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^"permissions":^"read":ӶӺ,"update":ӶӺ,"delete":ӶӺ,"admin":ӶӺ°,"user":^"id":6,"name":"Sarah Oberbichler"°,"id":"Jmpj0u7zw3","ranges":Ӷ^"start":"/divӶ3Ӻ/divӶ4Ӻ/divӶ1Ӻ/pӶ19Ӻ","startOffset":0,"end":"/divӶ3Ӻ/divӶ4Ӻ/divӶ1Ӻ/pӶ19Ӻ","endOffset":1675°Ӻ,"quote":"Both educational scientists and teachers in the field of mathematics education try to model the children’s mathematical reality and how that reality may be cognitively built up piece by piece. The first, the scientists, may be mainly interested in establishing the hard core of a mathematics learning theory that would be applicable to as large a number of children as possible, but the viability of that theory, to quote Lakatos again, depends on “confirmations or ‘verifications’ that sustain a scientific research program. ” Consequently, in order to “confirm” or “verify” their theory, the scientists must “test” it by observing individuals. But – and this is crucial from the cognitive point of view – the tests in this context do not primarily concern the level of performance of new children but rather the question of whether or not the model can be maintained in the face of observations and teaching experiments with new children. However, it is not only in the context of justification but also in the context of re-invention that the scientific investigators need to observe individuals. In order to formulate even the most tentative model of cognitive change, educational scientists must witness the growth of mathematical knowledge in particular children and clarify and substantiate their interpretations by means of deliberate interventions. Conceptual analysis alone is simply not sufficient as a source of insight in model building. It is only on the basis of models of particular children, that a more general model can eventually be abstracted – and the models of particular children are a natural bridge between educational scientists and the teachers.","highlights":Ӷ^"jQuery3210198867490764852772":^°°,^"jQuery3210198867490764852772":^°°,^"jQuery3210198867490764852772":^°°Ӻ,"text":"","category":"Argumentation2","data_creacio":1560273386304°
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