Derek J. Keenan, Ed.D,
Vice President,
Academic Affairs,
ACSI
The mass media and the professional press ululate about the sorry state of mathematics education today. We encounter claims such as "Only four out of twelve math books used in middle schools were rated as satisfactory" (USA Today, October 14, 1999, p. 14A) and "Standard algorithms for addition, subtraction, and multiplication are not taught" (American School Board Journal, April 2000, p. 55). A recent headline in the Colorado Springs Gazette noted, "Students Can’t Do the Math" (July 26, 2001). The horrific results of United States students in the Third International Mathematics and Science Study were ballyhooed in the popular press.
How do we as Christian school educators respond to these results? Do we look at our own achievement test results and note that by and large we are so many months above the national average? I hope we are not overly satisfied with our mathematics performance—because we should not be. The number of Christian school students attaining National Merit Finalist status equals about one percent—the same as in government schools. The recently released National Assessment of Education Progress test indicates that "conservative Christian schools" are the lowest performing group in mathematics in private education.
There are some positive facts that standardized tests used in Christian schools tell us. We do very well at teaching students to add, subtract, multiply, and divide. Our students score extremely high in computation. In ACSI schools, most students take math classes, including advanced ones, in at least three of their high school years. These are commendable achievements.
Other indicators, however, reveal that we are not teaching students to understand mathematics. The Stanford 9 test results of ACSI students in relation to the ACSI performance standards (criterion-referenced assessments) reveal that the percentage of students scoring at the high levels (three to four) diminishes rapidly after fifth grade. At all grade levels, in problem solving and number sense, our students score well below their computational skill levels.
In mathematics education, in Christian and public schools, we have for years followed the premise that instruction focusing on correct answers, speed drills, and repetitive problem solving would result in mathematical competence. The sad fact is that these methods lead to computational fluency but not to understanding.
We would never think that oral reading is the measure of reading proficiency, so why in the world do we think that computational skill is the measure of mathematical competence? Yet in many cases, such as in accepting that premise or in using textbooks viewed by some Christian educators as mathematics gospel, we would appear to trust this fallacious way of measuring results. As educators, we can never forget that the goal for our students is understanding! We need computational skills for balancing our checkbooks, figuring the cost of interest, and completing a myriad of other tasks; but applying those skills mechanically does not make us mathematical thinkers.
What are some strategies that develop grade level–appropriate understanding? From the earliest math instruction, we can emphasize concept mastery and understanding. Mathematics allows us to break these concepts into digestible, age-appropriate elements. We can use manipulatives, which are essential for most students to understand mathematics as they see and feel it. And we can use drill and practice in moderation for number fluency.
Mathematics is a marvelous discipline, a good gift from God to stimulate us to think about pattern, design, order, and sequence. (Would our day-to-day world function without numbers?) The understandings required for dealing with variables and unknown quantities, the analytical skills needed for life, are enhanced when students learn to see the beauty and grace in the logic of mathematics.
Editor's Note: Can They Do the Math 5.4