Instruction in Arithmetic Devastated Under Superintendent Grasmick
By Jerome Dancis, Associate Professor Emeritus, Math Dept., Univ. of MD
Math Education Website: www.math.umd.edu\~jnd
I handed the young cashier five quarters; she wanted to enter the amount into the cash register, but could not calculate their total worth. So she had to ask a coworker what is the total; which is: $1.25. This simple type of Arithmetic problem is barely taught. Under the guidance of Dr. Nancy Grasmick, retiring Maryland’s (MD) State Superintendent of schools (since 1991), learning Arithmetic is no longer a requirement for high school graduation.
Many Maryland (MD) students are learning Arithmetic poorly. This is a natural consequence of the marginalization of Arithmetic, which occurred in two waves of “reform” implemented under Grasmick. The first was instituting the MD state MSPAP tests of the 1990s: As Robert C. Embry, Jr, former head of the Maryland State Board of Education, wrote (December 1996): "... one [MSPAP] question had students manipulating a dozen small pieces of paper to figure out the area of a room--seemingly to avoid making a simple calculation [of length times width].”
The second wave of “reform” was the Maryland Voluntary Math Curriculum (which was not voluntary) and the Maryland High School Assessments [MD HSA].
Class time previously allocated to Arithmetic is now allocated to low level Algebra, Geometry, Measurement, probability, Data analysis and problem solving. (Example: measure the heights of the children in the class; find average, median and mode, then make a bar graph; repeat in many grades!) With so many topics to teach each year (in K-8), there is no way to have a coherent curriculum. Soon after a topic is started, it is time to move on to the next topic; this occurs before the learning is moved into long-term memory. This makes it easy for students to forget a Math topic within a month. Students are not remembering Arithmetic because far too little time is left for Arithmetic.
With weak knowledge of Arithmetic, students are at-risk in real Algebra classes.
Before Grasmick, it was common for high school Algebra I to be the Algebra I expected by colleges. No more! It has been replaced by the syllabus of the MD HSA on Functions, Algebra, Probability and Data Analysis. This so-called “HSA on Algebra” is mostly Grade 6 level background for Algebra. Basic, simple Algebra, like 2x + 3x = 5x, is omitted.
This has resulted in (when “Minimally Ready for College Math” is defined as knowing Arithmetic and real (not HSA) Algebra I.):
My analysis was based on data by the Maryland Higher Education Commission (MHEC) Student Outcome and Achievement Report (SOAR).
Caveat. This particular data counted only students who graduated from Maryland (MD) high schools in 1998 and 2006, then entered a college in Maryland the same year. (Not counted were graduates who went to colleges outside MD or did not go to college the same year.)
Under Grasmick’s guidance, MD has agreed to implement a third wave of reform, which will use the Common Core standards. In Math, this third wave of reform will bring back some serious instruction in Arithmetic – but will not go so far as to expect students to learn that 50% off means half price. Still this third wave of math reform will cancel much of the first two waves.
So it’s goodbye to Superintendent Grasmick and welcome back Arithmetic (hopefully).
Notes: Opinion of H.S. algebra teacher.:
"State and county math standards hurt student performance" in Silver Chips, (Dec. 18, 2003), the student newspaper of Blair High School (Silver Spring, MD) Two quotes: "MCPS [Montgomery County Public Schools] mandated changes to the Algebra I curriculum to align the course with the tested material [MD's HSA 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."
Re. Table: See my [Univ. of Maryland] Faculty Voice article,
“More Remedial Math [at MD Colleges]? [YES]” at
scroll down to bottom of Page 1;
more in "Pretend K-12 Mathematics Curriculum Produces Freshmen Who Know Less Algebra", My talk at a Mathematics Department Colloquium at Morgan State University. On the web at www.math.umd.edu/~jnd/Pretend_Math.pdf