Math for All

Recently, an old friend, colleague, and philanthropist from New York, who is funding a new urban independent school for disadvantaged children, asked me to advise her about an appropriate math program. She plans to have the school be a showcase for mathematics education, especially for children who don’t have the advantage of rich mathematical experiences at home with their families. My first thoughts were about whether a stellar math program is different in that context than it is in a context which, like ours, includes significant parent support. We want all of our children, whether they are from rural or urban settings, advantaged or disadvantaged backgrounds, or fall along other continuums, to be productive contributors and leaders in the 21^st century world they will encounter after school. The skills emerging adults will need to be successful members of our increasingly global society won’t be different because of their backgrounds.

            So what are those essential mathematical skills, and how are they best taught? Over the first five years of math instruction (K-4), the two most important emphases of a mathematics program are (1) basic computation skills in all four operations, including automaticity with math facts, and (2) an underlying conceptual understanding of how numbers are put together. Using these two things together, a student can figure out how to do most everything else. The first provides the skills so that children don’t need to spend precious intellectual energy on these basics as they are trying to learn the more difficult applications of them. The latter is essential to mathematical reasoning. These two things should be learned at the same time, since they give the child a reason (#2) for learning the “boring stuff” (#1). Learning in context is always better than learning in a vacuum, as it provides a structure for students to hang their new knowledge upon. Many programs focus only on basic computational skills, supposing that children can’t start thinking about mathematics before they know how to compute, and these programs do a disservice to children. The students may become great computers, but they have missed the opportunity to make critical connections during the developmental period when their brains are most malleable.

If students have had a strong program that integrates these two aspects of math education during the early years, they will be able to move to a more traditional program (pre-algebra, algebra, geometry, etc.) in the Upper Primary or Middle School years. This upper level math program should focus on applications. Again, learning without context is less efficient, not to mention less interesting. Just as in the Lower Primary program, conceptual understanding is essential. We certainly encounter students who need to learn procedurally, but the goal is always to move them from applying procedures to applying their minds.

Regardless of their backgrounds, as our students leave school to become members of adult society, they will need to do just that – apply their minds. We cannot know what specific procedures they might need for the jobs of the future. But we can arm our students with the ability to figure out what procedures are needed, based upon an underlying conceptual knowledge and skills base. We give our children a gift as we help them build that base – we give society a gift as we send our strong young mathematicians out into the world.