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As Long as We Remember...

March 18, 2008

Understanding the Problem

Nick Diaz

“Make sure you take Algebra II!” So goes the typical admonishment by teachers, counselors, parents, directed at middle-school students in the act of planning their future high school program.


Many students do take Algebra II in high school, and find themselves facing a brick wall – not succeeding, consistently doing poorly on tests and quizzes, and simply not understanding the nature and purpose of mathematics in general, and algebra in particular.


I’m going out on a limb and flatly state that the main reason students are either not signing up for Algebra II or subsequent courses is simple: They barely got through Algebra I in 7th, 8th, or 9th grade.


Maryland’s High School Assessments (HSA) basically demonstrates this assertion. For many years I’ve observed many middle-school students having difficulties with the abstractions required in the learning of even the simplest algebraic concepts.


Why the difficulty? It goes to the poor quality of schools’ math curriculum and, more importantly, teaching methods in the lower grades.


Elementary math curriculum covers entirely too many topics, and does so much too quickly. At a given time, some children in a class may well have difficulty with division, then the course plan runs out of time and the class must then move on to, say, fractions.


Many parents work hard to compensate for the deficiencies in the current curriculum and teaching methods. They buy textbooks, software and flashcards, send their kids to private math tutors, and spend many hours remediating at home. I contend that the achievement gap that is evident in Algebra I HSA scores reflects the chasm between students whose parents have the means and/or ability to make up for the deficiencies in Maryland counties’ math curriculum.


Therefore, telling low-achieving high school students to take Algebra II is like closing the barn door after the cow has left. These kids are already damaged mathematically, long before they first walk through the high school doors.


I contend that our elementary school mathematics curriculum lacks focus and depth. Our math books and materials lack clarity, consistency, and continuity. Finally, our teachers lack the knowledge and skill to overcome the deficiencies in the curriculum and the materials they are given.


So, school administrators, in their infinite lack of wisdom, compound the problem by focusing their reform efforts on accelerating elementary and middle school students through its dizzying curriculum, rather than on ensuring that every child masters fundamental mathematics.


Many Frederick County Public School parents have been baffled by teachers’ messages, imploring them to make sure their children master the multiplication tables.


“Parents aren’t expected to teach multiplication!” So goes the argument by school educationists. What happens seems to be that some teachers become so overwhelmed with the high number of topics they’re expected to teach, that they understandably try to offload what seems to them to be a manageable task to the parents. I, for one, can’t blame them.


The old-style arithmetic is not the only math kids should be learning in elementary school. The patterns are relationships among numbers, established by a solid grounding in arithmetic, form a foundation for algebra and all higher mathematics. Imagine trying to solve equations without being able to divide.


Having large numbers of kids who can’t pass the equivalent of the old Maryland Functional Mathematics Test is a real problem at the high school level for both students and their teachers. The students keep hearing from people like myself, that they need to take and master math at least up through Algebra II – and preferably through calculus – which must be very frustrating to them when they still have trouble with the four basic operations.


High school math teachers are not prepared to teach their students at such a basic level. They aren’t trained to teach arithmetic, and they often resent being expected to do the job of elementary teachers, while still being held responsible for a math curriculum with a high level of expectations.


Elementary – and some middle school teachers – for their part, often don’t have enough knowledge to teach the math curriculum. This is usually not their fault, however.


To become certified as teachers, most of them were required to take a small number of watered-down math classes, often in the form of “math-for-teachers” courses, rather than real college math. This means they often lack a profound understanding of fundamental mathematics.


In recent years I participated in a teachers’ summer workshop on elementary mathematics curriculum writing. One of the tasks given the participants consisted in having us model simple algorithms such as “8 {divide} ½”. Very few of the teachers correctly modeled this little operations; most of them made up stories that should have been represented by “8 {times} ½. Instead of the correct answer of 16, most came up with the attractively incorrect answer of 4.


While many Maryland counties attempt to provide math training to elementary teachers, much more is needed. Elementary teachers are masters of their craft. They don’t need courses that emphasize teaching methods; they invented teaching methods.


As a long-time middle school math teacher, I’ve always had the utmost admiration for elementary teachers as artists and technicians. We need a coherent curriculum statewide, with clear materials and highly expert teachers who understand much more math than they’re expected to teach, and who are given time to deepen their understanding.


In the meantime, however, parents should continue to make and use those multiplication flash cards every day.

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