Recently I in process of prepare a text in according per-service elementary school's teacher conception of quadrilaterals and their classification.I need to make some explanation what is difference between notion of mathematics object and concept of mathematics concept.
In ordinary everyday English, notions and concepts can overlap, with concepts often being somewhat more formal or abstract. A conception involves a mental act that attempts to arrive at or express a concept. One can have a vague notion or conception of something and that vagueness is usually considered to be a shortcoming that derives from a shortcoming on the part of the conceiver. ("Conception" also has process/product ambiguity; it can refer to the process of conceiving or to the product of that process; cf. "building".) With a vague concept, the vagueness might be inherent in the concept and not imply any shortcoming (e.g. color concepts are inherently vague because colors on the spectrum don't have sharp boundaries).
However, some theorists might give "notion" and "concept" a technical sense that deviates from everyday English. In what mathematical context have you seen these terms used and differentiated?
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