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-world problems.
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 high school.
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. Yet today, one cannot read and understand Newsweek, USA Today, or countless other news sources without being able to interpret statistical information. As a student, I used a slide rule to do some computations; today, I use a calculator. I also spent endless hours doing computations and rarely learning to estimate. Now I rarely do any tedious computations but regularly call upon estimation to decide if a calculator result is reasonable.
True reform would allow calculators, graphing calculators, and other readily available technological tools to help students solve equations in an instant, replacing pages of written procedures and hours of work. A mathematics curriculum should reflect what is important for the future and include advances in technology.
My college-aged son benefited from the reforms used by progressive public high school teachers and standards-based reform mathematics curricula. His classes were driven by interesting problems that teachers used to challenge students' thinking and engage them in learning mathematics. He scored at the 99th percentile on the ACT and SAT and graduated from high school with more mathematical knowledge than I learned in my first two years of college.
My grandchildren are learning from standards-based reform mathematics curricula in public elementary school. They are actively engaged in problem solving. They are developing fluency with their basic facts and also using calculators. They realize that while it is not always easy, math can be fun to learn. They typify thousands of US children who are benefiting from a mathematics education that is better than what many of their parents and grandparents experienced. Their growth underscores the fact that the problem of low achievement is not in the unconventional ways of reform math, but in too little exposure to it.
Change in the real world is inevitable, and so, too, is change in the education of students who are preparing to enter that world. Approaches such as rote memorization proved to be ineffective in the 20th century.
The good old days of mathematics never were. It's time to help our current generation of children prepare for their future and kiss the good old days goodbye for good.
• Robert Reys, a former high school mathematics teacher, is a professor of mathematics education at the University of Missouri-Columbia.