01 The problem
A 40% pass rate on a test that gated the trade
YouthBuild programs serve young adults who left high school, combining a path back to a diploma with construction trades training. At my site, students preparing for the carpenters union entrance exam had to pass a math test to get into the trade. The pass rate was 40%.
The instruction they’d received — like most students nationally — followed standard textbook procedure: memorize the steps, don’t ask why they work. For arithmetic with whole numbers, fractions and decimals, that method is notoriously fragile. Students who never learned why an algorithm works have nothing to fall back on when they misremember a step, and under exam pressure, misremembering is exactly what happens.
I rebuilt the instruction from definitions rather than procedures, using the framework I learned studying under H. Wu at Berkeley — every algorithm derived from what the numbers actually mean, not memorized as a sequence of moves. My first cohort’s pass rate went from 40% to 80%.
I applied that fall with that result as the basis of my application, and was selected as one of five YouthBuild USA National Fellows — drawn from a network of 270 sites — to spend a year developing an independent project.
02 The audience
Two audiences, a year apart
Easy to collapse into one, but they needed different things.
First: my own students
Young adults, many with a history of feeling failed by math instruction, working toward a specific, high-stakes credential with a fixed test date. They didn’t need enrichment. They needed to pass.
Second, a year later: instructors at other sites
The fellowship group — myself and four other fellows, working alongside the YouthBuild USA executive director for the full year — chose construction math as the national focus for a specific reason: the majority of YouthBuild sites run carpentry tracks. A math curriculum built around that trade had demand across the network before a single packet was written. That’s a network-level audience decision, not a classroom-level one.
But I wasn’t teaching those instructors directly. I was designing something they could pick up and teach for themselves, most with no exposure to a definitions-first approach and no support from me afterward. That constraint shaped everything about the build.
03 The design
Derive the algorithm; don’t decorate the procedure
The instructional problem, restated: standard procedural teaching of arithmetic — whole numbers, fractions and decimals, across all four operations — produces exactly the fragile, forgettable knowledge that shows up as failure under test pressure. The fix isn’t a better mnemonic. It’s teaching the algorithms as things that are true, derived from definitions, rather than steps to be remembered.
Three things followed from that.
Sequence over speed
Every algorithm had to be built in a logical order. You can’t derive fraction multiplication from a definition of a fraction the student hasn’t internalized yet. The sequence mattered more than covering material quickly.
Re-teaching the teacher is a different design problem
The instructors picking this up at other sites were mostly not math specialists. They needed the “why” made explicit for themselves first, in the packets, or they’d default back to procedural teaching by habit within a month. The materials had to teach the teacher the definitions, not hand them a lesson plan to perform.
No authoring software — the constraint that set the format
At the time I had no curriculum-authoring tools and no way to typeset mathematical content efficiently. Everything was compiled by hand into printed packets. That pushed the design toward something durable and low-tech: a teacher at any site, with no login and no software, could open the packet and teach directly from it.
In hindsight That portability was an asset, not just a limitation. The packets worked in buildings where nothing else would have.
04 The build
Packets that taught the teacher and the student at once
The deliverable was a set of hand-compiled instructional packets covering the correct, definitions-first derivation of every basic algorithm: addition, subtraction, multiplication and division, across whole numbers, fractions and decimals.
Each packet did two jobs simultaneously. It taught the mathematical reasoning behind the algorithm, and it modeled how to teach that reasoning — because the person reading it was as likely to be an instructor encountering the method for the first time as a student.
At the January fellowship presentation — with the YouthBuild USA executive director present, having tracked the project all year as one of the people who selected the fellows — the response was that this needed to go national. That wasn’t a first impression. It was a decision made with a year of context behind it.
At the national conference I introduced the work in two parts: a large-group session to a few hundred attendees, then breakout rooms that most attendees eventually rotated through. I grounded the presentation in the evidence that mattered most — before-and-after samples of actual student work, showing the same students’ reasoning change once they were taught the algorithm from its definition rather than as a memorized procedure.
From there the curriculum became available on demand to every YouthBuild site in the country. Not a one-time handout at a single event — standing national distribution. Any site with a carpentry track could request and receive the full set.
05 The result
One measured outcome, and one honest gap
At my own site the result was direct and measured: a 40% to 80% pass rate on the carpenters union entrance math exam, one cohort to the next, following the redesign.
The national result is real but different in kind — selection as one of five fellows from a 270-site network, an executive sponsor who backed the work after tracking it for a year, a national conference session and breakout series reaching several hundred attendees, standing distribution to any site that requested it, and press coverage of the methods.
What I can’t claim I have no post-distribution data — no pass rates from the sites that requested and used the packets. Tracking outcomes at adopting sites was never built into the fellowship, for any fellow’s project. The model relied on trickle-down: re-educate the instructor, trust that it reaches the student, with no return channel to confirm it did. That’s a real limitation of the design, not a footnote. It’s why I report the classroom result with confidence, the reach of the distribution clearly, and its downstream outcomes as unknown rather than assumed.
06 What I’d change
Three things, in order of how much they’d matter
Build the feedback loop into the distribution
The packets went out to every requesting site nationally and what happened after was never tracked. A version two would include a simple return mechanism — even a short survey from adopting sites — to close the loop the way I could in my own classroom, where the pass rate told me directly whether it worked.
Add lighter-weight teacher scaffolding
The packets taught the “why” well to a self-motivated reader. A short facilitator guide — how to introduce this to students who’ve spent years being taught the opposite way — would have made adoption more consistent across instructors with different comfort levels.
Stop hand-compiling
Correct at the time, and the first thing I’d change now. The same content with proper mathematical typesetting, a searchable digital format and easier per-site customization would spread further and hold up better than paper. That gap is what led directly to correctmath.io — the same definitions-first method and the same belief that procedural textbook instruction is fixable, rebuilt as a web system instead of a stack of packets.