• Research in Mathematical Education
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• v.13 no.4
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• pp.349-377
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• 2009

In this work we present a study undertaken with in-service mathematics teachers of primary and secondary school where we describe and analyze the didactical competences needed to implement an innovative design in geometry applying Van Hiele's models. The relationship between such competences and an ideal teacher profile is also studied. Teachers' epistemology is established in terms of didactical competences and we can see that this epistemology is an element that helps us understand the difficulties that teachers face in practice when implementing an innovative curriculum, in this case, geometry based on the Van Hiele theory.

• Research in Mathematical Education
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• v.14 no.1
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• pp.1-10
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• 2010

The paper focuses on a type of mathematics competence noted as synthetic. It is needed for success in multiple choice competition problems and it is crucial for the further development of advanced school students. The concept of synthetic competence includes a large fraction of mathematical competences, but also competences and skills related to informatics and linguistics. The general structure of a multiple choice competition is considered as the first level of assessment of the mathematics component of the synthetic competence. As the second level under consideration is the set of complex tasks in a competition test any of which is a bouquet of ideas. Our standpoint on the didactic specifics and goals of the two levels in perspective of the gifted education is briefly presented in the article and some examples are given.