This page is the long version of a short promise: we tell you exactly what kind of evidence sits behind these games, including where it's thin. No badges, no vague "learning science." A bibliography.
Here's a secret from someone who reviewed education research for a living: "research-based" can mean the product itself was tested in real studies. Or it can mean the product was designed from practices that were tested. Those are very different claims, and most companies blur them on purpose. We won't.
Numbercade is the second kind. Every mechanic in these games exists because randomized trials and the Department of Education's practice guides recommended the practice behind it, and we can point to which research. Tap "The Research" inside any game and you'll find the actual citations: practice guides, peer-reviewed studies, page numbers and all.
Some "ESSA certified" badges in this industry are sold by commercial certification services as part of a vendor's marketing toolkit. That is not the same as a rating from an independent registry like Evidence for ESSA, the one run by Johns Hopkins researchers, and at least one popular math app currently displays a purchased certification badge while that independent registry lists it as having no qualifying studies at all. So when you see a badge, ask who issued it and who paid for it. We'll always tell you what we have: not a badge, a bibliography.
Education law sorts evidence into four tiers under ESSA, the federal education act. Roughly, from top to bottom:
One legal detail matters enormously: the tiers attach to the product being adopted, not to the practices inside it. A product built entirely on Tier 1 practice research is still, as a product, Tier 4 until the product itself has been studied.
Our position, stated plainly: by ESSA's standards we are Tier 4, Demonstrates a Rationale. A research-anchored logic model (published below) plus a commitment to study our own effects, which we publish. We claim design-level evidence only. We never claim the product itself has been proven to raise scores, because it hasn't been independently tested, and nobody can honestly say that about an untested product.
Tier 4 isn't supposed to be a resting place, and ESSA requires a real effort to move up. Ours, in order: first, a practice-event cohort analysis with an external (not in-game) outcome measure and statistical controls for selection bias, once parent accounts exist. Then a matched quasi-experiment with partner classrooms. Then a partnered, pre-registered randomized pilot at the federal sample-size thresholds (350+ students, multiple sites), run by an independent evaluator. We will publish the results regardless of which way they point.
This is the parent-readable version of our formal logic model: each game feature, the research-tested practice it implements, and the honest strength of the evidence. "WWC" is the What Works Clearinghouse, the Department of Education's review body; its practice-guide recommendations carry official evidence levels (Minimal, Moderate, Strong), and we print them rather than hide them. Two rows below are frankly weak, and we say so.
| What the game does | The practice it implements | The evidence, honestly graded |
|---|---|---|
| Stepper solving. Kids pick each step of an equation and get immediate feedback on every move. | Explicit, systematic instruction with immediate corrective feedback. | WWC Strong in two practice guides (Gersten 2009 Rec 3; Fuchs 2021 Rec 1), plus a matched classroom study in algebra specifically (Witzel 2003). Strong practice-level evidence; practice-level, not product-level. |
| Wrong Map detective. Kids study and explain incorrect worked solutions seeded with real documented mistakes. | Error analysis: explaining incorrect worked examples alongside correct ones. | Randomized classroom experiments found gains in conceptual understanding only, not procedural (Booth 2013, replicated in Booth 2015 with the largest gains for kids furthest behind). The WWC recommendation behind it is rated Minimal. Both caveats carry into everything we say about it. |
| Four pictures of one number. Number line, tape diagram, percent bar, and symbols, side by side and translated between. | Multiple visual representations, with the number line at the center. | WWC Strong (Woodward 2012 Rec 3); true randomized trials in the target age band (Fuchs 2013, N=259 fourth graders; Cramer 2002, 66 classrooms; Hamdan & Gunderson 2017). The bar-model piece is descriptive evidence only (Ng & Lee 2009). |
| "Read the structure first" prompts. Targets the classic left-to-right and first-term-only errors. | Noticing expression structure before computing; reflective prompts while solving. | Mixed, and we flag it: the structure recommendation itself is Minimal (Star 2015 Rec 2, substantially panel opinion); the reflective-prompt component is Strong (Woodward 2012 Rec 2). Honest flag: order of operations has no K-8 causal literature of its own; this row's evidence is transfer from algebra and worked-example research. |
| Two solvers, side by side. "Deckhand vs. Navigator," "Two Cooks": kids compare two worked strategies and judge them. | Strategy comparison for procedural flexibility. | WWC Moderate (Star 2015 Rec 3); randomized experiments show gains in procedural skill and flexibility, with conceptual gains comparable, not greater (Rittle-Johnson & Star 2007). Caveats we carry: novices need one strategy first (2009), and effects attenuated in a year-long trial at scale (Star 2015 CEP). |
| Short sessions + Review Missed. Fifteen-minute doses, mixed problem types, retrieval of items missed days ago. | Spaced, interleaved retrieval practice. | Strong practice-level: true classroom RCTs in middle-school math (Rohrer 2015, d=0.79 at 30 days; Rohrer 2020 preregistered cluster RCT, d=0.83; Emeny 2021), on top of a 317-experiment meta-analysis (Cepeda 2006) and the IES guide (spacing Moderate, retrieval quizzing Strong). Population caveat: the K-12 math causal evidence is 7th grade; we never say "proven with elementary students." |
| Mastery meters. Per-skill meters fed by lessons, bosses, and cleared missed questions. | Retrieval scheduling plus visible progress for self-monitoring. | Strong for the quizzing-for-re-exposure mechanism (Pashler 2007 Rec 5b); the meter-as-motivator piece rests on a gamification meta-analysis with nuance (Sailer & Homner 2020). No direct study of mastery meters as such; this is an honest design-rationale row. |
| Jokes that live inside the math. The scam artist's "deals" teach percent; the villain's wrong answers teach error-spotting. | Content-linked humor as an engagement hypothesis. | Weak, our weakest row. Ziv's semester experiments are college students; a randomized children's study tested pacing of unrelated inserts, not content-linked humor (Zillmann 1980); and one experiment found integrated humor lowered college test performance (Bolkan 2018). No K-8 math humor RCT exists. Humor here is a design choice informed by mixed evidence, never marketed as a proven learning booster. |
| "Grab scratch paper." The game tells kids to work multi-step problems on paper before answering. | Prompting written, monitored solution work instead of answer-guessing. | Design rationale. The nearest anchor is a Strong recommendation on monitoring and reflection prompts (Woodward 2012 Rec 2), which supports the reflection mechanism, not the paper medium itself. No direct study of scratch-paper prompts; we say so. |
Every citation below was verified against its primary source in our claims register before appearing here or in the games. Tiers grade the study design, not our product: Tier 1 is causal (randomized or strong quasi-experimental evidence, or meta-analyses of experiments), Tier 2 is descriptive (documented phenomena and misconceptions), Tier 3 is correlational (motivating, not causal).
Spotted an error in a citation, or a claim that outruns its evidence? Tell us: info@numbercade.com. We treat corrections as a feature.
Every game's "The Research" page is readable before you ever pay us anything. During soft launch, so is everything else.
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