Presentation of the learning game "Kill it or grow it". http://vbn.aau.dk/en/publications/kill-it-or-grow-it(a2a13900-a0de-462a-ada2-29f8c8c0f68c).html

1. Kill it or grow it
Computer game design for playful math-learning.
Andrea Valente (Medialogy)
Emanuela Marchetti (Centre for Design Learning Innovation)
Aalborg University Esbjerg

2. 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(?)

3. What is there now?
Three kinds of games were identified:
● computer-augmented exercises
● exploratory/manipulative environments
● very few genuine games
Our game?
+

4. Field study
our 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

5. Field study
tangible 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)

6. 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

7. Visualization of operations
and make primality visible
1 2 3 4 5 6 7 8 9 10 11 12 13 14 ...

8. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ...

9. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ...
12 / 2 = 6
6/2=3 2
3/3=1 1 6
2x2x3 4
3
:(

10. Visualization of operations
and make primality visible
Observation Division as cutting
Counting in unary -> factorization becomes a
sort of folding/grouping...
3x
Multiplication as pruning
3x2x
3x2x2

11. Primality and game mechanics
Factorization as slaying monsters Factorization as pruning bonsai trees
Additional visual clues!
Size = # prime factors

12. Demo

13. What now + Conclusions
Our 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

14. What now + Conclusions
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Questions?
● 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