Mathematics Problems before techniques
Math is problem-solving. Everything else is bookkeeping.
Most school mathematics runs backward: name the technique, demonstrate it, assign twenty near-copies of the demonstration. Children learn to pattern-match, and the first unfamiliar problem — on the Regents, on the SHSAT, in life — exposes the whole arrangement. We run it forward. Our classes work on the Art of Problem Solving curriculum — the books the strongest young mathematicians in the country actually use — where the problem comes first and the technique is discovered under pressure, then named, then practiced to fluency.
That takes a class of twelve, and it takes a teacher trained not to rescue too early. Being stuck is the lesson. What we add is the discipline our whole school is built on: fluency is trained deliberately — mental arithmetic and estimation drilled in Mental Arts until they are reflexes — and nothing is finished until it’s proved. “Prove it, then prove it a second way” was the standard in this city’s arithmetic books in 1825, where a problem could end “the remainder will be just 1000. Try it and see”; it is our standard now.
Gr 6
Prealgebra
AoPS Prealgebra, problem-solving seminar, mental arithmetic to reflex.
Gr 7–8
Algebra
AoPS Introduction to Algebra; Regents Algebra I sat when the mastery bar is met — not before, not later.
Gr 9
Geometry
AoPS Geometry → Regents Geometry; proof becomes the daily medium.
Then
Past the Regents
Algebra II onward — toward the proof-based and competition work selective colleges actually notice.
English Language Arts Whole books, daily writing
Reading whole works. Writing as thinking.
The anthology excerpt is the worksheet of literature — eight pages of a novel, three comprehension questions, next unit. We don’t use them. Our students read whole books, in volume, on a schedule that assumes they can: novels front to back, primary documents in the original, essays worth arguing with. Close reading gets its power from scale — you can only see what a chapter is doing if you’ve read the other twenty.
And writing happens every day, because writing is not how you report thinking — it is how you do it. Drafts get workshopped aloud and revised; grammar and vocabulary live in the spaced review queue, not in worksheet units that end on Friday; and every term, each student defends their reading out loud — the seminar table and the oral defense being the direct descendants of the public Examination Days on which this school’s tradition was built.
Gr 6
Whole novels
Novels front to back; weekly writing workshop; vocabulary on spaced review.
Gr 7
The research paper
First sourced research paper — claims, evidence, citation, revision.
Gr 8
Rhetoric
Close reading and rhetoric; Regents-level essay craft begins.
Gr 9+
Seminar
Literature seminar on whole works; the writing portfolio that follows a student to college applications.
A Tuesday The day, hour by hour — live online now, hybrid days from 2027
What Tuesday actually looks like.
Every class below is live and teacher-led — twelve students, cameras on, questions constant. Nothing is a video to watch later.
- 8:00
Arrival
The classroom opens — live, cameras on, twelve faces. The advisor takes attendance the way it will be taken every period, and spends two minutes on the only agenda that matters at 8 a.m.: who’s here, who slept, who’s stuck on something.
- 8:30
Mental Arts
First: fifteen minutes on the personal review queue. Every student works their own — the software schedules each fact and skill against that student’s own forgetting curve, so no two queues match. Then the day’s craft lesson: this week the class is building memory palaces for Living Environment terminology, and this morning each student walks a partner through their palace, room by room. The hour closes with a note-craft critique — one volunteer’s page of yesterday’s history notes on screen, the class improving it line by line.
- 9:30
Mathematics
The block opens with a problem nobody has been taught to solve. Not review — a genuinely unfamiliar problem, one notch past yesterday. Twelve students argue their way toward the technique for twenty minutes before the teacher names it; the wrong turns get as much board time as the right ones, because diagnosing a wrong turn is the skill. Then practice — and no answer is finished until it’s been proved a second way.
- 10:45
English
Twenty-five pages of the novel were read last night — the whole class, the whole book, no excerpts. The seminar opens with one question and the teacher mostly stays out of the way. Then a ten-minute write, and one paragraph — a volunteer’s — is workshopped aloud, sentence by sentence, until the class can say exactly why the revision is better.
- 12:00
Lunch
Off screen, at home — honestly, the least school-like hour of our online year. When hybrid days begin in 2027, lunch happens out in the city.
- 12:45
Sciences
Same engine, different discipline: retrieval check on last week’s material first, then new ground, then the lab notebook — this term’s at-home kit is optics, and today’s entry gets checked against the standard the Regents will eventually hold it to.
- 2:00
History & civics
A primary source on screen — a real one, the scan, not a textbook summary of it. Students interrogate it the way Mental Arts taught them to interrogate any claim: who wrote this, for whom, and how would we know if it were wrong?
- 3:15
Studio
The rotation — arts, code, PE — lighter in tone, held to the same habit: make something, show it, defend it.
- 4:00
Dismissal
The loop closes at home: tonight’s review queue is about ten minutes long — ten, not sixty, because spaced review done daily never needs to become cramming. That is the whole trick, and it’s the one most schools leave to Kumon.
None of this is exotic — it is what strong teaching looked like before packets, and what it still looks like wherever families can buy it by the hour. The only unusual thing we do is put all of it inside the school day, for every student, and hold ourselves to the result: 90 or better, in every Regents subject, for every child.