On the Role of Concept Trauma in Math Education Policy
Would you take relationship advice from someone in an abusive one?
Author’s Note: I’ve been holding off on writing about the notion of concept trauma for quite some time. The topic is a sticky one, and one that hits close to home for many of us, myself included. Thus, it is important to me to treat it properly, and as such I intend to write more on the topic later.
This piece, by virtue of its necessary brevity, is not a comprehensive exploration of the phenomenon.
Broadening the Scope
By now, you’ve probably heard about “math trauma” — the trauma-type response pattern that afflicts a great number of individuals in mathematical settings. Though this may sound dramatic to one who has not experienced it, the response is indeed genuine.
What often goes undiscussed regarding this phenomenon is the fact that it manifests on a conceptual level as well as on a procedural one. In other words, the trauma-type response is tied not only to the process of doing math, but to the fact of math itself. There is a prickly layer surrounding the referents — words describing the offending concepts, such as “calculus” and “derivative,” or images of “scary-looking” equations — that triggers the individual’s defenses whenever they get too close. This concept-layer response defines concept trauma.
Unsurprisingly, for many people, discussing even the idea of high school mathematics strikes a particularly emotional chord. (What, reader, is your experience? Take a moment to consider.)
This leads us to a very natural question:
Should a person working through trauma be tasked with writing policy regarding their trigger?
Unfit to Serve
Unsurprisingly to anyone who knows me or my work, my answer to the above is a resounding absolutely not.
That’s not to say that nobody who has ever experienced math trauma should be barred from weighing in on policy and curriculum reform. Rather, we need to be wary of the prevalence of normalized and untreated math trauma among the individuals tasked with educating our children.
The sad fact of the matter, at the time of my writing this, is that many adults wear their math trauma and innumeracy as badges of honor, viewing them perhaps as battle scars rather than wounds left to fester. But this is nothing new — perhaps a testament to the extent of the rot in America’s relationship to mathematics.
What’s more, in common parlance the scope of the phrase “math trauma” only functionally extends to the procedural, though the phenomenon itself winds deeply into conceptual and referential territory. This alongside the fallibility of self-reporting leads to failure to screen on a massive scale.
Hidden in Plain Sight
We would not knowingly invite someone illiterate to build our summer reading list. We would not seriously consider an illiterate person’s advice that “nobody actually needs to learn how to read” when considering how to formulate a language arts curriculum in the best interests of the students.
It is tempting to draw parallels to innumeracy here, but one quickly finds that these fall apart. Indeed, innumeracy stands apart from illiteracy in a collection of ways, first and foremost being that innumeracy is not at all notable. If an adult in today’s America cannot read, their experience of life will be markedly different from that of nearly everyone around them. If an adult in today’s America cannot read, the people around them will know it. The people who meet them will remember it. The same cannot be said of the innumerate.
Further, as mentioned in the previous section, innumeracy is often celebrated. Innumeracy brings social status. It is, in many circles, the norm. To defy this norm in any way is notable. And to be proficient at mathematics without any math trauma is basically asking for a pile-on. If anything, the latter is more prevalent than the former.
In short, it ends up being pretty damn easy to unknowingly consider the advice of someone math-traumatized and/or innumerate when building a mathematics curriculum, and what’s more, even if you did know, it’s entirely possible that the information would not have been salient enough to register as a really big red flag for this particular line of work. This is a recipe for disaster.
On Discomfort
Undoubtedly, the fact that so many people are left with lasting math trauma is a sign that something has been going wrong in mathematics education. Some have argued that it is precisely for this reason that we should not entrust professional mathematicians — the ones who “made it” — with curriculum redesign.
This argument has never felt particularly compelling to me, but I see its point. Perspective is important. Survivors will be biased.
Yet this implicitly endorses the notion that student comfort is somehow more relevant to this particular conversation than student learning. Observe that the question of curriculum redesign is only relevant when operating under certain assumptions, one of which being that kids should attend school at all, inherently prioritizing student learning over student comfort. Regardless of your personal views on compulsory schooling, I trust that you’re able to see the contradiction in the above.
And even if we choose to ignore the logical inconsistencies of the above, the notion that comfort should be prioritized in an educational setting strikes me as profoundly flawed.1 One of the greatest tools a math educator can give their students is the ability to handle frustration gracefully and productively. This skill is not built in the absence of struggle. Indeed, appropriate challenge in the classroom is the single most critical aspect of a child’s education.
Struggle, of course, is uncomfortable. Struggle often feels really bad. Take it from someone who very recently yelled at a diagram. Sometimes it sucks. And that’s okay. Hell, a lot of us would even go so far as to say that it’s good.
Finally, I would be remiss to ignore the very real subset of the population that has successfully worked to overcome their math trauma, especially given that I find myself among them. The notion of an inherent dichotomy between mathematicians and people who have “been there” is deeply and profoundly stupid.2 The notion that math trauma is forever is even stupider.
On Perspective: Who’s Fighting the War?
This brings us to the current “war on calculus” that has most recently found its spotlight in California.3 Whether or not you, personally, believe that the traditional calculus sequence is the best use of students’ time, it now seems pertinent to ask: who’s fighting? Who’s pushing for the proposed alternatives, and why?
A common thread that has surfaced pertains to the “relevance” of calculus in comparison to something like data analysis. This is telling. Although calculus has long since been established as critical to a wide variety of disciplines, these disciplines are not being viewed as “realistic” career paths for the average student. In particular, the individuals making the claim that calculus is not useful in everyday life cannot conceive of a version of everyday life in which calculus is relevant.
I won’t pretend to have researched any of the individual names behind the proposed changes, and it’s important to me to emphasize that this piece is not meant to criticize anyone in particular. Rather, we need to be honest with ourselves and with each other about where the fight is coming from. We won’t get anywhere otherwise.
One Final Thought
In any situation such as this, it is easy to find ourselves responding rather than pursuing. We desperately need education reform, but nothing sustainable will come from attempting to stitch change together from patches and scraps. Without a coherent vision, any such attempt will cause more harm than good.
In parallel, we must be wary of the novelty halo that any such vision, regardless of caliber, bears. Unity is inherently compelling. Vigilance is required should we hope to evaluate such things based on their merit alone.
I certainly hope that this requires no clarification, but in case it does: NO IT IS NOT OKAY TO LITERALLY ABUSE STUDENTS and also FRUSTRATION WITH COURSEWORK IS NOT THE SAME AS BEING ABUSED
One of the more pleasant things the Internet has brought us is easy access to stories that might not have been publicized in the past. In particular, it is trivial to find things along the lines of “I became a mathematician mostly out of spite” and I think that’s beautiful.
Not to be confused with the war on gifted education, which is a separate but not at all independent issue.