The Research Behind How We Teach

The foundational principles behind LTB's approach: Bloom's 2-sigma problem (tutoring produces 2 standard deviations of improvement), expertise reversal effect, cognitive load theory, the learning styles myth, why memorization is a prerequisite for higher thinking, and explicit instruction as the default mode.

The single best explanation of spaced repetition: the forgetting curve (Ebbinghaus 1885), desirable difficulty, increasing review gaps, and the Leitner box system. An interactive 20-minute comic that every tutor should complete.

Two 2026 studies show students who dramatically outperformed controls on retention tests performed identically on application tests. Remembering a rule and being able to deploy it are different cognitive achievements separated by a "fluency threshold." Retrieval practice works best as maintenance of meaningful learning, not its creation.

Everyone talks about student cognitive load, but the teacher's working memory is equally the bottleneck. Pre-built, structured lessons aren't a crutch — they're a cognitive offload that frees the tutor's working memory for the highest-leverage work: noticing the student, responding to their thinking, and adapting in real time. This is why LTB builds structured curriculum instead of asking tutors to improvise.

Productive struggle is intellectual effort within a student's reasonable capability — not a hands-off approach. The Zone of Proximal Development defines the sweet spot between boredom and cognitive overload. Tutors must match task difficulty to capability, using enabling prompts for novices and extending prompts for advanced students.

A randomized controlled trial with 591 at-risk 1st graders showed speeded timed practice outperformed nonspeeded practice on arithmetic and 2-digit calculations. Speeded practice helps at-risk kids compensate for weak reasoning ability. The debate around timed tests is genuine, but the evidence for harm is thin — the evidence for benefit is strong.

A collection of real-world evidence: a 6th grade teacher got 80%+ of students to the 97th percentile with 30-40 problems/day. Alpha School gets 2.5x learning speed with math fact fluency. A tutor with 10,000+ hours confirms drill produces automaticity. Every piece of evidence points the same direction: high volume + timed practice + interleaved review + human support.

Math Academy's knowledge graph is a handcrafted DAG of thousands of math topics with prerequisite edges, built by domain experts (not AI). Their adaptive algorithm emulates an expert tutor at scale using four components: static knowledge graph, student knowledge profile, diagnostic algorithm, and task selection. This architecture inspired LTB's own knowledge graph plans.

Explicit, sentence-level writing instruction embedded in curriculum content is the most powerful lever for building knowledge. Writers' workshop is broken because it focuses on personal narrative and demands length too early. The fix: start with because/but/so expansions at the sentence level, build to paragraphs only after sentence strategies are in long-term memory.

A critique of "faux-cohesion" in curricula where units are organized around themes but lack actual knowledge-building. Cohesive content requires dependency (later texts build on earlier), recurrence (vocabulary reappears), progression (ideas deepen), and appropriate density. Judging a curriculum by individual texts is like judging a blanket by its yarn.

20 sentences demonstrating heteronyms (same spelling, different pronunciation and meaning) prove that phonics alone isn't sufficient for English literacy. Context, vocabulary knowledge, and meaning-focused instruction are essential alongside decoding. Especially relevant for ESL/ELL students we serve.

FASE reading (Fluent, Automatic, Self-monitoring, Expressive) is the gold standard for reading fluency. Automatic decoding frees working memory for comprehension. LTB measures reading progress in words per minute: 20 WPM in kindergarten, building to 150+ WPM by 5th grade.

A detailed audit of 4 LTB courses using cognitive science frameworks. Overall grade: B-. Five systemic gaps identified: no spaced practice across lessons (biggest gap), missing hints and scaffolding, cognitive load violations, no interleaving, and drill banks without pedagogical structure. This audit drove our curriculum redesign.

The strategic transformation from "free tutoring in any subject" to structured, curriculum-based math, reading, and writing courses for K-9. Driven by the need for measurable outcomes, tutor confidence, and donor accountability. Curriculum IS the session now, not a supplement.

A practical 3-phase plan to layer a knowledge graph onto LTB's existing platform: one new database table creating a DAG of prerequisite relationships, bootstrapped from existing course ordering, eventually enabling adaptive diagnostics and intelligent task recommendation. No rewrites, no big-bang migrations.

After a hand injury shifted his finger spacing and affected his shooting, Kobe Bryant made (not took) 100,000 shots in one summer. Not academic research, but the purest illustration that mastery requires purposeful, high-volume practice with precision and feedback. The next season the Lakers won their first of three straight championships.

Alpha School claims students master academics in ~2 hours/day using adaptive AI (really spaced repetition + mastery-based progression + immediate feedback) with human "guides" providing motivation. Key finding: math fact fluency produces 2.5x faster learning; without it, only 0.8x. The platform alone gets 1x growth — the human guide + culture bundle is what drives results.

A professor calling declining math scores "a positive thing." 98% of 8th graders reading below grade level. College freshmen who can't do middle school math. A 10th grade teacher quitting because students can't write a sentence. This collection of real examples shows why organizations like LTB exist.

Our core beliefs: phonics for reading (inspired by Mississippi's reading turnaround), The Writing Revolution for writing, memorized math facts as foundation, explicit instruction over discovery learning, and equitable access to quality education. Reading and memorized math facts are "the greatest equalizers."

The educators and researchers whose work directly informs how we build: Justin Skycak (Math Academy), Judith Hochman & Natalie Wexler (The Writing Revolution), Zach Groshell (Just Tell Them), Karen Vaites (curriculum advocacy), Carl Hendrick (learning science), Doug Lemov (Teach Like a Champion), Daniel Willingham (cognitive science of education), Barak Rosenshine (explicit instruction), and E.D. Hirsch (Core Knowledge).