Why Johnny can't calculate: Teachers follow the vibes, not the evidence

Why are so many students are doing so badly in math? Teachers don't learn much math content in prep programs, writes Bell Ringer Holly Korbey. Few are "taught how the human brain learns." As a result, many teachers aren't well-prepared to help students who struggle with math.

Sadly, the National Council of the Teachers of Mathematics (NCTM) is not on the job. A new position paper, “Changing the Professional Culture of Teaching Mathematics,” has little to say about teaching or math, she writes. Instead, the group's 70,000 members are urged to expand the definition of "mathematical competence" to include "the diverse ways different cultures learn and express understanding, such as through storytelling, collaborative problem solving, and practical applications."

If teachers "investigate their personal beliefs," and make math "more relevant to students’ lives," NCTM promises, students "will see themselves and their peers as powerful mathematical thinkers and doers.”

That confidence is supposed to lead to competence. But does it?

NCTM is calling for "math teachers to become much less concerned with whether students can do actual math," Korbey writes. "How else to interpret the idea that students will be doing some other kind of math that allows them to shine in ways current methods aren’t?"

The suggestions "rely heavily on belief and emotion instead of evidence" on how students learn math, she writes.

"Vague teacher tactics like “valuing the community,” aren’t supported by any current research on how students learn math — and are impossible to measure," writes Korbey. If teachers understood cognitive science, they'd know that "all students, no matter which community or culture they hail from, learn math in similar ways."

Coursework is "the gatekeeper to advanced mathematics and career aspirations," NCTM complains.

No, writes Korbey. Students can't learn advanced math or pursue STEM careers because they haven't mastered math. "It sounds stupidly obvious but teaching the material really matters in how much students are able to learn."

"Practices like using the instructional hierarchy to adjust instruction and committing math facts to memory have proven track records of success with all students, even ones who really struggle with math," writes Korbey. But many teachers haven't been told what the research shows about what's effective. Instead, they get "vague bromides" and calls for positive thinking.

As I wrote in a comment: "The besetting sin of education is the tendency to pretend that things are OK when they're not. Let's pretend the kids who can't solve math problems have some other, just-as-good knowledge or skill we're not measuring. That relieves us of the burden of trying to teach them. It doesn't relieve them of the burden of innumeracy."

Education need to start paying attention to research, instead of recycling fads that "have failed to show any benefit for student learning," write University of Toronto professors Nidhi Sachdeva and Jim Hewitt.

Teacher-prep programs "often offer a buffet of strategies, theories and ideologies," they write. Assignments might include writing a personal philosophy of teaching, or designing a lesson that aligns with a particular educational theory. But there’s rarely pressure to review the research literature to see if a recommended instructional approach actually improves student learning."

While professions such as medicine keep improving, education is "constantly recycling ineffective ideas under new names rather than building on proven ones."

I remember the self-esteem movement in California schools. "Students" became "scholars" or "mathematicians" or "scientists." Teachers reminded them they were "special" and then "brilliant" and then "geniuses."

Most kids were too smart to fall for it. But, to the extent that anyone did, it implied that they were already wonderful and had no need to improve. I remember a book that told an illiterate badger that his kindergarten teacher "loves you just the way you are." No, she doesn't! Your parents love you. Your teacher wants to change you to someone who can read. And do math.