Math practices

By ERIC WALSTEIN BrookevilleSunday, March 1, 2009; Page C07 Washington Post

As a teacher in the Montgomery County Science, Mathematics, Computer Science Magnet program, I have the privilege of teaching some of the best young minds in the United States. But even as standardized test scores have risen and the county has claimed great strides in math instruction, our program has had to offer a week of remedial math classes during the summer for our entering ninth-graders.

This past summer, the teachers administered a test of concepts we thought the students should know coming out of algebra, geometry, and algebra II. I constructed the test, and the other teachers reviewed it. We grouped the students into four levels based on their magnet qualifications. We gave them one hour to complete the exam. We did not let them use calculators. It had 27 questions and yielded eye-opening results.

I was assigned to the top group, which averaged only 15 questions right. The other groups scored commensurately lower, some as few as three or four questions right. Students found many of the ideas of algebra and geometry foreign, reporting that many core ideas had never been taught. This process of giving summer math help has been going on for five years now, and the knowledge trend has been down each year. This is a direct consequence of policy decisions of the Montgomery County Board of Education to eliminate course objectives, to push students to take algebra earlier -- often before they are ready -- and to rely heavily on calculators.

Cumulatively, these decisions leave students in an untenable position. They lack the rich math background to fully understand their current work. So, to get their work done, they have no option but to memorize the current work and punch unfamiliar buttons on a calculator. This technique masks their lack of connection between current tasks and previous concepts they supposedly know.

Calculators used incorrectly enable children to "solve" problems they don't actually understand. They not only hide the intellectual connections between ideas that mathematicians seek to have students understand, but they also impair math strategy, long a staple of math curriculum design. Used correctly, calculators can be an important tool. Used incorrectly, they subjugate mathematical progress and reasoning to a list of questions with a corresponding list of answers.
A Montgomery school official once told me that calculators are important because they give more students "access to math." That's wrong. They give students access to answers disconnected from math concepts. Many of my current students complain that curriculum acceleration made them move too quickly without proper understanding. Take the calculators away, as we did, and even the county's brightest bulbs now get a failing grade on material they supposedly have learned with top marks.

Our magnet program students bring to the table a significant amount of mathematical knowledge and talent. Their work ethic is impressive; they make extensive use of the additional materials that a school with real resources can provide.

The students have the ability, but the school system is not matching their commitment.