's ninth- graders.

Prince George's County, with about 133,300 students, is the state's
second-largest school system after Montgomery County, which has about
139,400.

Virginia also has an algebra graduation test; D.C. public schools do
not. Many area school systems are pushing students to finish Algebra 1
in middle school -- in eighth or even seventh grade. Experts say early
algebra proficiency lays the foundation for further math courses in
high school: geometry, advanced algebra, trigonometry and calculus.

Prince George's has also promoted an early-algebra track in recent
years. Now, however, the county is expanding its late- algebra track.

"We have to be honest with ourselves about this issue," said the
county's interim schools chief, Howard A. Burnett. "Ninth-graders
across the country and across this county are failing and have been
failing. It hasn't worked, the way we've been doing things. And so we
have to start doing things differently." Burnett sent letters this
month to parents of affected students.

At several Prince George's high schools, the percentage of students
shifted into the two-year algebra track appears substantial. Donald
Horrigan, principal of Parkdale High School in Riverdale, said 223 of
the school's 481 Algebra 1 students are moving into Algebraic Concepts
this week. That's 46 percent.

Horrigan lauded the decision to pull students back from an academic
precipice. But he said the onus remains on schools to raise student
achievement. "It's our obligation to teach them," he said, "not to
document their inadequacy."

For months, educators in Prince George's and elsewhere have worried
about Maryland's algebra/data analysis test, one of four in a sequence
called the High School Assessments. That test will begin to have
consequences this spring for ninth-grade algebra students. The other
assessments come after English, biology and government courses that
typically are taken in 10th grade or later. By 2009, the state will
require students to pass all four examinations or get at least a
minimum score on each and a combined passing score for all four to
receive a diploma.

Last spring, about 35,000 students statewide failed the algebra/ data
analysis test -- 46 percent of those who took it. The failure rate was
69 percent in Prince George's and even higher among the county's
ninth-graders.

Seeking to improve, Prince George's schools began linking some algebra
classes through interactive television this year to help inexperienced
teachers work with veterans at other campuses. The county also has
intensified its use of quarterly tests to identify lagging students.
And Burnett's staff closely tracked algebra grades given after the
first quarter in October and the second quarter in December.

There were far too many D's and failing grades (E's), Burnett found. He
called an emergency meeting of principals and other senior staff Dec.
22. They decided to act immediately, reorganizing algebra classes at 21
high schools. Students who missed 10 or more days of instruction and
failed both quarters or had a D in one and failed the other were
designated for reassignment. The result: 110 new Algebraic Concepts
classes countywide -- 90 minutes a day at a pace meant to help students
catch up. Burnett estimated that at least 2,500 students would be
shifted into the classes.

Many teachers and parents cheered the move.

Joseph Sutton, a ninth-grade algebra teacher at Charles H. Flowers High
School in Springdale, said too many students arrive at high school with
poor fundamentals. "These are kids that got pushed through or socially
promoted, and now they're really hurting," Sutton said. "They're just
not ready for a course like this."

Ed Hendel, president of the Parent-Teacher-Student Association at High
Point High School in Beltsville, said: "This is at least a step.
Somebody said, 'Oh, these kids are going to fail. What else are we
going to do?' So this is something, instead of just writing them off."

But school board member Abby L.W. Crowley (Greenbelt) cautioned that
the action will only postpone an academic reckoning. "I imagine that
there will be students who do what the school system recommends and
still fail the course or the test in grade 10," Crowley said. "What
about them?"

How did the students react? "Some were relieved because it was too
difficult in algebra," said Carey Pico, a High Point math teacher.
"Others were clasping their algebra books as I have never seen, in
hopes of having one more chance to prove their ability to succeed."