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Abstract
We assembled the ideas about mathematics and about its teaching which were expressed by mathematicians and mathematics educators into two pairs of ‘official’ (collective) conceptions: mathematics is either static or dynamic, and mathematics teaching is either closed or open. These polar conceptions produce a 4-pair relationship between the conceptions of mathematics and its teaching. The adherence to official conceptions was tapped by a questionnaire encompassing 176 Israeli high school mathematics teachers, aimed at examining the relationship between their conceptions of mathematics and its teaching. The majority of these teachers either hold a single conception in one of the domains or do not adhere to any conception, and a quarter of them hold either the static-closed or dynamic-open pairs of conceptions that prevail among teachers in other countries. Consequently, we define a conception of an entity as a comprehensive and homogenous set of ideas about a particular characteristic or feature of that entity. Reality is that teachers practice their profession without adhering to any official conception, and perhaps are (/to be?/) praised for their reluctance to blindly adopt the clear-cut rigid official conceptions of mathematics and its teaching while maintaining their individual and independent blends of ideas.