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^"permissions":^"read":ӶӺ,"update":ӶӺ,"delete":ӶӺ,"admin":ӶӺ°,"user":^"id":6,"name":"Sarah Oberbichler"°,"id":"Hdau9eyin5","ranges":Ӷ^"start":"/divӶ3Ӻ/divӶ4Ӻ/divӶ1Ӻ/pӶ28Ӻ","startOffset":0,"end":"/divӶ3Ӻ/divӶ4Ӻ/divӶ1Ӻ/pӶ28Ӻ","endOffset":1267°Ӻ,"quote":"The symbols used in mathematical computations designate operations that someone has to carry out. As Reuben Hersh put it: “Symbols are used as aids to thinking just as musical scores are used as aids to music. The music comes first, the score comes later” (Hersh, 1986, p.19). Even on the simplest level, for instance of 2+2=4, the symbol ‘2’ is meaningless for someone who has not abstracted the concept of ‘one’ from experiential items such as fingers, chocolates, or poker chips, and has then learned that sequences of these items can lead to the abstraction of compound units that are symbolized by ‘2’, ‘3’, ‘4’, etc. All other mathematical symbols similarly can be understood only by a thinker who knows and is able to execute the designated mental operations (cf. Steffe et al., 1983).\nAs for measurement, it, too, is contingent on the creation of units - units in the form of things to be counted or units of measurement to count ‘continuous’ items that are experienced without articulation of their own. In both cases it clearly is an active experiencer who creates the units. What is not so obvious, is that the discrete entities that are counted, as well as the continuous ones to which units of measurement are applied, are also an experiencer’s creation.","highlights":Ӷ^"jQuery321070364888847511052":^°°,^"jQuery321070364888847511052":^°°,^"jQuery321070364888847511052":^°°,^"jQuery321070364888847511052":^°°Ӻ,"text":"","order":"mw-content-text","category":"Argumentation2","data_creacio":1580152505784°
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