Out on Good Behavior: It continues

Because I teach during the school year, there has been a long hiatus in my series “Out on Good Behavior: Teaching Math While Looking Over Your Shoulder”. With the onset of summer break, the series has returned for those of you who wish to follow the adventures of our math teacher hero.

Chapter 14 of the series is now up and running, so be sure to check it out and leave a comment (or two) if you are so inclined. Tell your friends (and enemies) as well!


NCTM, Dept.

A recent article proclaims with great fanfare two new publications of the National Council of Teachers of Mathematics (NCTM). One is for elementary teachers and the other for middle school teachers. In the words of the article, the publications address “how to help all students view themselves as “capable learners and doers” of math.” 

Something tells me that the report isn’t strong on students learning their addition/subtraction and times tables by heart. And it probably is not big on practice, or worked examples, and scaffolded problems, but I’m just guessing here. I could be completely wrong.

The article states that the reports stress the importance of teaching math using methods that are “consistent with research-informed and equitable teaching practices.”

Nothing wrong with research informing your practices, but it really depends on the research. Is it research that is done with controls in a scientific manner, or the typical “action research” based on observation with reference to the same people writing these studies and taking in each others’ laundry for years? And what do they mean by “equitable teaching practices”?

If it were me defining the term, it would mean teaching all students what they need to know to succeed in math. This means teaching math effectively from the start, rather than continually backfilling because of inadequate and ineffective methods touted to be superior to “traditional” methods.

The organization also promoted the importance of schools helping their students build a “strong foundation of deep mathematical understanding” through pathways that might vary by grade level but ensure that each child is getting a “high-quality” math education.

“Strong foundation” is fine, but of “deep mathematical understanding”? That can mean drilling understanding by drawing pictures or doing convoluted procedures in lieu of the standard algorithm. In any event, what they had in mind is what they consider “high quality”. And I’m guessing that “teaching by telling” and providing explicit instruction is considered low quality.

And of course, we have the nod to the ultimate inequity: “Ability grouping”

NCTM pointed to the use of “ability grouping” and tracking students, which the council called “inequitable,” since their use tends to steer students into “qualitatively different courses.” According to the reports, these practices “perpetuates privilege for a few and marginality for others.” 

But the experts in charge have a solution: differentiated instruction. This means placing students of varying ability in the same classes. The result is not differentiated instruction but differentiated expectations.

In the name of equity, some school districts have done away with algebra for eighth graders. So even in a class with ‘differentiated instruction”, those students who would otherwise qualify for algebra are given a class in which they are given more access to “challenging assignments”. But it isn’t algebra.

What is inequitable is the use of ineffective practices for teaching math in lieu of methods that have been shown to be effective. Students who come from families with means have access to tutoring or learning centers. Students from low-income families do not.

But don’t tell NCTM that. They’re too busy selling the following:

“All stakeholders must examine beliefs about who is capable of doing and understanding mathematics, disrupt existing inequitable practices and catalyze change toward creating a just, equitable and inclusive system in early childhood and elementary mathematics.”