Three sources of data on Mathematical knowledge are analyzed here in detail, leading to four main conclusions. First, reasoning principles underlying written and oral Mathematics appear to be the same. Second, there are diverse ways of understanding and using mathematical concepts which depend upon the cultural conditions under which Mathematics is practised. Third, schools transmit culturally perfected mathematical tools (such as numeration systems, algorithms, and formulas) and tend to make students good model-users but are perhaps carrying out this function at the expense of meaning. Fourth, Mathematics learning in daily life produces meaningful procedures which may, however, be of restricted applicability.
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