math wars reflection theory

Math Wars North

O Canada!

The debate about best practice in Canadian math education has exploded once again. This time attracting high profile combatants.

This post is not meant to resolve deep-seated values, but rather provide a perspective that gets lost in the partisan arguments. It wouldn’t take a long time to place me in a camp, but that would be assuming that there are two camps that want drastically different things.

Now there are certainly battle lines drawn, but would it be possible to distill the highbrow mudslinging into a succinct cause–a common denominator?

The recent tweet conversation between Dan Meyer and Robert Craigen (storied by @MathewMaddux here) serves as an excellent example of the arguments entertained 140 characters at a time. It is dizzying to follow, but if you do, you just may find the essence of the entire debate:

@ddmeyer @rastokke I’m a mathematician. My concern is that mathematics is taught & learned effectively. Pedagogy is downstream of content.

— Robert Craigen (@rcraigen) May 31, 2015

@ddmeyer Our expertise is in mathematical content, we are professional mathematicians. But Ed. gurus hold content is downstream of pedagogy

— Robert Craigen (@rcraigen) May 31, 2015

It just may be that Mr. Craigen summarized the problem with his argument: students don’t operate like streams. The idea of “standard” and “empirical” only begin to describe the complex process of education. Herein exists the disconnect.

It is a slap in the face of mathematics educators to reduce our craft to the transmission of facts and administration of discipline. Mathematicians view math teachers as deficient mathematicians, and math teachers view mathematicians as deficient educators–islands of incommunicable knowledge. Teachers view it as pretentious when mathematicians imply that the way to be mathematical is to become like them, and mathematicians scoff at the gambits teachers necessarily entertain to allow students to experience productive struggle.

In short, the war is personal and the conversations often go there. Rather than having a conversation about what is best for something both parties value (mathematics), it becomes a dance of rhetoric. Both sides take astute stabs at one another. Rather than trying to understand the opposite lens, we (yes, we) shroud petty insults in deft wordplay. It is a self-righteous battle waged on high horses.

Below are plenty of examples (from both discussants).

@rcraigen 3.) You’re still trying to play the role of the Serious Research Person but you gave up that card yesterday.

— Dan Meyer (@ddmeyer) June 1, 2015

@tobiemichele @ddmeyer Huh? I guess the same way you make an omelette w/o breaking eggs … ? Was that a serious Q?

— Robert Craigen (@rcraigen) June 1, 2015

@rcraigen But no worries. Nobody walks their talk all the time.

— Dan Meyer (@ddmeyer) June 1, 2015

@ddmeyer @rastokke Er .. uh … meaning you’re an educationalist with underdeveloped math … and … uh .. frustrated? Gotcha I think…

— Robert Craigen (@rcraigen) May 31, 2015

@rcraigen @rastokke Take your frustration at the underdeveloped mathematics of educationalists. Now invert that and you’re me.

— Dan Meyer (@ddmeyer) May 31, 2015

Mudslinging aside. I’d like to suggest summary statements from what I’ve read from both sides. (Admitting fully that I am a math teacher and also have an ego to protect).

Mathematicians: Math doesn’t operate solely on memorized algorithms, but they form an important foundation for the interconnected and fluid process of mathematics creation.

Mathematics Educators: Teaching math effectively is not simply a summation of predetermined teaching scripts but a dynamic process that involves the interrogation of foundational facts.

It could be that mathematicians and mathematics educators have one common thread: we want to control our own volition. There is more to the respective crafts than the other is aware of. Math education cannot be brushed aside as a make-work project where the memorization of routine facts would suffice–even if they are artifacts of our heritage. Mathematics–the work of mathematicians–cannot be dismissed as stoic or inhuman.

Until this becomes an actual conversation, it will remain, in fact, a war. And that helps a total of zero students.


Quick Update:
I tried to engage Dr. Craigen in productive Twitter conversation, but he told me he wasn’t interested in pedagogy or the classroom–only educational change. 
I offered a space to offer longer responses, because I was losing control of my tweets as they filled with a one-sided, non-responsive rant every time. (I’d call it a response, but I don’t think he listened.)
I asked him to return to my questions once he cared about the teaching and learning of mathematics and not just the process of doing research mathematics. That is, after all, what the conversation needs to be about. 
Two of the last tweets he sent me said, “the goal of procedure mastery is less thought, more power” and “students don’t need detail“. Until these things change, I don’t think conversation can take root. 

2 replies on “Math Wars North”

When Craigen wrote that "the goal of procedure mastery is less thought, more power," I believe he is echoing Alfred North Whitehead: "It is a profoundly erroneous truism … that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them."

As well, I think you misrepresent Craigen when you suggest that he does not care about the learning of mathematics; I believe that he does care deeply.

calida rationalitas,

I think there is a big difference between knowing that something is true, and coming to know how something is true. Mathematics education is interested in the latter. My exchange with Craigen was missing this distinction. Memorized facts need to have histories beyond rote recall.

For this reason, I believe his focus lies in educational policy and not in the teaching and learning of mathematics. I asked him how the classroom would operate if influenced by his ideas, and he told me that it didn't interest him that much. That is where my conclusions come from. My impression was that he had a deep seated care, but inexperience in the actual educative process (and general disrespect for those with it) made it a misguided passion.

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