Paper · October 2026 · pencil 0.1.0, MIT
Back to Paper, Done Properly: Seeded Versions, Fair Marking and Item Analysis for Printed Tests
The pencil contributors. Answer all questions. Every figure is computed by the library on this page.
Summary
A printed test has to do four things well that a screen did for the teacher: give neighbours different papers, keep every key in step with its paper, mark short answers fairly, and show afterwards which questions worked. pencil does all four from one plain-text test. Its item statistics equal an independent numpy implementation to within 2e-15. Its answer matcher marks 36 of 40 held-out answers as a teacher would, and wrongly accepts none.
Background
On 7 October 2026 the school board of Frederick County Public Schools, in Maryland, voted 6-1 to ban student use of AI from pre-kindergarten through grade 12, with exceptions for lessons about the technology and for students with disabilities [2][3]. Only weeks earlier the district had let middle and high school students use one AI assistant, Google's Gemini, with a teacher's permission; board members cited the lack of warning to parents, misuse elsewhere and the fact that teachers could not switch the tool off on student devices [2][3]. The president of the county teachers' association said some teachers were returning to paper-and-pencil assignments because they worried students would use AI to do the work [2]. The lone dissenting member warned that older students could be left less prepared for college [3].
Not connected. pencil, this site and $PENCIL have no connection with Frederick County Public Schools, its board, its teachers' association, Google or any school, and none of them has seen this paper. pencil takes no side on the ban; it is a tool for teachers who use paper, for whatever reason.
Versions
Questions are shuffled within each part and options within each question, by a small generator seeded with the test's seed and the version's letter, so a version can be rebuilt exactly. Options marked to stay in place ("none of the above") keep their position. Every version keeps a map back to the master. Over 4,000 shuffles of a four-option question the right answer lands in each position between 880 and 1,120 times (the tests check it).
Marking
Choice answers are compared by letter on the pupil's own version, then mapped to the master option, so wrong answers can be counted per master option. Short answers follow a policy fixed in advance (Question 7 on this page). The held-out set of 40 answers, each with the verdict a teacher would give, was written before the matcher: pencil agrees on 36. The four it gets wrong are all rejections of answers a teacher would accept: "5 centimetres", "in 1945", "seven", "the Nile". A matcher that is too strict sends work to a teacher; one that is too generous gives marks away, so the policy errs toward strict and lists every rejected answer for review.
Item analysis
For each master question: difficulty p (the share of marks earned), the upper-lower index D (top 27% of pupils by total minus bottom 27%), and the corrected point-biserial r (the question against the total of all other questions). For the test: mean, standard deviation, Cronbach's alpha and the standard error of measurement. Flags: very easy (p above 0.9), very hard (below 0.25), barely separating (r below 0.15), working backwards (r below 0), a wrong option nobody chose, and a wrong option chosen more than the key.
| Pupils | Mean | SD | Alpha | SEM |
|---|
On the simulated class, question 6 ("Which fraction is closest to 1/2?", where 2/5 and 3/5 are both 0.1 away) comes out with r = -0.20: the analysis finds the question with two right answers.
Limitations
The sample class is simulated from a simple ability model; it shows what the analysis can find, not how real pupils answer. Item statistics from one class of 28 vary a lot from class to class, so the flags are questions to look at, not verdicts. The matcher does not read number words, units written out or extra words, and because numbers match by value it cannot insist on "lowest terms". The same people wrote the policy, the held-out answers and the sample tests. pencil does not mark essays, and does not read scanned answer sheets.
Use
Write the test once; print two or more versions for neighbouring desks; keep the seed; mark from the pupils' sheets; look over the list of rejected short answers; then read the item analysis before using the test again.
References
- pencil 0.1.0, the library on this page (MIT).
- R. Thubron, TechSpot, 9 October 2026: the school district's U-turn on AI. techspot.com
- S. Lindström, Tech Insider, 10 October 2026: the Frederick County ban in all grades and the Gemini pilot. tech-insider.org
End of paper. Check your work.