Why Crystal Caverns Works

The core mechanics in Crystal Caverns are tied to published evidence, and the evidence is sorted by strength. Green badges mark causal evidence: randomized trials and IES/WWC practice-guide recommendations. The guide panels grade each recommendation's evidence MINIMAL, MODERATE, or STRONG (minimal-evidence recommendations rest partly on panel expert opinion), and every section below prints the level it leans on. One more note: these studies test the teaching practices the game borrows, not this game itself.

The area square: n² is DRAWN as a real square with side n, every time

Concrete and semi-concrete representations are a STRONG-rated WWC recommendation (Fuchs et al., Rec 3; all six recommendations in that guide are rated Strong). In this game a square number is literally a square: players see WHY 9 is 3 by 3, so square roots become side lengths instead of magic symbols.

GUIDE Fuchs et al. (2021), WWC 2021006, Rec 3: concrete and semi-concrete representations (Strong).

Trapping √150 between pure crystals: locate it on the number line FIRST, compute second

The WWC fractions guide makes the number line the central representational tool and recommends estimating before computing (Siegler et al., Recs 2 and 3, both rated MODERATE). Note: that guide is about fractions; this game borrows the same magnitude-and-estimation logic for roots. Trapping √150 between √144 and √169 IS estimation: the player places the number on the line and brackets it between anchors before any arithmetic.

GUIDE Siegler et al. (2010), NCEE 2010-4039, Recs 2-3: number line as central tool; estimation before computation (Moderate).

Wrong options that are the documented errors (like splitting √(64+36) into 8+6), each explained on a miss

Randomized in-vivo classroom experiments in algebra found that studying and explaining incorrect examples alongside correct ones improved students' CONCEPTUAL understanding beyond correct examples alone (no differences were found on procedural measures). The game's distractors are the classic root-and-exponent mix-ups, and the feedback explains why each one fails.

RCT Booth, Lange, Koedinger & Newton (2013): randomized experiments with correct and incorrect examples (algebra classrooms).

REVIEW MISSED: the cave re-asks exactly what you got wrong

Re-exposure through quizzing (retrieval practice) is a STRONG-rated recommendation in the IES practice guide on organizing instruction and study (Pashler et al., Rec 5b). Review mode re-asks the exact problems a player missed instead of letting them scroll past the answer.

GUIDE Pashler et al. (2007), NCER 2007-2004, Rec 5b: quizzing to re-expose (Strong).

References

Booth, J. L., Lange, K. E., Koedinger, K. R., & Newton, K. J. (2013). Using example problems to improve student learning in algebra: Differentiating between correct and incorrect examples. Learning and Instruction, 25, 24-34.

Fuchs, L. S., Newman-Gonchar, R., Schumacher, R., Dougherty, B., Bucka, N., Karp, K. S., Woodward, J., Clarke, B., Jordan, N. C., Gersten, R., Jayanthi, M., Keating, B., & Morgan, S. (2021). Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades (WWC 2021006). Washington, DC: National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education.

Pashler, H., Bain, P. M., Bottge, B. A., Graesser, A., Koedinger, K., McDaniel, M., & Metcalfe, J. (2007). Organizing Instruction and Study to Improve Student Learning (NCER 2007-2004). Washington, DC: National Center for Education Research, Institute of Education Sciences, U.S. Department of Education.

Siegler, R. S., Carpenter, T., Fennell, F., Geary, D., Lewis, J., Okamoto, Y., Thompson, L., & Wray, J. (2010). Developing Effective Fractions Instruction for Kindergarten Through 8th Grade (NCEE 2010-4039). Washington, DC: National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education.

All WWC practice guides: ies.ed.gov/ncee/wwc/PracticeGuides

This page makes no product-level efficacy claim: the studies test the teaching practices the game borrows, not this game. Full methodology, logic model, and claims register: numbercade.com/why-it-works.