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Independent research · Active development · Las Vegas, NV

Available for work — ed-tech, research, curriculum development

Students & teachers Researchers, engineers & employers

Adaptive learning
built from
first principles.

The Lacefield Pedagogical Framework is a formally documented system for how mathematical understanding develops — built from seven years of direct classroom research, now being implemented through an AI-assisted adaptive learning platform. The tutoring practice is the research environment.

Read the framework documentation → White papers & academic work Available for work →
7years classroom
research
11published
white papers
361concept nodes
mapped
state avg GED
pass rate, 2014

Start here

Employers & collaborators

Available for work now

Ed-tech, research, curriculum development, consulting. See what I bring and what I'm looking for.

Researchers & academics

11 white papers + tech spec

Full documentation of the framework, evidence base, and adaptive system architecture.

Students

Research participants

The tutoring practice is the research environment. Students who participate generate the data that trains the adaptive system.

Tutors & Teachers

Join the research program

Implement the framework with your own students. Co-generate the research data. Early participants shape the platform.

Who built this

Gregory Stuart Lacefield — independent researcher and former GED instructor. No university, no institution. Self-taught mathematician. Las Vegas, NV.

Full author record →

Where it came from

Seven years GED instruction, Florida DOC. 9 of 90 statewide GEDs in first 6 months of 2014 overhaul. 44% first-attempt pass rate. No internet, no textbooks, mixed-ability classroom.

Full origin account →

Evidence base

Independently derived principles validated against cognitive load theory, productive failure research, spaced retrieval meta-analyses, and schema acquisition literature.

Framework provenance →

The system

Not a product.
A research program.

The goal is a precision adaptive learning system that does what no institutional platform will build: diagnose the exact schema failure responsible for a student's errors, generate problems calibrated to their specific cognitive state, and iterate with the precision of a well-trained human tutor.

The framework was developed independently — without access to formal educational literature — from direct observation of what actually produces durable mathematical understanding. It has since been validated against existing research in cognitive load theory, schema acquisition, and productive failure.

The platform is in active development. The first implementation runs through human tutors. That is intentional: the tutor-administered sessions generate the training data that will make the automated system precise.

AI-assisted methodology documentation →
01 — For students

Schema-level diagnosis, not symptom treatment

Every session begins with a structured intake that identifies where understanding is genuinely sound and where it is corrupted or absent. Work starts at the actual schema floor — not where the student should be.

02 — For tutors

A documented framework that makes instinct precise

The methodology gives tutors the diagnostic language, concept maps, and session structure to implement adaptive instruction consistently — not dependent on years of accumulated intuition to develop independently.

03 — For research

Every session generates data that refines the system

Early tutors who implement this framework are co-generating the research data that will train the adaptive engine. This is applied education research — with real students, real outcomes, real data.


Ten principles the
framework is built on.

Each emerged from observation, not theory. Each has a corresponding body of evidence. Each has a published white paper.

Performance vs. understandingStudying to pass a test and studying to understand are distinct cognitive modes requiring different practice structures. Conflating them produces students who can neither perform reliably nor understand durably.
Reading as mathematical foundationOriginal correlation analysis on 130+ students showed reading comprehension predicts applied math performance more reliably than language arts scores. Most math errors in word problems are language errors upstream of the mathematics.
Productive struggle — calibratedCore practice targets ~80% success rates. An additional 15–20% reinforces mastery. The ratio reflects the cognitive conditions under which learning consolidates — not aesthetic preference.
Foundational fluencySingle-digit arithmetic, multiplication tables, and fraction operations must achieve automaticity. Slow basic computation consumes working memory needed for higher-level reasoning.
Precision of definitionImprecise definitions produce unstable understanding that collapses under novel conditions. Every concept is traced to its definition before procedures are introduced.
Incorrect correctionTelling a student they are wrong when their reasoning is sound causes more lasting damage than the original error. Evaluation must distinguish wrong reasoning from imperfect notation.
Confidence as variableConfidence is not a personality trait. It is produced by specific conditions: accumulated evidence that effort produces results at appropriate difficulty levels. It can be designed for deliberately.
Perseverance over aptitudeFor the mathematical goals most students pursue, ordinary IQ differences are less predictive than sustained engagement. Students fail because they stop engaging before momentum develops — not because they cannot.
Active recall over passive reviewMemory is strengthened by retrieval, not recognition. Session structure begins with attempted recall before review. Delayed recall several hours later produces significantly stronger retention.
Mathematics as metaphysicsMathematics describes logically necessary relationships. Understanding this changes how students relate to the subject. Errors become logical contradictions to resolve — not random failures to accept.
Full framework documentation with academic citations →

