Children who are native speakers of English do something extremely interesting and simultaneously frustrating for some parents who fret over whether or not their children are smart and whether or not their children speak "properly."

At some point, that child will utter something like, "Mommy, he goed," and the adoring parent will respond with something like, "No, honey, he went."

While this event should be an exciting and positive experience for parents, it is more often frustrating since the child will persist with "he goed" for some time, regardless of the parents' corrections. The reason for this (and you might be wondering what this has to do with algebra) is that linguistic constructions of verbs may be strongly rooted in human biology (thus children can generate past tense patterns—add "-d" or "-t" sound—once that pattern has been triggered, but they must learn and be capable or learning irregular verbs); therefore, when children have yet to reach the stage of brain development (abstract reasoning) that supports understanding and negotiating abstract systems (grammar and algebra), direct instruction is futile. [1]

And more importantly, characterizing "goed" as "not smart," and then when a child can generate "went" as "smart" are both tremendous mistakes—in effect, they are lies we tell our children (and ourselves).

Missing the Target by Aiming at Algebra

Andrew Hacker (The New York Times, July 28, 2012) has sparked a debate about whether or not all children should be required to take algebra in their schooling. While the narrow debate itself, I believe, is a distraction, what we should be rethinking more broadly because of the debate is often being left unsaid since the narrow debate is couched in the lies we tell children and ourselves.

The algebra debate is essentially the Common Core State Standards (CCSS) debate, and both are new bottles for old wine—the basics skills or cultural knowledge argument.

Let me pause here to offer a few caveats. First, I graduated high school intending to major in physics (it combined two academic loves, math and science) and received my As in high school in math and science—not English, in which I eventually majored and then taught for almost three decades. I, then, am no math hater; in fact, I believe we are failing children miserably in fostering the numeracy they need that parallels the literacy they need to be happy, successful, and significant members of a democracy.

This commentary is not math bashing.

Next, I could write a very similar piece about English—how we badger children with grammar rules (grammar books, worksheets, and tests) and destroy their love of reading by requiring The Scarlet Letter when they want to read what they choose to read (see Alfie Kohn on creating non-readers).

And that caveat leads to my first main point about algebra: Instead of asking if all students should take algebra, let's start with this: Why are we teaching algebra in the first place? What does the teaching of algebra accomplish that is either essential or not?

This foundational question is far more important because it asks us to reconsider content. And herein lies the primary flaw I see in basic skills or cultural knowledge arguments: Confusing the acquisition of a fixed body of knowledge with learning.

If our goal is to foster learners (dynamic, critical, and thoughtful humans who can discover and create themselves while discovering and creating the world, a free and democratic world), then content knowledge acquisition as an ends is counter-educational.

To argue that acquiring algebra for algebra's sake is essential is flawed just as arguing that all children must read The Scarlet Letter—especially if and when these acts of compelling children more often than not detract from their acquiring numeracy and literacy.

Currently and historically, we have tested children for early algebra readiness and from that system sorted children as "smart" (and by deduction, "not smart"). As my anecdote at the beginning noted, however, algebra readiness tests identify brain development, not "smart" (whatever that is).

This is the child prodigy trap that does more disservice than good to both those labeled "smart" and "not smart."

The question of whether all children should take algebra is irrelevant as long as we continue to use early algebra readiness to label and sort children, as long as we continue to confuse brain development with smart.

Further, then, let's use the algebra debate to address some other serious issues surrounding algebra and math instruction:

• Let's stop confusing what skills children need to succeed in a course with what that course teaches. Algebra is often heralded as a way to teach abstract reasoning and critical thinking skills. This argument is confusing what those students need with what they learn—especially in terms of brain development.

• If, however, we are seeking to foster critical thinking, we must consider if and how algebra accomplishes that in some unique way—if it does, then require it, but if it doesn't, students may well be better served in something other than a required algebra class.

• Let's also stop justifying algebra with circular logic: Algebra is necessary for improved SAT scores because the SAT has built in algebra skills as necessary to achieve high SAT scores. (This parallels justifying algebra by abstract reasoning/critical thinking outcomes.)

• If algebra and math are essential, let's stop teaching students lessons that work against those fields of knowledge. Stop giving children scores on math tests over 100 (test scores are percentages); stop telling math students "Here's a trick, you don't have to understand it"; stop giving math students extra credit and heavily weighted homework grades to counterbalance their poor test scores, thus distorting their final math grades.

• If math is sequential and linear, let's stop allowing children to score poorly on the test of Chapter Two on Friday, and then picking up with Chapter Three on Monday. If math is truly sequential and linear, then let's honor that (I suspect, by the way, that it isn't—see below).

Broadly, I am deeply skeptical about compulsory anything, especially when we say we want human freedom, agency, and autonomy. I am also deeply skeptical that much of any specific content is truly essential, including algebra (or British literature).

As an adult, I now can say that years of economics and statistics in my formal schooling would have served me better than my trip through traditional math courses that were built on my early readiness for algebra (yes, I was labeled smart, and suffered that delusion until I was old enough to know better).

And those algebraic ways of thinking and mathematical moves likely could have been better learned in the context of courses in economics and statistics (again, we have a seriously flawed view of needing basic skills before taking a course instead of acquiring those skills in whole experiences).

Compulsory algebra is a mistake, but it is also just one specific example of the larger problem with compulsory content acquisition.

So, as I stated in my caveats, let's not use this algebra debate to pile on algebra, but to step back from that argument and reconsider the many and varied ways we lie to our children and ourselves by labeling and sorting those children, and in effect, compelling them to hate the very knowledge we claim is essential.

[1] The average age for developing the abstract reasoning ability needed to understand algebra and grammar is 20. Consider how that impacts the labeling and sorting we do to children and young adults throughout schooling.