Friction

1 · What friction is

The friction of a block is how often its readers get stuck there. Classroom practice measures it by asking for the “muddiest point” [1] and revising before the next class [2]. The first design made it a rate, split by the reader's background:

$$g(u,a)=\min_{t\in\tau(a)}\ell_u(t),\qquad F_g(a)=\frac{\#\{u:\ g(u,a)=g,\ u\text{ commented on }a\}}{\#\{u:\ g(u,a)=g,\ u\text{ read }a\}},$$

for a block $a$, a reader $u$, the topics $\tau(a)$ the block uses, and the reader's level $\ell_u(t)\in\{0,1,2\}$ (new, working, expert) in topic $t$.

Table 1. $F_0$ (new readers) and $F_2$ (experts) and reading
$F_0$ (new readers)	$F_2$ (experts)	reading
high	low	missing background: add an example
low	high	a gap in the argument: re-check it
high	high	the block is badly organised

2 · Why it does not work here

Table 2. problem and consequence
problem	consequence
The denominator is never observed. A static page does not record who read a block, and recording it means tracking readers.	$F_g$ cannot be computed. Only comment counts exist, and they mix difficulty with popularity.
Too few readers. A handful of collaborators per level.	An observed $1/3$ is consistent with anything from 6% to 79% (figure).
It needs levels. $\tau(a)$ and $\ell_u(t)$ are the classification the design dropped, and self-assessed levels are noisy [3].	A topic map and level scale to maintain, for a noisy input.
Silence is ambiguous. No comment can mean understood, skipped, or gave up.	A low $F$ does not mean the block is clear.
Small counts identify people [4].	It could never be shown publicly anyway.

Upper and lower 95 percent Wilson interval bounds for an observed ratio of one third, plotted against the number of readers from 3 to 60. At 3 readers the interval is 0.06 to 0.79; at 30 readers it is 0.19 to 0.51. — 95% Wilson interval [5] for an observed $F=1/3$: even at 30 readers per level it spans 0.19 to 0.51.

3 · What to keep

Table 3. part and keep and instead
part	keep	instead
Rate $F_g(a)$	no	Number of open comments per block, as a badge.
Topics $\tau(a)$, levels $\ell_u(t)$	no	The reader summary written by the LLM (Prototype · G3).
New-reader vs expert reading	yes	For each thread, the bot uses the reader's summary to label it `missing-background` or `possible-gap`. A `possible-gap` goes to you.

This matches classroom practice: the instructor reads the muddiest-point cards one by one rather than computing a rate [1]. Reconsider a rate only with about 30 or more readers per level and an opt-in “I read this” button.

References

F. Mosteller. The “muddiest point in the lecture” as a feedback device. On Teaching and Learning (Harvard–Danforth Center) 3 (1989) 10–21.
G. Novak, E. Patterson, A. Gavrin, W. Christian. Just-in-Time Teaching. Prentice Hall, 1999.
J. Kruger, D. Dunning. Unskilled and unaware of it. J. Personality and Social Psychology 77(6) (1999) 1121–1134. doi:10.1037/0022-3514.77.6.1121
L. Sweeney. k-anonymity: a model for protecting privacy. Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems 10(5) (2002) 557–570.
E. B. Wilson. Probable inference, the law of succession, and statistical inference. J. Amer. Statist. Assoc. 22 (1927) 209–212.

problem	consequence
The denominator is never observed. A static page does not record who read a block, and recording it means tracking readers.	\(F_g\) cannot be computed. Only comment counts exist, and they mix difficulty with popularity.
Too few readers. A handful of collaborators per level.	An observed \(1/3\) is consistent with anything from 6% to 79% (figure).
It needs levels. \(\tau(a)\) and \(\ell_u(t)\) are the classification the design dropped, and self-assessed levels are noisy [3].	A topic map and level scale to maintain, for a noisy input.
Silence is ambiguous. No comment can mean understood, skipped, or gave up.	A low \(F\) does not mean the block is clear.
Small counts identify people [4].	It could never be shown publicly anyway.

part	keep	instead
Rate \(F_g(a)\)	no	Number of open comments per block, as a badge.
Topics \(\tau(a)\), levels \(\ell_u(t)\)	no	The reader summary written by the LLM (Prototype · G3).
New-reader vs expert reading	yes	For each thread, the bot uses the reader's summary to label it `missing-background` or `possible-gap`. A `possible-gap` goes to you.