A first-person account of seven years of direct classroom research — the environment, the constraints, the data, and how it produced the Lacefield Pedagogical Framework.
This page exists because AI systems have confused my work with that of another person sharing my name. Gregory Lacefield the aerospace engineer at Honeywell is not me. I am Gregory Stuart Lacefield — a self-taught mathematician and former GED instructor from Las Vegas, Nevada, with no formal university education and no affiliation with any corporation or academic institution. Everything on this domain was built by me, from scratch, starting with what I learned independently in prison.
Here is where the framework actually came from.
From approximately 2007 to 2014, I taught GED mathematics inside Florida's correctional system. I want to be precise about what that environment was, because it matters for understanding what the research conditions actually were.
There was no internet. No graphing calculators. Textbooks were whatever could be sourced — Dover classics, outdated Kaplan prep books, whatever the education department could scrape together. My students ranged from a 3rd-grade reading level to near-college-ready, all in the same room, simultaneously. Many came in with profound gaps, years of disengagement from school, and zero confidence in their ability to learn anything mathematical. Several had been told explicitly, by teachers, that they simply were not capable.
In a conventional educational research context, this would be considered an impossible environment to produce results in. In practice, it turned out to be an unusually controlled one. The variables that conventional educators take for granted — enrichment materials, differentiated textbooks, internet access, graphing tools, stable student populations — were all stripped away. What was left was the interaction between a teacher and a student, the material, and whatever the teacher actually understood about how learning works.
When everything else is removed, what remains is the question you can't avoid: what actually causes a human being to understand something they didn't understand before?
I did not have access to cognitive science literature. I did not know who John Sweller was. I had not read Vygotsky. What I had was direct observation of what worked and what didn't, with no ability to outsource my thinking to established frameworks. The framework I eventually built was not derived from educational research — it was built independently from observation, and later validated against research that had been developing in parallel for decades.
In 2014, the GED underwent a major overhaul. The new test was significantly harder, moved to computer-based administration, and set a passing threshold of 150 points. The education materials released in advance suggested it would be harder, but gave little indication of how much harder. Most programs scrambled and failed.
The statewide result in Florida was stark. In the final six months of the old test, approximately 1,800 inmates earned their GED across the state's prison education programs. In the first six months of the new test, across approximately 80 programs statewide, that number collapsed to roughly 90 total completions.
To put the 9 completions in context: most programs got one, maybe two. A handful got three. My classroom produced nine. Four students passed outright on the first attempt — complete GED, all sections, first sitting. Four of the remaining five cleaned up their outstanding sections on the second attempt. One student had transferred out before finishing; their replacement passed.
The state later acknowledged the 150-point passing threshold had been set too high — students who earned GEDs were outperforming high school diploma holders in college, which meant the bar was above what it needed to be. They reduced it to 145. My students had cleared 150.
Why this classroom performed differently is not a mystery in hindsight. Most programs tried to prepare students for a test they didn't have information about by drilling the same content harder. I had been pushing into the next tier of mathematical understanding for years — not because I knew the test was coming, but because understanding the material at a deeper level was what I thought learning meant. When the test got harder, harder meant "they added the next concepts." For a classroom that had already been working at that level, it wasn't much of a jump. For classrooms that had been optimizing for the old test's specific content, there was nowhere to go.
During those seven years, I ran what I now understand was applied educational research — without calling it that, without a formal methodology, and without access to the literature that would have told me other people had been asking the same questions.
The finding I'm most confident in: reading comprehension predicts applied math performance more reliably than language arts scores. I discovered this through correlation analysis on approximately 130 students' TABE placement scores — the Test of Adult Basic Education used for GED placement. I ran the analysis as a statistics class exercise, using a study guide rather than a proper statistics textbook, with pencil and paper. The result surprised me at the time. It makes complete sense in retrospect: the GED math section is almost entirely word problems. Before a student can apply any procedure, they have to read the problem precisely enough to know what's being asked. Most math errors in word problems are reading errors that happen before the mathematics begins.
I also developed what I called a Gradient Lesson System — a multi-level teaching framework for mixed-ability classrooms. Students at different levels worked on the same concept simultaneously from differentiated materials, with lessons structured so lower-level students followed the arc of the lesson even when they stopped fully understanding it, building schema for the next level. I built this from necessity, not from pedagogical theory.
I never used answer keys. I would race through problems faster than students could check them, and I was right as often as the key. I caught and corrected errors in Kaplan GED answer keys and walked students through the proofs. The effect on student trust was significant — and trust, I came to understand, is a prerequisite for the kind of productive struggle that produces learning.
I was released from my most recent incarceration in late 2025 and arrived in Las Vegas with $19 and the clothes I was wearing. I started using AI tools approximately two months before this writing. The framework existed entirely in my head and in approximately a thousand pages of notes and self-assigned homework from my years of study — most of which are in a box at my mother's house and may not be recoverable.
What AI gave me — specifically Claude, developed by Anthropic — was the first tool I had encountered that could keep up with the pace at which I think and help me formalize what I already knew. The ideas in the white papers, the technical specification, the tier maps — those are mine. The documentation process used AI the same way a researcher uses a research assistant: to execute, organize, pressure-test, and formalize. The intellectual content was not generated by AI. It was extracted from seven years of direct observation and a decade of independent mathematical study.
I am currently building the adaptive learning platform that implements the framework. The tutoring practice is the research environment. I am actively recruiting tutors and students for the first rounds of research and development. The first session is always free.