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⛏️💎🔮

CRYSTAL CAVERNS

RADICAL MINING

Crack square roots. Charge up exponents.
Descend to the Deep Dark!

💎 🕯️ 🔮

WHO'S MINING?

💎
TEDDY
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🔮
TOBY
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⛏️ MINE SHAFT MAP
💎 0 ⭐ 0
MINER
🕯️
WORLD 1
Torchlight Tunnel
☆☆☆
-10m
🔊
WORLD 2
Echo Chasm
☆☆☆
-60m
🔮
WORLD 3
Geode Grotto
☆☆☆
-150m
⚒️
WORLD 4
Crystal Forge
☆☆☆
-320m
🌑
WORLD 5: BOSS
The Deep Dark
☆☆☆
-666m

Tap any world to jump there, even locked ones. Miners dig where they like.

WORLD 1 Pure Crystals ● ○ ○ ○ ○

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📚 THE RESEARCH

FOR PARENTS & TEACHERS: The core mechanics in Crystal Caverns are tied to published evidence, and the evidence is sorted honestly. TIER 1 lists 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 card below prints the level it leans on. One more honest note: these studies test the teaching practices the game borrows, not this game itself.

TIER 1: CAUSAL EVIDENCE (randomized trials and WWC evidence syntheses)
🎮 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.

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). Honest 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.

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.

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.

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

FULL 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

📝

GRAB YOUR
SCRATCH PAPER!

Real miners sketch the vein before they swing.

💎 CRYSTAL RUSH!

SCORE: 0 10

Tap the crystals when they pop up! 💎 = 3 points!

⛏️ TIME!

W1 Q1/6
❤️❤️❤️
💎 0

THE DEEP DARK DEFEAT THE WARDEN WITH RADICAL POWER!
WARDEN HP
5/5
VS
YOUR HP
3/3

WORLD 1 CLEARED!

💎 +0
👑

RADICAL MASTER!

You cleared all 5 caverns
and defeated the WARDEN!

0
GEMS
0
STARS
🏆 ISEE MIDDLE LEVEL READY!
🔮 REVIEW MODE Q1/5
⛏️ THE PRACTICE SHAFT

Endless practice with fresh crystals every time. No hearts down here. A wrong answer just teaches you and goes on your review list. Every correct answer earns +1 gem.

💎 Practice gems today: 0/15