What is constructionist math, and how does it differ from the traditional approach to learning math?

Many of today’s parents recall with trepidation their own elementary and junior high school exposure to the “new” math (base 3, base 7 etc.) When faced with another “new” theory about learning math, they are, therefore, understandably skeptical.

The traditional approach includes skill practice in the foundations of computation such as number facts and practice drills. Students using the traditional approach memorize the multiplication tables and learn how calculate long division problems using the four-step process (divide, multiply, subtract, bring down). The sequential approach to math expects that students will master their computation skills before they progress to more complicated procedures like “order of operations,” mathematical properties, and problem-solving formulae.

On the other hand, The National Council of Teachers of Mathematics presents the constructionist approach (including Connected Math) as an attempt to more fully engage students in their learning of math. This approach eschews drill and practice and rejects memorization. Rather, it emphasizes an “inquiry” program for pupils to “construct” their own knowledge through reasoning. This approach often introduces calculators into the classroom as early as first grade with the hope that the students will learn math in the process.

And so, another nationwide “math war” ensues in this country. Critics of the traditionalist movement call it “drill and kill.” Opponents of the constructionist approach cite examples of children being unable to compute correct change or solve basic multiplication problems. They maintain that students who have not built a solid foundation of math facts at an early age have difficulty in high school math.

An article in a recent edition of the NY Times reported that parents in one Rochester suburb went so far as to send a petition to their board of education requesting that students have the option of taking traditional math. Although, the board initially rejected the petition, it did acknowledge the legitimacy of some complaints; it has begun supplementing the constructivist classes with lessons in computation. As a result, the board had to petition the State Board of Education for a postponement of the statewide Regents exam.

America’s students do not fare well in math ability when compared to those in other industrialized nations. One typical example is the 2003 math exam sponsored by the “Program for International Student Assessment.” Fifteen year old students from 34 countries took part in the exam. Results reported in late 2004 indicated that US students ranked 29 of the 34 nations, ahead of only 4 Mediterranean countries and Mexico. Three Asian nations, China, Japan, and Korea ranked at the top. These countries ascribe to a very traditional math curriculum, replete with incessant skill and practice work.

Anyone who questions the importance of these mathematics standings need only glace at current economic headlines. Undereducated American workers compete for jobs globally, and outsourcing to foreign nations is a common phenomenon. The summer edition of The Atlantic included a speech at the University of California by a member of several corporate boards in Europe and the United States who maintained that about 30% of American high school graduates are unprepared for the workforce, as opposed to about 15-20% in Europe.

Recent changes in the SAT, the college entrance exam taken by most students on the East Coast, includes increased higher order math content. Will the constructionist method help or hinder these students? Will it allow American students to be more prepared for challenges in the work force or universities? Whether the constructionist theory will have the desired effect of producing individuals with a solid knowledge base remains uncertain. The impact of the constructionist movement may take some time to filter through high school and college classes.