What Are the Algorithims?

The Merriam-Webster Online Dictionary defines an algorithm as “a set of steps followed in order to solve a mathematical problem or to complete a computer process.”  The traditional approach to math includes the fundamental algorithms for the four basic arithmetic functions (addition, subtraction, multiplication, and division) as well as for algebra, geometry, and higher math.  These tend to be sequential, so mastery of one is a prerequisite for successfully proceeding to the next level. However, the members of the “reform” math movement have been espousing a different philosophy.  This reform, or constructivist, math program has appeared under different guises throughout the nation. “TERC Investigations,” currently in use in Branford, and “Connected Math,” part of the Guilford curriculum, represent two versions of the same program.

In June, two educators published an article in the New York Times that questions the tenets of the reform math movement.  Alice Crary, associate professor of philosophy at the New School, and W. Stephen Wilson, professor of math and education at Johns Hopkins University, expressed their concerns about the faulty logic of the reform math movement.  They maintain, “At the heart of the discipline of mathematics is a set of the most efficient — and most elegant and powerful — algorithms for specific operations. The most efficient algorithm for addition, for instance, involves stacking numbers to be added with their place values aligned, successively adding single digits beginning with the ones place column, and ‘carrying’ any extra place values leftward.”  That procedure is absent from reform math, which teaches students to subtract from left to right in the lower grades!  Algebra students are expected to develop graphic representations like boxes to express an algebraic expression. The authors specifically cite the Investigations program: “Second grade students are repeatedly given specific addition problems and asked to explore a variety of procedures for arriving at a solution. The standard algorithm is absent from the procedures they are offered. Students in this program don’t encounter the standard algorithm until fourth grade, and even then they are not asked to regard it as a privileged method.”

Some educators explain that the standard algorithms are too difficult for many students.  Do they really believe that “dumbing down” the curriculum is beneficial for anyone?  The article continues:  ”Standard algorithms should be avoided because, reformists claim, mastering them is a merely mechanical exercise that threatens individual growth. The idea is that competence with algorithms can be substituted for by the use of calculators, and reformists often call for training students in the use of calculators as early as first or second grade.”

College math professors (NOT math education professors) decry the reform program because they argue that it does not prepare students for studies in the STEM disciplines (science, technology, engineering, math).  ”They express outrage and bafflement that so much American math education policy is set by people with no special knowledge of the discipline.”

Where are the empirical data that prove that this new movement is better than the traditional approach? Why have several local districts embraced it? Who is benefitting from this new approach to  math? Educators should abandon this nebulous program and insert some rigor into the curriculum.

2 Responses to “What Are the Algorithims?”

  1. category theory

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    • Laura Maniglia

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