Monday, November 9, 2009
Constructivist vs. Traditional Math Programs
Typically it is the “lattice” method of multiplication that pushes parents over the edge. This method taught to elementary school students under the Everyday Mathematics program, one of several national programs collectively labeled “constructivist” math, is so jarring to those raised in a traditional math program that it ends up being the last straw.
Is there really a problem? Is this a case of parents stuck in their ways, unable to see beyond their own childhood experience? Do constructivist math programs like Everyday Math offer innovative strategies for modern students, or do they simply confuse students with pointless computational methods removed from the real world? Is traditional math instruction any better?
Lee Stiff, a past President of the National Council of Teachers of Mathematics, rejects the label “constructivist” math. The term was coined because these programs aim to have students construct their own knowledge through their own process of reasoning. He prefers the term “standards” based mathematics, but whatever the term the program is the same. In a defense of these programs Mr. Stiff writes:
“Reform-minded teachers pose problems and encourage students to think deeply about possible solutions. They promote making connections to other ideas within mathematics and other disciplines. They ask students to furnish proof or explanations for their work. They use different representations of mathematical ideas to foster students' greater understanding. These teachers ask students to explain the mathematics.
Their students are expected to solve problems, apply mathematics to real-world situations, and expand on what they already know. Sometimes they work with other students. Sometimes they work alone. Sometimes they use calculators. Sometimes they use only paper and pencil.”
It is hard to argue with a statement like that. Who would disagree that students should not have a deeper understanding of math?
It might be that some of the roots of constructivist math are in the field of early childhood education where preschool and Kindergarten aged children have long been encouraged to understand mathematical concepts in multiple physical and intuitive ways.
Maria Montessori pioneered the use of what modern teachers call “manipulatives.” These physical teaching aids, which might be a simple as blocks, help young minds grasp the nature of mathematical concepts through their senses. Just as two times six equals twelve on paper, two piles of six blocks equals twelve on the classroom floor. Such techniques are long recognized as useful and necessary to promote developmental growth. A variety of available physical outlets for understanding mathematical concepts means that young children will be able to develop a comfortable relationship with numbers on their own.
That same sort of philosophy is part of the constructivist math program. The idea that children could have different methods for reaching the same answer or those children should be allowed to find a method with which they are personally most comfortable is not inconsistent with established early childhood educational norms.
Yet, there is one key difference with constructivist math programs: now we are much further along on the developmental scale. Everyday Math and similar national programs are used not in preschool but in elementary school and on up to sixth or even eighth grade. In writing curriculum, “invented” spelling is allowed in lower grades so as not to stifle creativity for the sake of accuracy. In later grades, though, spelling is examined and corrected and eventually accurate spelling is required. It is often said that this principle does not seem to have a corollary in constructivist math. The disparaging term “fuzzy” math is a reference to this fact. In fact, it is the teacher's emphasis on efficiency and proficiency that matters in this case, not the "program".