Helping Children Learn Mathematics
"What caused you to quit school?" That's the main question that researchers from the United Negro College Fund asked of 62 high school dropouts in a West Virginia Job Corp program last year.* Most had the same answer: mathematics.
The finding is hardly surprising. Many Americans regard the subject of mathematics with fear and loathing—probably because people tend to dislike the things they're not good at. And, for several decades, American students' inadequate mathematics achievement has been well documented by national and international assessments, studies, and reports. Although math scores increased somewhat for both fourth- and eighth-graders on the most recent National Assessment of Educational Progress long-term trend report, the increases weren't large enough to close the gap between the U.S. and the world's high-achieving countries and, disappointingly, scores for 12th-graders remained stagnant.
For those involved in education, persistent reports of students' low mathematics achievement can be frustrating—especially since mathematics education, like the teaching of reading, has been the subject of one type of reform plan or another for the past half a century. Like reading, math is universally accepted as one of the core academic subjects. Both are taught from the earliest grades, are regularly included in high-stakes assessments, and are understood to be gateways to future learning opportunities. Mathematics in particular is the gateway to future studies in the economically vital fields of science, engineering, and technology. But unlike reading, which has been carefully studied for roughly 40 years, the study of math education has been much more haphazard. As a consequence, the research on improving mathematics instruction is still dismayingly thin. One result is that much of the debate over mathematics education reform has been based, in the words of William Schmidt, not "on scientific evidence, but rather on opinion and someone's ideology."
So what do we know? Thanks to the work of Harold Stevenson (see this issue's "Notebook"), James Stigler, and others, we know that the culture of schooling is an important factor in how mathematics is taught and learned. The data on some 50 countries, collected and analyzed as a part of the Third International Mathematics and Science Study, reveal the central importance of a mathematics curriculum that is focused, logical, and coherent—characteristics that are sorely lacking in U.S. curricula (see "The Role of Curriculum"). And, perhaps most important, we know that teachers' knowledge of the mathematical content to be taught is absolutely crucial.
But what else do mathematics teachers need to know? To teach multiplication to third-graders, for example, is it enough to know how to multiply reliably oneself, or does the teacher also need to know how to quickly diagnose and correct students' mistakes? What about knowing how to react if a student gets the right answer by making up a new algorithm? Broadly speaking, is there a deeper knowledge of elementary mathematics that is needed "just" to teach multiplication to third-graders?
Fortunately, Deborah Loewenberg Ball and her colleagues have been asking questions like these for over a decade. They don't yet have definitive answers—but they do have an exciting program of research that has already tied teachers' mathematical content knowledge to student achievement and, in the years to come, promises to identify exactly what knowledge successful mathematics teachers need to have. Deborah Ball, Heather Hill, and Hyman Bass explain their work and findings to date (see "Knowing Mathematics for Teaching")
While Ball and her colleagues have been working on large-scale assessments of teachers' mathematical knowledge and its connection to student achievement, Ron Aharoni has been in the classroom discovering, through many less-than-perfect lessons and the occasional home run, what elementary mathematics teachers need to know. A professional mathematician, Aharoni accepted the challenge of working in elementary math classrooms several years ago. We open this special section on teaching mathematics (see "What I Learned in Elementary School") with his personal reflections and insights.
*Viadero, D. (March 25, 2005). Math emerges as big hurdle for teenagers. Education Week. www.edweek.org/ew/articles/2005/03/23/28math.h24.html. (back to article)