Alice Crary and W. Stephen Wilson conclude that reform math has swept out the traditional math. In the New York Times 2013, they wrote, "Today, the emphasis of most math instruction is on numerical reasoning (i.e., reform math's new jargon). This is in contrast with a more traditional focus on understanding and mastery of the most efficient mathematical algorithms. Crary and Wilson point out, "The standard algorithms are either de-emphasize to students or withheld from them entirely." Moreover, "The staunchest supporters of reform math are math teachers and faculty at schools of education." Now you know the reason that reform ideas persist in our classrooms.
In reform math, reasoning is much more important that learning content knowledge. But it isn't. Problem-solving depends on knowing stuff. To perform arithmetic and algebra well, students must know in long-term memory factual and procedural knowledge. But, to reformers, facts don't matter much.
The ideas, skills, and uses of arithmetic or algebra are not meant to teach students creative reasoning. Students do not take calculus to improve their creativity. Crary & Wilson explains that in all disciplines, including mathematics, science, and history, "Children need to master bodies of fact, and not merely reason independently."
Indeed, learning facts in biology, chemistry, and physics or history "do not stunt students' growth [creativity, imagination, or curiousity] and prevent them from thinking for themselves." The same goes for arithmetic. To do arithmetic well means to know facts and standard procedures, which requires memorization and practice-practice-practice. Guess which nations soar far above U.S. kids in problem-solving? The more "rote" learners in East Asia. Knowledge enables problem-solving. Critical thinking is a product of knowledge, as are innovation and creativity. We are not all equally creative or innovative. Problem-solving is domain-specific. All the reasoning in the world will not help you solve a trig problem unless you know the trig.
Today, all we hear is critical thinking this, critical thinking that, but without a solid mathematical knowledge base, critical thinking (i.e., problem-solving in mathematics) is a moot point, but not to the reformers who believe that students can become good problem solvers without knowing basics (i.e, core arithmetic). The reform idea violates a fundamental cognitive science finding that critical thinking is domain-specific.
Part 2 Distractions
Textbooks are filled with colorful graphics and pictures that distract students from learning math. Likewise, covering the walls with colorful posters, sitting in small groups where kids face each other, and using gadgets (e.g., graphing calculators, laptops, tablets, etc.) distract students from learning. Consequently, students learn less. It is a conundrum in U.S. classrooms. Distractions can cause learning gaps.
Similarly, when students are introduced to multiple strategies to do multiplication, such as arrays, areas models, latices, and partial products, cognitive overload in novices is often produced. The working memory is limited, so when extras are tossed into the mix, such as multiple strategies for doing math or writing explanations, novices often become confused and learn less.
Clark and Feldon ("Five Common but Questionable Principles of Multimedia Learning") conclude "Multimedia does not increase student learning beyond any other media including live teachers." Extraordinary teachers can produce amazing students, but multimedia won't. Personalized learning, adaptive software, and blended learning lack evidence of effectiveness, so students learn less. The hype is not evidence.