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Derivita & The 2 Sigma Problem

Bloom named the problem. Here's what solving it looks like for your district.

In 1984, Benjamin Bloom demonstrated that one-on-one tutoring could produce two standard deviations of improvement over conventional instruction. His follow-on question became the defining challenge of modern education: can we achieve outcomes like that at scale? Derivita was built to answer it.

+2σ
What's Possible
Bloom's tutoring study demonstrated two standard deviations of improvement is achievable. Not a ceiling — a proof of what's possible.
+0.34σ
Derivita's ESSA Result
+0.34 SD gain. 1,647 students, 17 teachers. Third-party verified. No prescribed implementation model.
+13
Percentile Points
Teachers whose practice naturally integrated Derivita saw their students score 13 percentile points higher than comparable peers — verified by independent researchers.
The Problem · 1984

Bloom demonstrated what's possible. The question was always scale.

Benjamin Bloom ran a controlled experiment with identical students, identical materials, and identical time. The only variable was the learning condition. One group sat in a conventional classroom of 30. Another worked one-on-one with a tutor.

The tutored group outperformed 98% of conventionally taught students — two full standard deviations above the mean. Bloom was explicit: two sigma is not a ceiling. It's a demonstration of what's achievable. The problem is the cost. One-on-one tutoring at that scale is out of reach for almost every school system on earth.

His follow-on question — the one that has driven education research for 40 years — was: what can we do at scale, and affordably, to close the gap between conventional instruction and what we know is possible?

Bloom's Three Conditions

+2σ shift → Conventional Mastery (+1σ) Tutoring (+2σ)

Same students. Same time. Same materials. The tutored group's average student outperformed 98% of the conventionally taught group. Notably, the distribution also narrowed — students clustered closer to the higher mean, meaning fewer were left behind.

Bloom's Table I · The Map

He didn't just name the problem. He mapped the solution.

Bloom identified the alterable variables that most move student achievement — ranked by effect size. Most educational technology addresses the low-impact variables. Derivita was designed to address the high-impact ones. The variables marked below are what Derivita directly operationalizes.

 
Variables Derivita directly leverages
 
Variables outside Derivita's primary scope
Variable Effect Size How Derivita Leverages It
Feedback-corrective
 
1.00 / 84th %ile
Core CAS function — context-specific formative feedback on every student response
Cues and explanations
 
1.00
Dynamic worked-out solutions that motivate each step and connect prerequisite concepts
Student time on task
 
1.00
LMS-native integration drives daily use — 85%+ license utilization vs. ~10% industry average
Student classroom participation
 
1.00
SpotCheck drives whole-class discourse and Building Thinking Classrooms workflows
Homework (graded)
 
0.80
Auto-graded open-ended homework with instant results, not just right/wrong
Cooperative learning
 
0.80
SpotCheck enables whole-class mathematical discourse, including anonymous participation that reduces the friction of low confidence, so every student can engage in the conversation.

Beyond the classroom, PLC common assessments with automated data aggregation give instructional teams a shared data set to work from, extending cooperative practice to the professional level and turning teacher collaboration into a genuine collective practice rather than a comparison of individual impressions.
Higher order questions
 
0.30
CAS enables open-ended questions competitors can't ask — or grade
New science & math curricula
 
0.30
Derivita supports any curriculum. Switching alone moves the needle far less than changing teaching practice.

Variables Derivita directly leverages  ·  Source: Bloom, B.S. (1984), adapted from Walberg (1984).

Devlin Daley · Founder & CEO
"Derivita is drenched in good pedagogy. Absolutely drenched. We just disguise it as a math quiz."

Technology existed in 1984 — automated systems, programmed instruction, early adaptive tools. None of them moved the needle. Not because they were digital or analog, but because they didn't change what teachers did in the classroom. Derivita was designed around the variables that do.

The Mechanism

How Derivita's feedback loop is what Bloom was describing.

A great tutor doesn't hand you the answer when you're wrong. They recognize what you were trying to do, name the specific error, and send you back into the problem. That feedback is corrective, immediate, and tied to your actual thinking, not a generic hint. This is Bloom's highest-impact variable: feedback-corrective instruction, effect size 1.00. Derivita delivers it at scale, automatically, on every single response.

QuestionPresented StudentAttempts CASInterprets FeedbackDelivered Try Againor Mastery TeacherSees Data

Every student response leads to one of three outcomes: targeted feedback, a worked solution, or mastery — Bloom's feedback-corrective mechanism at scale (1.00σ).

Four Pillars · Built Around Bloom

Every design decision traces back to the same research.

01 · Question Design
Higher-order questions at scale
Built backward from the desired understanding. 150,000+ questions authored by mathematicians who understand both pedagogy and software. Bloom's Table I: effect size 0.30. Only possible because the CAS can grade them.
02 · Interaction
Students engage with real math
Live preview on every keystroke. Accepts mathematically equivalent expressions. Single input field for expressions and equations. Students construct and symbolically represent math — not select from a list.
03 · Response Processing
Feedback-corrective at scale
Interprets student intent, not just output. Error-specific feedback matched to what the student was trying to do. Dynamic worked solutions that connect prerequisite concepts. Silence when uncertain, by design. Bloom's Table I: effect size 1.00.
04 · Teacher Amplification
The teacher drives the outcomes
Bloom's research showed the highest-impact variables all require a teacher to change their practice — not a student, not a curriculum, not software alone. Derivita automates the data infrastructure, PLC reports, common assessments, and blueprint analytics so teachers can act on the right information without adding to their workload.
The Evidence

Independent research you can trust.

We built Derivita on a research-backed theory of action — a documented logic model showing exactly how expert question design, targeted feedback, and seamless integration with daily instruction translate into scalable math gains. Then we asked independent researchers to measure what actually happened in classrooms. The results held up.

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Bloom named the problem.
Let's solve it for your district.

Derivita brings mastery-based learning into the classroom at scale, inside the LMS your teachers already use, without adding to their workload.

Supplemental math · Grades 6–Calculus III · ESSA Level III & IV evidence · 26 states