[ Towards . . .] A Geometry of Care*

Context -

"Introduction: We present a new model of skilled performance in geometry proof problem solving called the Diagram Configuration model (DC)." p.577.

INDIVIDUAL

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INTERPERSONAL    :     SCIENCES               

HUMANISTIC --------------------------------------  MECHANISTIC      

SOCIOLOGY  :   POLITICAL 

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GROUP

"A safe abstraction only ignores irrelevant details, i.e., details which only discriminate between objects that are functionally equivalent with respect to the problem solving task." p.582. DIAGRAMMATIC REASONING So much to consider here, I may be overstretching analogies but then Hodges' model can act as both a conceptual rack and resolver.

"For instance, to use the side-angle-side rule for inferring triangle congruence a problem solver must locate three congruence relationships - two between corresponding sides of the triangles and one between corresponding angles. In searching for a list of statements for these three relationships, one might need to consider numerous possible combinations of three statements that exist in the list. However, if these relationships are marked on a diagram, one can quickly identify them since the side-angle-side configuration comes together in each triangle at a single vertex. In other words, related information is often easier to find in a diagram because it is typically in the same locality whereas the same information may be separated in a in a list of statements. This is the locality feature of diagrams." p.584.

not just 'local' -

- but intra- interdomain - with constant stress on safety.

Koedinger, K.R. & Anderson, J.R. (1995) Abstract Planning and Perceptual Chunks. In  Diagrammatic Reasoning: Cognitive and Computational Perspectives. Janice Glasgow, N Hari Narayanan, B. Chandrasekaran (Eds.). Massachusetts: AAAI PRESS / MIT Press. pp.577-625.

Book cover: https://dl.acm.org/doi/book/10.5555/546459

*There may be several? But -

"One of the places where the Geometry tutor expert (GTE) gets bogged down while attempting difficult problems is in the fruitless application of algebra inferences. Algebra expressions can be combined and manipulated in infinite variety and as a result, algebra inferences often lead problem solvers into black holes in the search space from which they may never return." (17.4.3 Avoiding Algebra in the Diagram Configuration Space),  p.593.