Research participation

Recruiting tutors
and students for
early-stage R&D.

The first implementation of this system requires human tutors implementing the framework with real students. If you teach math or GED subjects and care about the structural mechanisms behind how learning works — I want to talk to you.

Tutors

What participation looks like

Implement the framework with your own students. Use the diagnostic intake protocol and Dynamic Learning Profile. Log session data using the published tutor manual. Early participants are acknowledged as co-researchers and shape how the platform develops.

Students

What you get

Tutoring from the framework directly — diagnosis-first, calibrated difficulty, schema-level instruction. First session is always free. If you have been told you simply aren't a math person, this framework was specifically built to address that diagnosis.

Las Vegas, NV · In-person & online

Start a conversation.

Whether you are a tutor interested in the research program or a student ready to try a different approach — call, text, or use the booking link. First session is free, no commitment required.


Subjects

Research subject areas.

The framework was built in a GED context and has been extended across all major mathematics subjects. Research sessions are available in these areas — each one implements the full diagnostic intake and DLP protocol.

GED / HiSET
GED Mathematics
Quantitative reasoning, algebra, geometry, data analysis
GED / HiSET
GED Language Arts
Reading comprehension, grammar, extended response writing
MATH-ALG
Algebra 1 & 2
Equations, functions, quadratics, systems — schema-first
PFD
Fractions, Decimals & Percents
The arithmetic foundation most students need rebuilt
CALC
Pre-Calculus & Calculus
Limits, derivatives, integrals — understanding before procedure
FLUENCY
Foundational Fluency
Arithmetic automaticity — the cognitive load reduction layer

Research participation
rates.

The tutoring practice is the research environment. Every session implements the full framework and generates data that refines the adaptive system. These are research participation rates.

$30
per hour · online
Online tutoring
Full framework implementation via video. Same diagnostic intake, same session protocol.
$160
5-session package
Research participant package
Includes full DLP build, progress tracking, and research data contribution.
Free
first session
Diagnostic intake
One hour. Schema assessment, reading baseline, fluency evaluation. No commitment.

Call or text: (702) 274-4299  ·  email: glacefield87@gmail.com

Background

Independent researcher.
Systems engineer.
Active tutor.

I am Gregory Lacefield — a self-taught mathematician, former GED instructor, and the designer of the Lacefield Pedagogical Framework. I have no formal university education. Everything I know — calculus through abstract algebra, statistics through differential equations, numerical analysis — was learned independently from primary texts, in environments with no internet, no professors, no graphing calculators.

I taught GED mathematics for seven years in Florida's correctional system. That environment was an unusually controlled laboratory: fixed resources, students ranging from 3rd-grade to near-college-ready in the same room, no access to formal educational literature. I built curriculum, designed diagnostic tools, and developed a theory of how learning works from first principles. During the 2014 GED overhaul — when statewide Florida completions collapsed — pass rates from this classroom ran at roughly twice the state average against a 150-point threshold later acknowledged as too high and reduced to 145.

The framework that produced those results is now being formally documented and built into a functioning adaptive learning platform. The tutoring practice is not separate from the research. It is the research environment — generating the data that will make the automated system precise.

Full background → Academic papers & white papers → AI methodology documentation →