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Research & Evidence · 2026

Derivita & The 2 Sigma Problem

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

In 1984, Benjamin Bloom proved one-on-one tutoring produces the largest learning gains ever documented. He called finding a scalable version of that the defining challenge of modern education. Derivita was built to answer it.

+2σ
Bloom's Ceiling
One-on-one tutoring produces a +2 standard deviation gain — the largest ever documented in education research.
+0.41σ
Derivita's ESSA Result
+0.37–0.45 SD gain across a 50,000-student district. Third-party verified. No prescribed implementation model.
More Effective
The largest published effect size for point intervention products is 0.14. Derivita's is 0.34–0.45. It's not close.
The Problem · 1984

Bloom proved 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 called it the 2 Sigma Problem — not because 2 sigma is the limit, but because we already know it's possible. The problem is we can't afford to do it for everyone.

His follow-on question — the one that has driven education research for 40 years — was: can group instruction ever approximate what a great tutor does?

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.

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 addresses
 
Variables Derivita supports indirectly
Variable Effect Size How Derivita Addresses It
Feedback-corrective
 
1.00 / 84th %ile
Core CAS function — error-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
Homework (graded)
 
0.80
Auto-graded open-ended homework with instant results — not just right/wrong
Student classroom participation
 
1.00
SpotCheck drives whole-class discourse and Building Thinking Classrooms workflows
Higher order questions
 
0.30
CAS enables open-ended questions competitors can't ask — or grade
Cooperative learning
 
0.80
PLC common assessments with automated aggregation and comparison reporting
New science & math curricula
 
0.30
Derivita supports any curriculum. Switching alone moves the needle far less than changing teaching practice.

Variables Derivita directly addresses  ·  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."

Sales Team Training · May 2026

Technology didn't make Bloom's list in 1984. Not because technology doesn't matter — but because technology that doesn't change teacher practice doesn't move the needle. Derivita was designed around the variables that do.

The Mechanism

Why 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

The three outcomes correspond to Bloom's feedback-corrective mechanism — the highest-impact alterable variable (1.00σ) short of one-on-one tutoring.

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 someone else wrote.
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
D-type variables, teacher-led
Bloom's highest-impact variables are teacher-driven. Derivita automates the data infrastructure — PLC reports, common assessments, blueprint analytics — so teachers can change their practice without changing their workload.
District Impact Calculator

What would this mean
for your district?

The ESSA Level III study found that good teaching practices enabled by Derivita — PLCs, formative homework, common assessments — naturally result in one additional question per day. That's not a prescription. It's what happens when teachers engage with the platform. Enter your district size to see what the research suggests.

1
Set your baseline percentile
Where your students perform today (default: 50th)
2
Slide to see projected impact
Additional Derivita questions per day above your current baseline
District average — default is 50th (national median)
1 / day 5 / day
1 additional question per day

The ESSA study found teachers using PLCs, formative homework, and common assessments naturally averaged 1 additional question/day — without being told to.

↓ Your Projected Impact

With 1 additional Derivita question per day, students at the 50th percentile would be expected to reach the 63rd percentile — an above-average outcome driven by good teaching practice.
63rd
Projected average percentile
+0.33σ
Standard deviation gain
 
 
Before Derivita
 
With Derivita

Progress toward Bloom's 2 Sigma ceiling

 
0σ (Baseline) +0.33σ (Your district) +1σ (Mastery) +2σ (Bloom's ceiling)

* Based on 2026 ESSA Level III study findings (+0.33–0.45 SD per additional question/day). Individual district results vary. Gains are associated with good teaching practices enabled by Derivita — not from software alone.

The Evidence

Independent research.
Not vendor math.

We didn't tell teachers to assign one more question a day. We taught them about PLCs, formative homework, and common assessments. The additional questions were a natural byproduct of good teaching practice. Then a third-party research firm measured what happened.

The study covered 50,000+ students across a full school year with strong statistical controls for prior achievement and teacher effects. Not self-reported data. Not vendor-claimed outcomes.

ESSA
IV
ESSA Level IV — Logic Model
Research-based logic model showing how Derivita's instructional design leads to improved math outcomes
ESSA
III
ESSA Level III — 2026 Study
+13 percentile point gain. +0.37–0.45 SD. 50,000+ students. Independent third-party researchers.

The largest published effect size for point intervention products is 0.14. Derivita's is 0.34–0.45 — as a supplemental tool with no prescribed implementation model.

Read the Full Study
Request a Quote

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