COMMENTS ON STATEMENT ON
MATHEMATICS PREPAREDNESS
By Jerome Dancis
College math professors are distressed by the low level of
understanding of Algebra by masses of students as they enter college; this even includes many students, who
have taken calculus in high school.
Yes, students have to complete several years of Algebra, before being
admitted to a high school calculus class, but still many are not proficient in
Algebra. Absurd! Of course, calculus students, who score
4 or 5 on the AP
Calculus exam are usually well trained and they get to skip the first year of
calculus in college.
The bulk of the students in the calculus courses on my
campus have taken calculus in high school as have perhaps one in three students
in the Pre-calculus classes. Yes,
it is absurd, that a student, who has taken calculus in high school, will need
to repeat Pre-calculus. This
concerns college math faculty.
The many students, who have taken calculus in high school,
but are not proficient in Algebra, are AT-RISK, when they retake calculus or
Pre-calculus in college.
So, the MD/DC/VA SECTION OF THE MAA has broken tradition by
issuing its first statement ever on high school math education. It is "ON MATHEMATICS
PREPAREDNES" of students as they enter college. The statement may be accessed from the * 1/22/2005 entry at http://www.morgan.edu/maa/home.html .
( The MAA is the Mathematical
Association of America, the professional association, for college math
instruction, of college and community college professors of mathematics)
This
statement ends with:
"In
conclusion, the best mathematics preparation for college is … a strong
background in algebra and geometry, and [having] an ability to solve multi-step
'word problems' … ."
Note that calculus, statistics and probability are NOT on this list.
In
contrast, statistics and probability are major strands of both Maryland's
mandated state Math curriculum thru Grade 9 and the NCTM PSSM. But, allocating sizable amounts of time
in K-8, to statistics and probability, greatly reduces the time available for
mastery of arithmetic, the foundation of Algebra.
Even Assistant MD State Superintendent for Testing, Gary
Heath, said, "We would be the first to tell you it doesn't have a lot of algebra,
nor was [the MD Algebra exam] intended
to." (Washington Post
Aug16, 2002)
University of Maryland, Baltimore County President Freeman
A. Hrabowski III expressed concern,at a MD State Board of Education meeting,
that his university and many others are forced to give remedial help to
students who should have been prepared in high school.
Also that U.S. schools, including those in Maryland, aren't
expecting enough. Algebra standards are especially weak. Also MD state standards are woefully
inadequate. (Baltimore Sun, March
31, 2004)
An
important sentence, in the MAA statement, is:
"However,
we should never place a higher value on exposure to calculus … than on
mastery of Algebra I and II and Geometry." This is a polite way of saying
greatly reduce the numbers of students taking calculus in high school to those
who have actually mastered Algebra.
To me,
the key recommendation is #2, which I paraphrase as:
Students should be able to
perform basic calculations, both numeric and symbolic, without the assistance
of calculators or computers, …
. "Basic symbolic
calculations" refers to calculations with symbols, that is "x's", like * solving 2x = 8, by
dividing by 2, or * knowing x + 2x = 3x or * adding fractions.
These and all other symbolic calculations are EXCLUDED from Maryland's
mandated state pretend Algebra I syllabus. As the head of math instruction for the state, Donna
Watts, said "There is a limited population who can do math symbolically,
the way mathematicians do. … "
(Washington Post, December 25, 2003; Page GZ06
http://www.washingtonpost.com/ac2/wp-dyn/A28031-2003Dec24?language=printer)
The phrase, " without the
assistance of calculators " is an indirect way of decrying the overuse of
calculators as a substitute for students acquiring real Algebra skills. Donna Watts, disagrees. "The
technology is there. It's not going to go away." ((Washington Post, December 25, 2003; Page GZ06
http://www.washingtonpost.com/ac2/wp-dyn/A28031-2003Dec24?language=printer)
Maryland's HSA
pretend Algebra exam allows and effectively mandates this overuse of calculators.
Recommendation #1 ends with: "[M]athematics programs should avoid pushing students
ahead until they have mastered the appropriate material, … ." This should mean, students
should master arithmetic before studying Algebra and should master Algebra
before Calculus. This is in
contrast to the Maryland's state mandated pretend Algebra I syllabus, which
makes "MD Algebra I" altruistically accessible to students, who have
not learned Arithmetic.
Therefore, as schools align their Algebra I course with
Maryland's state mandated pretend Algebra syllabus, the problems, mentioned
above, will get worse and the numbers of At Risk students in college math
courses are likely to increase.
The following quotes are relevant:
Silver Chips, the student
newspaper of Blair High school, Montgomery county, MD 2/18/2003
by Elliott Wolf,
Online Staff Writer, Technical Staff
http://silverchips.mbhs.edu/inside.php?sid=2639
Changes in the Algebra I curriculum brought about by the new
Maryland High School Assessment Tests (HSAs) and a push by MCPS to have more
middle school students take algebra have caused many students to be seriously
unprepared for higher level math, according to numerous Blair teachers and
administrators.
…
Shortly before the introduction of the HSA, MCPS mandated
changes to the Algebra I curriculum to align the course with the tested
material. … "We don't think the material is what they need to know
to be successful," said Blair algebra lead teacher Maria Costello.
Changes in the curriculum are cited as a main cause for
students' deficiencies in basic algebra, which are manifesting themselves in
higher level math courses that require an understanding of concepts [previous]
taught in Algebra I. "Our Algebra II students are worse than ever. Our
Pre-Calculus students are worse than ever. It's falling apart as we go up the
ladder," said Costello.