MD’s Pretend Algebra Exam Versus Students Learning Simple Math
Comments by Dr. Jerome Dancis (associate professor of mathematics, UMCP) jnd@math.umd.edu Presented at the MD State Board of Education meeting, Jan. 27, 2004
State School Superintendent Nancy Grasmick was quoted (in the Calvert Recorder 1/21/04): "I am unhappy when I hear an employer who has to interview 50 students to get three who can do simple math or fill out an application [properly]," The high number of Maryland graduates who need to take remedial classes the first year of college is also disturbing, she said.
I strongly agree. Having MD graduates fluent in Arithmetic and not needing to take remedial Algebra in college should be made the first two math priorities of Maryland State Department of Education (MSDE). Unfortunately, the main math priority, of MSDE, is expressed by its pretend Algebra Exam.
In fact, MSDE’s math curriculum for Grades 1-8 and the MD pretend Algebra Exam are going to reduce the number of students, who can do simple Arithmetic and will increase the already high number of MD graduates who will need to take remedial Algebra classes in college.
A major reason for this incongruity is that students get to use their trusty graphing calculators on MD’s pretend Algebra Exam (See Note #1 below). Not only do graphing calculators multiply and divide, they also graph functions and provide spread sheets. Given data, the graphing calculator will easily provide a graph of a so-called “straight line of best fit”, even when it is inappropriate to use a straight line fit (See Note #2 below). In fact, graphing calculators do graph a function and a “line of best fit” and provide a spread sheet in constructed response answers to items on the MD sample Algebra Exam, which appear on MSDE’s website.
Calculators are the reason that MD state Board of Education member, Dr. John Wisthoff expressed concern, at the December Board meeting, that MD’s Algebra Exam did not require students to do calculations by hand.
"Do not worry about the students understanding algebra -- Just be sure they can put anything on their Hand calculators" -- this is how a 1999 staff development session for Algebra I teachers by Montgomery county Public Schools (MCPS) was summarized to me. This is a good strategy for maximizing the number of students who will pass MD’s pretend Algebra Exam, but it is also an effective strategy for increasing the number of students who can not do simple Arithmetic and those who will need to take remedial Algebra in college.
Yes, it is important to teach students how to do math with graphing calculators. But they should also be required to learn how to multiply 23 x 37 and to solve 4x = 2x + 10 the old fashioned way, without the aid of a graphing calculator. But neither multiplying 23 x 37 or solving 4x = 2x + 10 (by hand) is included in the syllabus for MD’s pretend Algebra Test.
MCPS aligned its K-8 Math and Algebra I curriculum with the state’s Math curriculum, and so MCPS now allocates too much time in Grades 1-8 to superficial geometry and superficial data analysis and pretend Algebra. There has been a massive reduction in class time allocated to Arithmetic. A teacher complained to me that she is now getting students in her middle school Algebra classes who have difficulty with 5 + 7; this occurred in a upper middle class school in Montgomery County. This will produce more students who cannot do simple Arithmetic, the crucial background for learning real Algebra.
Since MD students are no longer required to know how to multiply 23 x 37 and since the trusty graphing calculators do the bulk of the Algebra and data analysis on MD’s pretend Algebra Exam, it is debatable whether making MD’s pretend Algebra and pretentious Data Analysis Exam a graduation requirement, is increasing or decreasing the math standard for graduation. (It is the reading that causes the most difficulty on MD’s pretend Algebra Exam, where the reading comprehension level is higher than the math level; I discussed this in my September 8, 2002 Washington Post article, on the web at http://www.washingtonpost.com/wp-dyn/articles/A49346-2002Sep7.html)
Deputy state superintendent Gary Heath, did say, "We would be the first to tell you [MD’s Algebra Exam] doesn't have a lot of algebra, nor was it intended to." (Washington Post, Aug16, 2002)
But MD’s pretend Algebra Exam is also determining the syllabi for Algebra I and K-8 math. The extent that this is mucking-up Algebra II and Pre-calculus courses is described in the attached article from Silver Chips (12/18/2003), the student newspaper of Blair High School, which includes (on the web at http://silverchips.mbhs.edu/inside.php?sid=2639):
“ … MCPS mandated changes to the Algebra I curriculum to align the course with the tested material [MD’s Algebra Exam]. "We don't think the material is what they need to know to be successful [in Algebra II and Precalculus]," said Blair H.S. 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 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.”
This will also increase the already high number of MD graduates who need to take remedial Algebra classes in college.
Note #1. In the1990s, students were not fluent in the use of calculators, then they could make only limited use of them. This has changed. Karin Chenoweth has observed that her children have been well trained in school in the use of their trusty graphing calculators; this enabled her to quickly realize that the use of graphing calculators results in “Pretend” Testing, [which is] a Poor Imitation of Preparing Students [in Algebra](hence the title of her article) (http://www.washingtonpost.com/ac2/wp-dyn/A28031-2003Dec24?language=printer)
Note #2. UMCP Physics Professor, Tom Cohen's, observations, of his child (a student in Montgomery County) doing her "Algebra" homework on "best fit" are below. His observations are consistent with Best Response #2 to MD Algebra sample test Item #17, (on the state website).
"However, the way data analysis is taught and tested troubles me. In particular, the use of linear regressions (done by a calculator) to fit lines is not appropriate for algebra one students, in my view. The students are NOT taught what a "best fit" line means mathematically, how to judge whether the model fits the data well (i.e. chi square or other statistical measure) nor even given any clear way to understand whether the data ought to fit a line. If you ask the calculator for a line which will fit points which lie on a parabola the calculator will spit back a line and the students will dutifully write it down. The issues are subtle and Algebra I students are not prepared to deal with them. Thus, the students are being miseducated in data analysis and statistics.
In my view this treatment
is worse than useless, it is positively destructive. Students are told in essence to plug things in which they
don't understand and then to trust the answers. This is diametrically opposed to the critical reasoning
about data analysis that we need to instill in students.”
Note #3. A
big No-No in real Algebra is never
using the same variable to mean two different things in the same problem.
This occurred in the statement of Item #32 on the sample MD Algebra
test. I informed MSDE of this
error on Oct. 30, 2001. The following
was added to the webpage for this item:
"The variable y is used to represent both the income for selling x tubes of toothpaste and the production cost for x tubes of toothpaste. This is an error in the use of a variable."
A similar error in the use
of a variable occurs in Item #17 in
the 2002 version of the MD Algebra test.