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Sven Spöde Stefan Schneider Benjamin Angerer Alexander Blum
sspoede@uos.de stefschn@uos.de bangerer@uos.de ablum@uos.de

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If we do not want to believe that ideas are innate
or God-given, but the result of subjective
thinkers' conceptual activity, we have to devise a
model of how elementary mathematical ideas
could be constructed – and such a model will be
plausible only if the raw material it uses is itself
not mathematical.
(Ernst von Glasersfeld)

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Grounding
genesis of the first schemas

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20 20,5
Tagging Turn-Taking
16 25 23,5
Objects with
Distribution Slots
Alignment
Grounding
genesis of the first schemas

6. COUNT Abstraction
STUDY PROJECT psychological and mathematical ideas

7. COUNT Abstraction
STUDY PROJECT psychological and mathematical ideas
What is being Abstraction mechanisms
abstracted?
● temporal order ● Interiorisation
● rhythm ● Coordination
● alignment ● (...)
● neighbourhood
● successor

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number concept

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Clearly, in the head we do not have every
number (infinite instances) represented.
Instead, we have procedures to
operate with them. So whenever I face a
number symbol, I know what can be done
with it.
number concept

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Methodology
- research in theoretical literature
- integration with studies in developmental
psychology and mathematics education
- qualitative studies in problem solving /
formation of mathematical ideas in adults

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Outcome
in general: a mechanism that accounts for
the development of concepts
empirically motivated theoretical framework
bridging developmental psychology and AI

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Questions?