Kill it or grow itComputer game design for playful math-learning.
Andrea Valente (Medialogy)Emanuela Marchetti (Centre for Design Learning Innovation)
Aalborg University Esbjerg
Our goal● Transpose abstract mathematical concepts into playful visual interaction
● prime factorization● nice and formalized solution procedures -> algorithms● related to change of base, Gödel encoding, cryptography, ...● prime numbers are:
– central in number theory (fundamental theorem of arithmetic)– primality also leads to classical algorithms– fascinating artistic aspects -> charts, audio, ...
● ... but factorization is pretty abstract -> good challenge for transposition!
● playful visual interaction● there are plenty math-related games online and off● few have really to do with math● none have to do with abstract or procedural knowledge within math● How to proceed?
playful learning + visualization + interactivity = game(?)
What is there now?Three kinds of games were identified:
● computer-augmented exercises
● exploratory/manipulative environments
● very few genuine games
Our game?
+
Field studyour guidelines
● Findings from a one year Participatory Design process
● in cooperation with an after-school institution● a group of 25 children involved in co-designing a game about urban development
in history
● Aim:
● transposing historical processes into playful interactions● provide a more tangible grounding to abstract and dynamic aspects of
historical processes, whose meaning and implications are quite difficult to be grasped
● to support more engaging and playful forms of interaction
Field studytangible augmented-reality prototype
MicroCulture
prototype
● The focus with Prime Slaughter is on:
● playful interaction with mathematical processes● visual (instead of tangible) representation of abstractions (e.g. primality)
Play as a self-driven activity● Observations -> different forms of play
● some children adopted a form of military board games play (e.g. strategy games)
● others engaged in a form of designerly play, suitable for construction bricks or managerial games like SimCity
● Rogoff’s theory of apprenticeship in thinking● children learn by engaging in goal-directed activities within informal contexts● usually supported by adults when reaching the boundary of their current
knowledge
● For us:● computer games offer motivation and flow● peers or adults can help in solving/understanding a particular passage of a game
Visualization of operationsand make primality visible
1 2 3 4 5 6 7 8 9 10 11 12 13 14 ...
1 2 3 4 5 6 7 8 9 10 11 12 13 14 ...
1 2 3 4 5 6 7 8 9 10 11 12 13 14 ...
12
346
2 x 2 x 3
12 / 2 = 66 / 2 = 3
3 / 3 = 1
:(
Visualization of operationsand make primality visible
ObservationCounting in unary -> factorization becomes a
sort of folding/grouping...
3 x
3 x 2 x
3 x 2 x 2
Division as cutting
Multiplication as pruning
Primality and game mechanics
Additional visual clues!Size = # prime factors
Factorization as slaying monsters Factorization as pruning bonsai trees
Demo
What now + ConclusionsOur transposition works this way:
● abstract concepts: visual representation + elements of the game
● procedural aspects: goal-directed activities within game framework + integral part of the gameplay
● and support different forms of play -> kill AND grow
● Next: test prototype through a series of participatory workshops, involving children within our target group
● emergent play styles? Playability and actual support for learning? -> redesign● Experiment more and redesign:
● with interaction among elements of the game: monsters VS bonsais● multiplayer
What now + ConclusionsOur transposition works this way:
● abstract concepts: visual representation + elements of the game
● procedural aspects: goal-directed activities within game framework + integral part of the gameplay
● and support different forms of play -> kill AND grow
● Next: test prototype through a series of participatory workshops, involving children within our target group
● emergent play styles? Playability and actual support for learning? -> redesign● Experiment more and redesign:
● with interaction among elements of the game: monsters VS bonsais● multiplayer
http://www.greenfoot.org/scenarios/3870
Questions?
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