The emerging of teachers' conceptions of new subjects inserted in mathematics programs: the case of informatics

The changes in mathematical curricula induced by the introduction of informatics in school represent the general framework of this research. In particular we focus on the teacher's role by analysing the different choices taken by mathematics teachers when faced with a curriculum reform induced by the introduction of informatics in secondary school courses (age 14–16). Our hypothesis is that these choices are the consequence of conceptions teachers have about informatics and its teaching in relation to the teaching of mathematics. Thus, through a case study research method, we focus on mathematics teachers' conceptions of informatics and its teaching. An attempt is made at outlining a typology of these conceptions, based on the different orientations identified.     

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 the need to address prospective teachers’ belief that they must reproduce the style of mathematics teaching seen in their school days. Towards this aim, I argue that the prospective teachers need a context allowing them to look at the topics they will teach in a different manner. This context may be provided by the history of mathematics. In this paper I shall discuss how history affected the construction of teaching sequences on algebra during the activities of the ‘laboratory of mathematics education’ carried out in a 2 year education program for prospective teachers. The conditions of the experiment, notably the fact that our prospective teachers had not had specific preparation in the history of mathematics, allow us to outline opportunities and caveats of the use of history in teacher education.     

The role of concrete materials in Emma Castelnuovo’s view of mathematics teaching

Emma Castelnuovo (1913–2014) was an Italian mathematics teacher of grades 6 to 8 in secondary school. During the crucial period of the 1950s and 1960s, when important reforms were proposed, she was involved in significant events such as the first CIEAEM meetings and the Royaumont Seminar. She was an active contributor to the development of international cooperation in mathematics education and was one of the first authors in the journal Educational Studies in Mathematics. Thanks to pioneers such as Emma, the figure of teacher-researcher took shape and the milieu of mathematics education was forever changed. The main aim of Emma’s work as an innovative teacher was to actively involve learners. In outlining Emma’s action as a mathematics educator, we will pay particular attention to the use of concrete materials as this was a favorite means by which she pursued her aims.     

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 this observation, we present a reflection on the presence of affective and cognitive factors in the process of proving. Proof is considered as a special case of problem solving and the proving process is studied adopting a perspective according to which both affective and cognitive factors influence it. To carry out our study, we set up a framework where theoretical tools coming from research on problem solving, proof and affect are present. The study is performed within a university course in mathematics education, where students were given a statement in elementary number theory to be proved and were asked to write down their proving process and the thoughts that accompanied this process. We scrutinize the written protocols of two unsuccessful students, with the aim of disentangling the intertwining between affect and cognition. In particular, we seize the moments in which beliefs about self and beliefs about mathematical activity shape the performance of our students.

Rethinking Mathematical Concepts with the Lens of the History of Mathematics: An Experiment with Prospective Secondary Teachers

In this paper we present the main lines of a course on the history of mathematics for prospective secondary school (students’ age range 14–19) mathematics teachers, enrolled on a 2-year postgraduate teacher preparation program. In order to integrate the historical objectives with the educational objectives of the program we adopted the following strategy: on the one hand we focused on some important concepts taught in upper secondary school that required the prospective teachers to reflect on the difficulties linked to these concepts; on the other hand we proposed original sources intended to enhance the students’ reflection through challenging some existing beliefs on these concepts. We informed the prospective teachers that they were participating in a research project. This fostered a collaborative atmosphere and an active involvement that guided our students towards the final step of the course, where they were requested to outline a teaching sequence for presenting the concepts in the classroom.     

Book Review: A common ground of mathematics and mathematics education for the classroom and for researchers. Erich Christian Wittmann (2021) Connecting mathematics and mathematics education. Collected papers on mathematics education as a design science

Educational Studies in Mathematics -