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.