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?