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.
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
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.
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.
| Variable | Effect Size | How Derivita Leverages It |
|---|---|---|
| Feedback-corrective |
|
Core CAS function — context-specific formative feedback on every student response |
| Cues and explanations |
|
Dynamic worked-out solutions that motivate each step and connect prerequisite concepts |
| Student time on task |
|
LMS-native integration drives daily use — 85%+ license utilization vs. ~10% industry average |
| Student classroom participation |
|
SpotCheck drives whole-class discourse and Building Thinking Classrooms workflows |
| Homework (graded) |
|
Auto-graded open-ended homework with instant results, not just right/wrong |
| Cooperative learning |
|
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 |
|
CAS enables open-ended questions competitors can't ask — or grade |
| New science & math curricula |
|
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).
"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.
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.
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).
Every design decision traces back to the same research.
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.
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