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Rethinking Characterizations of Beliefs
In this chapter we consider beliefs and the related concepts of conceptions and knowledge. From a review of the literature in different fields we observe that there is a diversity of views andExpand
Every unsuccessful problem solver is unsuccessful in his or her own way: affective and cognitive factors in proving
It is widely recognized that purely cognitive behavior is extremely rare in performing mathematical activity: other factors, such as the affective ones, play a crucial role. In light of thisExpand
Teacher education through the history of mathematics
In this paper I consider the problem of designing strategies for teacher education programs that may promote an aware style of teaching. Among the various elements to be considered I focus on theExpand
The history of mathematics as a coupling link between secondary and university teaching
During the years they spend in university, many mathematics students develop a very poor conception of mathematics and its teaching. This fact is bad in all cases, but even more in the case of thoseExpand
The use of original sources in the mathematics classroom
The study of original sources is the most ambitious of ways in which history might be integrated into the teaching of mathematics, but also the most rewarding for students both at school and at teacher training institutions. Expand
History and Mathematics Education: A look around the World with Particular Reference to Italy
: Having served for four years (2000-2004) as a chairperson of the Study Group HPM (The International Study Group on the Relations between the History and Pedagogy of Mathematics) affiliated to ICMI, I have collected a good amount of information on the role of the history of mathematics in mathematics education. Expand
Conceptions of Proof – In Research and Teaching
This chapter first analyses and compares mathematicians’ and mathematics educators’ different conceptualisations of proof and shows how these are formed by different professional backgrounds andExpand
Historical Conceptual Developments and The Teaching of Mathematics: From Philogenesis and Ontogenesis Theory to Classroom Practice
Using a unified method to make elliptic, hyperbolic, and other graphics. From this process, we can see what is the key to make dynamic geometry .It is necessary to use the thinking and methods ofExpand
To produce conjectures and to prove them within a dynamic geometry environment: a case study
This paper analyses a case study of a pair of students working together, who were asked to produce conjectures and to validate them within the dynamic geometry environment Cabri. Expand
History of mathematics education