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
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
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
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.