I, the ghost of Franz Kafka, having been provided with a keyboard, a blog password, and some instructions on how to use WordPress, shall now briefly summarize the system known as mathematics education.
1. Its Structure: The society’s children are gathered in a series of rooms, sorted by age. Each day, at a designated hour, an authority demonstrates certain rules for manipulating marks on paper, and then asks the children to imitate the performance. This process continues for roughly a decade.
2. Its Purpose: Three explanations are offered for this regime. It is justified as (1) useful for daily life, (2) necessary preparation for a small number of desirable technical professions, and (3) intrinsically beautiful.
From the child’s perspective, the third of these is verifiably false, while the first two can be dismissed as contradictory. (A commonplace practicality cannot also be the exclusive purview of elite technicians.) The inadequacy of these justifications suggests that, in the eyes of the authorities, no justification is necessary.
Still, as law and custom both mandate one’s participation, most children soon acquiesce. The cause of survival is better served by resignation than by resentment.
3. The Keeping of Records: To compel genuine effort, rather than mere passive compliance, the system employs an ingenious system of record-keeping.
At regular intervals, the children are instructed to perform the prescribed manipulations in silence, under strict time limits. During such a trial, to communicate with another child is a disqualifying offense. Performance under such conditions is recorded in a permanent file.
This file is later transmitted to the child’s parents (who provide food and shelter) and to prospective employers (who provide the means to purchase food and shelter). Students thus come to perceive an obscure yet definite connection between (1) their performance on math tests, and (2) their access to food and shelter.
The individuality of the assessment is crucial. Pitting children against one another, in zero-sum competition, helps to muffle and dissipate any revolutionary sentiment.
4. The Role of the Teacher: By maintaining the all-important records, the teachers wield significant influence over the child’s future economic opportunities. Interestingly, many teachers consider themselves to be low-level functionaries, issuing neutral and objective reports, wielding little if any true power.
Such denialism only makes their judgments more whimsical and dangerous.
5. Conceptual Understanding: When the children reach the late teenage years, the authorities may abruptly change the nature of the game. Instead of symbolic manipulations alone, they demand a more elusive virtue, known by several names (“comprehension,” “conceptual understanding,” “critical thinking,” and so on).
For the children, this baffling reversal violates years of training. They have fought bitterly to succeed under the old regime, and they regard the new one as an illegitimate foreign usurpation. At this juncture, the authorities inflict their last and greatest irony:
They judge the children to be incurious and narrow-minded, thereby attributing to the victim the qualities of the crime.
Not that I’m disagreeing with what you said, but I’m curious about your thoughts on how an individual teacher can make the system better?
To be clear, these aren’t really my views!
But if they were, then I’m not sure the teacher’s role is to make the *system* better. Seems to me the teacher’s role is to create a quiet space where students can learn and grow, tucked away from the system’s winds and rain.
Easier said than done, obviously! But in any case, I conceive of the teacher’s role as fundamentally local and personal – a duty to the students in their care.
Oh, dear, I really like this and it’s awful too and funny. My daughter just finished her first year teaching school, student teaching 8th grade. However, she and the math teacher were tasked with writing and teaching the first computer course to the 155 8th graders. This makes me hopeful, with her helping write a course one week and teaching the next. I got to be the clueless guinea pig who had to have four tabs open to follow what was happening. I was slow and my daughter would mutter “Well, that is not going to work.” I felt useful as well as clueless! She finishes the year this Friday, does a grad student course this summer and goes back for round two next year. They were virtual until late March, so now she has done some classroom too!
If one removes glasses from eyes, pods from ears, and hands from keyboard, reality begins to set in.
Take care, Franz. You may fall into Pandora’s Box.
Next, let’s explain phys ed using quotes from _The Metamorphosis_.
On the cramps experienced when trying to run a mile for the first time: “I cannot make anyone understand what is happening inside me. I cannot even explain it to myself.”
It can be very hard to get students to look again upon what they’ve learnt before with fresh eyes.
We call it “I know it because I’ve seen it before”.
It appears a difficult problem.
You can generalize this toward schooling in general.
The idea that learning may be a satisfying endeavor and an end in itself did not occur to me until my academic career was nearly over. Instead, school was something to be endured until I had reached an age at which it would no longer be required.
Yeah, I was hoping this little piece of writing would land as satire, but really, formal schooling is exactly the kind of bureaucracy that Kafka wrote so incisively about. I’m not really extending Kafka here, just weakly recapitulating him!
If music were taught like math, no one would sing. Imagine having rote scales and arpeggios for years before playing or hearing a tune.
1+1 : nursery rhymes :: Mozart’s Requiem : integral calculus
I believe undergraduate math courses ought to begin with an introductory lecture titled “How You’re Going to Have to Think in Order to Do Well in This Course.” That would have saved me a lot of time discovering for myself that I, though both curious and open-minded about math, was not going to get more than a C on a steep curve in Real Analysis even though I had breezed through Calc and Differential Equations. That step between pushing symbols around on the pages of an exam booklet and understanding much more abstract concepts is a steep one.