Pittsburgh — AMERICAN children have been bad at math for well over a century now. As early as 1895, educational reformers lamented Americans’ “meager results” in the subject. Over the years, critics of math education in this country have cycled through a set of familiar culprits, blaming inadequate teacher training, lackluster student motivation and faulty curricular design. Today’s debates over the Common Core mathematical standards are just the latest iteration of this dispute.

Although these issues are important — no reform can ever succeed without considering teacher training and textbook design — resolving them will never make the underlying question of how to teach math “go away.” This is because debates about learning mathematics are debates about how educated citizens should think generally. Whether it is taught as a collection of facts, as a set of problem-solving heuristics or as a model of logical deduction, learning math counts as learning to reason. That is, in effect, a political matter, and therefore inherently contestable. Reasonable people can and will disagree about it.

Perhaps no reform has illustrated this point as clearly as the wide range of mid-20th-century curricular changes known as the new math. Many of these reforms promised that the introduction of sets, nondecimal bases and formal definitions would lead students to think of math as more than just a bunch of dusty facts: It was a powerful and rigorous way of approaching complex problems.

The new math was widely praised at first as a model bipartisan reform effort. It was developed in the 1950s as part of the “Cold War of the classrooms,” and the resulting textbooks were most widely disseminated in the 1960s, with liberals and academic elites promoting it as a central component of education for the modern world. The United States Chamber of Commerce and political conservatives also praised federal support of curriculum reforms like the new math, in part because these reforms were led by mathematicians, not so-called progressive educators.