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ORDER UP!

THE GRUB GALLEY

Every recipe is an expression.
Cook the steps in the RIGHT ORDER!

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WHO'S COOKING TODAY?

🍳 THE GRUB GALLEY

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👨‍🍳 COOK

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STATION 1

Prep Station

order of operations

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STATION 2

Parentheses Pantry

containers + powers

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STATION 3

Tray Service

distributive property

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STATION 4

Mix and Match

commutative + associative

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STATION 5: BOSS

The Critic's Table

mixed gauntlet + boss fight

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Tap any station to jump there, even locked ones. Cooks know the back door.

STATION 1 Lesson 1/4

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Order up!

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YOU'RE ON FIRE, COOK!

4 in a row! You clearly run this station.
Want to skip straight to the last order?

S1 Q1/6

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STREAK:

Question

🎩 THE CRITIC'S TABLE 🎩 IMPRESS THE GRIM GOURMET!

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YOU

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VS

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GRIM GOURMET

GOURMET'S DISDAIN

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Question

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SERVICE!

STATION 1 CLEARED!

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HEAD CHEF
OF THE HARBOR!

You ran all 5 stations
and won over the Grim Gourmet!

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TIPS

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STARS

🏆 ISEE ORDER OF OPERATIONS: READY!

🔮 REVIEW MODE Q1/5

🍳 THE PREP KITCHEN

Endless practice with fresh numbers every time. No hearts in the prep kitchen. A wrong dish just teaches you and goes on your review list. Every correct dish earns +1 tip.

💰 Practice tips today: 0/15

📖 THE COOKBOOK: MATH WORDS

📚 THE RESEARCH

FOR PARENTS & TEACHERS: Every mechanic in Order Up! is tied to published evidence, and the evidence is sorted honestly. TIER 1 lists causal evidence: randomized controlled trials and strong quasi-experiments that justify the game's instructional choices. TIER 2 lists descriptive research: studies that document the misconceptions the game targets (no causal claim needed to know an error is common). Where a source is descriptive, it is labeled as such.

TIER 1: CAUSAL EVIDENCE (randomized and quasi-experimental trials)

🎮 The wrong-chef kitchen: Lefty, Chef Rigatoni, and Basil serve botched dishes, and players find the bad line

Randomized in-vivo classroom experiments: studying INCORRECT worked examples, and explaining what is wrong and why, improved students' conceptual understanding of algebra beyond correct examples alone (no differences were found on procedural measures). Every error-analysis plate in this game is an incorrect worked example targeting a documented order-of-operations error.

Booth, Lange, Koedinger & Newton (2013): differentiating correct and incorrect examples.

🎮 Two Cooks side by side (left-to-right vs the real order), and smart-regrouping choices ("which pair makes 100?")

Randomized classroom experiment: students who compared solution methods side by side gained more procedural knowledge and flexibility, with comparable conceptual gains, than students who studied the same methods one at a time. The two-cooks lessons and the pick-the-easy-pair regrouping steppers are direct comparisons of strategies on the same problem, and each lesson teaches one method before comparing, since comparison helps most once students already know one strategy.

Rittle-Johnson & Star (2007): comparing solution methods.

🎮 The NEXT BITE stepper: read the expression's structure and pick WHICH piece computes next, before touching any arithmetic

The IES/WWC algebra practice guide is an evidence synthesis that grades each of its recommendations minimal, moderate, or strong; where trial evidence is thin, recommendations also rest partly on panel expert judgment. Recommendation 2, teach students to notice and use structure before manipulating, is a minimal-evidence recommendation reflecting expert consensus and emerging research. The stepper forces a structure decision on every single step, and wrong picks get a targeted explanation, not just a buzzer.

Star et al. (2015), Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students (NCEE 2015-4010), Rec 2.

