Children need to learn algorithms to understand math, write Alice Crary, a philosophy professor, and W. Stephen Wilson, a math professor, in the New York Times.
. . it is true that algorithm-based math is not creative reasoning. Yet the same is true of many disciplines that have good claims to be taught in our schools. Children need to master bodies of fact, and not merely reason independently, in, for instance, biology and history.
Mastering an algorithm requires “a distinctive kind of thought,” they write. It’s not “merely mechanical.” In addition, algorithms are “the most elegant and powerful methods for specific operations. . . . Math instruction that does not teach both that these algorithms work and why they do is denying students insight into the very discipline it is supposed to be about.”
Some commenters claimed math reformers advocate a “balanced” approach that includes algorithms, writes Barry Garelick in Education News. He is dubious.
I am reminded of a dialogue between a friend of mine—a math professor—and an public school administrator. My friend was making the point that students need basic foundational skills in order to succeed in math. The administrator responded with “You teach skills. But we teach understanding.”
. . . The reform approach to “understanding” is teaching small children never to trust the math, unless you can visualize why it works. If you can’t “visualize” it, you can’t explain it. And if you can’t explain it, then you don’t “understand” it.
According to Robert Craigen, math professor at University of Manitoba, “Forcing students to use inefficient procedures that require ham-handed handling of place value so that they articulate “meaning” out loud in every stage is the arithmetic equivalent of forcing a reader to keep his finger on the page and to sound out every word, every time, with no progression of reading skill.”
The power of math, however, is allowing for exploration of concepts that cannot be visualized. Math is what takes over when our intuition begins to fail us.
Garelick, who’s launched a second career as a math teacher, links to a 1948 math book’s illustration of different ways to do mental multiplication:
Figure 2 (Source: Study Arithmetics, Grade 5)