Dragon Hatchery teaches a skill first, then has kids practice it, with no clock and no way to fail out. Every question about a graph shows the graph, drawn from the same numbers the answer is computed from, and every wrong option is a documented mistake (the middle of the unsorted list, the mode's count instead of its value, averaging two means of different-sized groups). Each design choice below implements a practice with independent research support. The studies test the practice, not this game; we make no product-level efficacy claim.
The median is taught as the middle dragon in a sorted line, and the mean as the level line when every dragon's fish are poured into one trough and shared evenly. The What Works Clearinghouse practice guide on mathematical problem solving in grades 4 through 8 recommends teaching students to use visual representations, and rates that recommendation STRONG evidence. The same guide's recommendation to prompt students to monitor and reflect during problem solving (the "write TOTAL = first" nudge on multi-step mean problems) is also rated STRONG.
GUIDE Woodward, J. et al. (2012). Improving Mathematical Problem Solving in Grades 4 Through 8 (WWC practice guide, NCEE 2012-4055), Recs 2 and 3. Evidence levels as printed in the guide.
Interview studies of fourth through eighth graders found that many children who could compute an average had no idea what it represented, and used "average" to mean the most common value or the middle, while a smaller group reasoned about it as a fair share or a balance point. The Feeding Trough teaches the fair-share meaning first and only then the procedure, and the Rival Hatchery world spends a whole set of lessons on when the mean misrepresents a typical value.
DESCRIPTIVE Mokros, J. & Russell, S. J. (1995). Children's concepts of average and representativeness. Journal for Research in Mathematics Education, 26(1), 20-39.
A widely cited review of graph comprehension research distinguishes reading the data (a single value off a bar), reading between the data (how many more, the biggest increase) and reading beyond the data (predicting from a trend, judging whether a claim is supported). The worlds are ordered that way on purpose: Nesting Grounds reads values, Flight Logs reads between them, and the Rival Hatchery reads beyond them, including axes that do not start at zero.
DESCRIPTIVE Friel, S. N., Curcio, F. R. & Bright, G. W. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32(2), 124-158.
Mean, median, mode, range, histogram, outlier and stem-and-leaf are test vocabulary, and the questions turn on the words ("at least", "how many more", "which measure changes"). The WWC guide on elementary math intervention recommends explicit instruction in mathematical language and rates it STRONG evidence for its population (students struggling with math). The Keeper's Field Guide gives each term a definition, an example and the specific trap to avoid.
GUIDE Fuchs, L. S. et al. (2021). Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades (WWC 2021006), Rec 2.
Each world's run mixes authored questions with generated ones, the boss mixes every measure at once, and the practice lobby serves endless fresh questions by topic. In a preregistered cluster-randomized trial with 787 seventh graders, interleaved math practice roughly doubled scores on a delayed test compared with blocked practice. The WWC organizing-instruction guide rates interleaving worked examples with practice MODERATE evidence.
RCT Rohrer, D., Dedrick, R. F., Hartwig, M. K. & Cheung, C.-N. (2020). A randomized controlled trial of interleaved mathematics practice. Journal of Educational Psychology, 112(1), 40-52. Pashler, H. et al. (2007). Organizing Instruction and Study to Improve Student Learning (NCER 2007-2004), Rec 2.
No study has tested this game itself. Lessons before challenges, visual models, explicit vocabulary, mixed review and misconception-driven distractors are the design principles borrowed from the research above; the dragons are ours. See numbercade.com/why-it-works.