🎮 Jokes that ENCODE the math: cookie-swapping for commutativity, trays that feed every item for distribution

The design basis is Ziv's two semester-long randomized experiments with college students (same instructor, same syllabus, only the content-related humor varied): humor groups scored significantly higher on the same final exams. Separately, randomized experiments with young children found well-PACED humorous inserts, unrelated to the lesson content, increased attention and information acquisition from educational TV; that supports attention and pacing effects, not content-linked humor itself. Honest caveat: experimental evidence on classroom humor in K-8 is thin, and one recent college experiment found integrated humor REDUCED learning. That is exactly why this game's humor follows strict content-linked guardrails: load-bearing jokes restate the concept, a joke option is never the correct answer, at most one per question, and never a defensible answer.

Ziv (1988): two randomized semester experiments, college students, content-related humor. Zillmann et al. (1980): randomized experiments, pacing of humorous inserts in children's educational TV. Bolkan, Griffin & Goodboy (2018): college experiments where integrated humor lowered test performance.

TIER 2: WHAT WE TARGET (descriptive research documenting the misconceptions)

🎮 The left-to-right chef (8 − 2 + 3 served as 3) and the rigid-PEMDAS chef (12 ÷ 4 × 3 served as 1)

Descriptive studies of students' structure sense in numerical and algebraic expressions document exactly these failure modes: treating expressions as a left-to-right stream, and treating the PEMDAS letters as six strict ranks instead of four. Descriptive: it tells us WHAT goes wrong; the game names both wrong chefs and lets players catch them in the act.

Linchevski & Livneh (1999): structure sense in numerical contexts. Kieran (1979): children's operational thinking with bracketing and the order of operations.

🎮 Basil's tray mistake: 3(x + 4) = 3x + 4, feeding only the first item

The same structure-sense literature documents students applying an operation to only the first term inside a grouping. The game teaches the tray model and the sliced-rectangle area model first, then serves the classic error as a plate to inspect. Descriptive, labeled as such.

Linchevski & Livneh (1999); Kieran (1979), cited via the later literature (Linchevski & Livneh is the load-bearing source).

📋 An honest note on the evidence base for this topic

We could find no randomized trials of order-of-operations training in grades K-8. The misconceptions are well documented (the descriptive studies above), and a recent preregistered experiment with 130 adults found the same misconceptions persist into adulthood and brief reminders are not enough to fix them. Direct training trials are lacking, so this game's design extrapolates from adjacent strong evidence on worked examples, error analysis, and structure, and we say so rather than implying trials that do not exist.

Eaves, Attridge & Gilmore (2025): preregistered experiment with adults, Learning and Instruction.

FULL REFERENCES

Bolkan, S., Griffin, D. J., & Goodboy, A. K. (2018). Humor in the classroom: The effects of integrated humor on student learning. Communication Education, 67(2), 144-164.

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.

Eaves, J., Attridge, N., & Gilmore, C. (2025). Misconceptions of the order of operations and associativity use. Learning and Instruction, 97, 102074.

Kieran, C. (1979). Children's operational thinking within the context of bracketing and the order of operations. In D. Tall (Ed.), Proceedings of the Third International Conference for the Psychology of Mathematics Education (pp. 128-133). Coventry: Mathematics Education Research Centre, Warwick University.

Linchevski, L., & Livneh, D. (1999). Structure sense: The relationship between algebraic and numerical contexts. Educational Studies in Mathematics, 40(2), 173-196.

Rittle-Johnson, B., & Star, J. R. (2007). Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations. Journal of Educational Psychology, 99(3), 561-574.

Star, J. R., Caronongan, P., Foegen, A., Furgeson, J., Keating, B., Larson, M. R., Lyskawa, J., McCallum, W. G., Porath, J., & Zbiek, R. M. (2015). Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students (NCEE 2015-4010). Washington, DC: National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education.

Zillmann, D., Williams, B. R., Bryant, J., Boynton, K. R., & Wolf, M. A. (1980). Acquisition of information from educational television programs as a function of differently paced humorous inserts. Journal of Educational Psychology, 72(2), 170-180.

Ziv, A. (1988). Teaching and learning with humor: Experiment and replication. Journal of Experimental Education, 57(1), 5-15.

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

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SCRATCH PAPER!

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🥞 FOOD FLING!

BASIL'S PANCAKE CATAPULT: THE BACK DOCK

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Drag back from the pan. Release to fling!