This work examines some aspects of the problem of interpretation of mathematical understanding. Starting with the specific configuration of one of the basic context where this problem arises, a proposal for the interpretation of learning for understanding is developed. The proposed model is based on an operational model of the value placed on the understanding of mathematical content. Its practical potential is revealed through its application, with pre-service teachers, in the context of fractions. The evidence obtained using some fraction meanings, support a characterization of the understanding based on different priorities and availability in the use of this mathematical object, within its phenomenological and epistemological field.
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