The document describes the Prime Slaughter game, which was designed to teach mathematical concepts like prime numbers and factorization through play. It transposes abstract math ideas into a game where numbers are monsters that must be divided by swords representing their prime factors. A participatory workshop was held where kids interacted with the game and asked relevant math questions. Findings showed the game engaged players and supported learning as concepts became explicit through gameplay. The document concludes such games can effectively make abstract ideas concrete and allow playful exploration and experimentation to verify understanding.

1. The Prime Slaughter game
(and PlayDT)
Andrea Valente
(Medialogy)
Emanuela Marchetti
(Learning and Philosophy)
Aalborg University Esbjerg
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2. Our goal:
transpose abstract mathematical concepts into
playful visual interaction (e.g. games)
Focus on factorization and prime numbers…
because relevant and difficult to transpose
18/2 = 9
18/3 = 6
18/4 = X
...
9/2 = X
9/3 = 3
...
1 :D
2 :)
3 :)
4 X
5 :)
6 X
7 :)
8 X
...
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3. Survey of math games:
• computer-augmented
exercises
• exploratory/manipulative
environments
• very few genuine games
Number Ninjas
Refraction
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4. Our design:
• abstract concepts: visual representation of numbers
and their properties (e.g. primality)
as elements of the game
=
2
3
• procedural aspects:
goal-directed activities within game framework
& integral part of the gameplay
• support different forms of play (as from previous work)
-> kill AND grow
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5. The gameplay
• Numbers are monsters and swords
• Division as cutting
• Factorize: divide with the right sword(s)
Number 12 => 2*6, 6 => 2*3 => ...
=> 3*4, 4 => 2*2 => ...
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6. Walkthrough
http://www.greenfoot.org/scenarios/3870
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7. What we have done so far:
Start from participatory design results (MicroCulture)
Children adpot different forms of play
• military/strategy board-game play
• and designerly play
Used theories like apprentice in thinking (Rogoff)
• learning by engaging in goal-directed activities
within informal contexts
• children usually supported by adults
when reaching the boundary of their knowledge
Designed and implemented Prime Slaughter
Then we run a whole-day participatory workshop
to test the game, and collect feedback
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8. Findings
kids learning,
math relevant questions:
“what is the next prime number?”
“how can I/we define a prime number?”
interaction in the game,
engagement or frustration,
performance
makes epistemic assumptions
”every odd number is prime”
explicit
individual players were able
to play and get in flow,
pairs adapted to the UI in
creative ways
social interaction:
express emotional state,
talking & laughing & pointing
to indicate a playmate that an
action was required
teacher’s POV:
teaching aid (classroom),
clearer understanding of what each
student gets/find difficult,
better support individual needs
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9. Use cases
HOME
Learning:
self-directed
Individual or social
and/or network
2 versions:
PC & Tablet
SCHOOL
Traditional classroom teaching
But… math as an empirical study:
explore alternative hypothesis &
verify them through experiments
Learners move from cognitive to
experiential reflection
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10. Playful Domain-specific Knowledge Transposition
Based on MicroCulture, Prime Slaughter and other related work (e.g. 1D games)
Generalization:
a framework for the analysis and design of interactive games as media for learning
4 phases:
•
•
•
•
Analysis (concepts -> tasks)
Focusing
Analogy (narrative and mechanics)
Game design and creation
Theoretical background:
transposition
• structuralism and epistemology (Piaget and Papert)
• multiple modalities of play (Sutton-Smith)
• playful goal-directed activities (Rogoff )
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11. Conclusion
Is 15 prime?
a computer game can effectively turn
abstract math concepts and procedures
into a virtual artefact
learners can then probe it in a playful way,
explore alternative hypothesis and
verify them through experiments
2,3,5,7, ?
Guidelines are emerging towards a systematic
analysis and design of knowledge transposition games for playful learning
-> PlayDT (Marchetti, Valente and Jensen 2013)
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