I am tired of hearing from doomsday educational critics who would
have us abandon new ideas and return to the "good old days" -
particularly in math education, where American students fall way
behind the rest of the world.
Efforts to reform mathematics education are under way, but they
have not reached many classrooms in the United States. While some
math teachers are emphasizing thinking and problem solving, many
students still experience mathematics that is dominated by
memorization and drill, without any meaningful context. Reform
classrooms are using technology to model and explore ideas. Students
are challenged to find ways to solve problems based on what they
know and understand. They have opportunities to link math to real-
While some schools are embracing reform mathematics, many others
are persuaded by naysayers. But if schools continue to do more of
what they've always done, they'll continue to produce too many
students uninterested and unmotivated to study mathematics beyond
I graduated from a small Missouri high school more than 40 years
ago. Although I had caring teachers, and went on to major in
mathematics in college, my high school experience with mathematics
was weak. Most of my peers hated math. Algorithms and tedious
procedures were demonstrated with little or no explanation of why
they work. Sensemaking and understanding were not a part of my
experience of learning mathematics. Students left class thinking
that math consisted only of dull procedures and rules to memorize.
Performances over the past 30 years on the National Assessment of
Education Progress and the International Mathematics and Science
Studies document that traditional mathematics curricula and methods
of teaching have not been effective. However, research is emerging
that shows reform mathematics is increasing student learning.
The National Council of Teachers of Mathematics, a nonprofit
organization of mathematics teachers, has published a set of content
standards in math called Principles and Standards for School
Mathematics (http://nctm.com). Consistent with these standards, some
textbooks are now integrated - topics from arithmetic, algebra,
geometry, statistics, and probability are naturally connected.
Integration is commonplace in countries, such as Japan, whose
students excel on international mathematics tests. But most US
schools are still mired in a 19th-century course sequence of Algebra
I, Geometry, and Algebra II.
Throughout most of the 20th century, statistics and probability
were not taught in school. …