Participating projects
The MTA-ELTE Complex Mathematics Education project (2016-2020) is a research project supported by the Content Pedagogy Research Program of the Hungarian Academy of Sciences, unifying didacticians, teacher educators and teachers from five different cities of Hungary. It aims to revisit the „Complex Mathematics Education” reform led by Tamás Varga in the 1960s and 1970s; situate Varga’s approach in the international research field of mathematics education, work on its adaptation to nowadays educational needs, and help its more efficient diffusion among teachers.
Several subgroups work in the frame of the MTA-ELTE project: the one contributing to the present workshop is focused on the teacher’s role in Varga’s “guided discovery” approach. As we showed earlier (Gosztonyi 2016), the teacher’s work can be described on two main levels according to the guided discovery approach: the planning of short and long-term teaching processes in form of series of problems on one hand, and the management of classroom activities by guiding classroom dialogues on the other.
In the frame of the project, we examine existing series of problems published in different resources or created by the participating teachers (experts of the approach): we analyse their structure and didactical function. We analyse moreover teacher-student interactions in the participating teacher’s video-taped lessons.
In order to help teachers who are not familiar with the approach, we plan to create a commented collection of examples based on the examined series of problems, and experiment the use of this collection by teachers wanting to develop their practices in the spirit of the approach.
Our group at the Alfréd Rényi Institute of Mathematics, within the Content Pedagogy Research Program of the Hungarian Academy of Sciences, during the 4-year-long period of the project (2016-2020) focuses, on one hand, on the development of the application and the theoretical and comparative reconstruction of the Pósa method for discovery (inquiry-based) learning mathematics, and, on the other hand, on fostering the cooperation between teachers of special math classes in Hungarian secondary schools.
Built on the work of the weekend talent-care math camps with roughly 3 decades of history, we have started to develop new personal programs for the really top talented students.
As experimenting the Pósa method to be applied for less talented ones, we run workshops for interested 9 graders countrywide (Flying School) and study circles for disadvantaged 6 graders too.
Experimental classes in public education (full 4-year high school program for 9-12 graders) were launched in September 2017.
As part of the comparative and descriptive theoretical research on the Pósa method, studying foreign ‘discovery-like’ practises of teaching math is also of high importance for us.
More information about the project and and other activities related to the Pósa camps and the method can be found at the homepage of the The Joy of Thinking Foundation.
The research project “series of problems, a genre at the crossroads of various cultures” has been developed between 2012 and 2012 with the research “excellence laboratory” HASTEC (History and Anthropology of Knowledge [Savoirs], Techniques and Beliefs [Croyances]). This entity gathers some 25 Parisian research laboratories devoted to highly diverse domains, including history of sciences and techniques, history of philosophy, history of texts, anthropology of knowledge, etc.
Within this project; we studied in an interdisciplinary spirit several texts of very different periods (frome antiquity to contemporary period) and material aspects (clay tablets, manuscripts, printed material) having in common (i) the form of questions and answers, “questions largely referring to several possibilities, like mathematical problems, question in natural philosophy or modern experimental science, literary enigmas…; “answers” also referring to various “outcomes” like solutions, explanation, answers…(ii) the fact of being written – whatever the material support – but we are not dealing primarily with the activity of challenging others with problems and questions; and (iii) the fact that they are interesting subject of historical and anthropological studies, let alone because they usually long term processes of reappropriation of the underlying material and knowledge.
The first synthesis on the textual material and research questions tackled in the project, can be read online from the first publication of the group (2015): synthesis. Some of the articles belonging to the same volume bear on texts and issues that will be evoked during the workshop: Bernard on Diophantus (link), Gosztonyi on Varga's reform (link); others (summary) might give an idea of the variety of texts and periods studied, some of them can be read in English (Oaks, Cifoletti, Christianidis).
The “Institute for Research on the Teaching of Mathematics (IREM)”appeared in France at the end of the 60s with the following missions: to contribute to the training sessions of teachers, to develop the educational experiment and documentation. They are organized in a network (website). Their main originalité is to gather teachers and researchers at university, secondary and primary levels, in order to organize training sessions and to build resources for teachers – mainly of mathematics, but other disciplines (philosophy, French, history, technology..) might be concerned as well. The “history and epistmelogy” groups , as the name indicates, are focused on the integration of a historical and epistemological perspective in the teaching of mathematics (website of this sub-network, named "commission histoire et épistémologie").
In IREM de Paris Nord history and epistemology group, we pay attention to several subjects, such as the history of combinatorics and recreational mathematicas (Delannoy), history of mathematics for teachers of primary level, issues about mathematics, history and citizenship (focusing on the teaching of statistics and probability - see online video presentation), and issues about “series of problems”, in relation to the above mentioned HASTEC group . On these last aspects we organized since 2012 several in-service teacher training session, to which K. Gosztonyi regularly participated for the “Hungarian” part, and we are now working on several booklets for teachers, two of them being presented within the workshop (example).
For more information about the stakes and aims of the sub-group working on series of problems, see Bernard and Gosztonyi’s talk at ESU-7 (available on line) or the more developed paper (in French) to appear very soon in Trema 48-2 , p.17-33 under the title "La confrontation entre expérience professionnelle des enseignants et recherches historiques: une expérience transitionnelle?"
DREAM is a IREM group (in Lyon) which is composed by teachers in secondary school, teacher’s trainers and researchers in math education. Since 2005, the work of DREAM group is based on all the work developed around the “problème ouvert” by the IREM of Lyon for more than twenty years and on several research like “the link between logic and mathematical reasoning” (Durand-Guerrier, 2005) and “the experimental dimension of mathematics in the perspective of their learning” (Dias, 2008). In 2013 and in 2015, two theses continued this work on the experimental dimension of mathematics and the development of mathematical knowledge in situations of research problems (Gardes, 2013 ; Front, 2015).
The aims of the group are:
- Elaborate and analyse situations of research problems
- Elaborate a numerical resource the aim of which is to give aid to maths teachers to use research problems in their teaching
- Create a progression of mathematics teaching based on research problems
In 2010, the group produced a CD-ROM (Aldon et al., 2010) which present seven research situations for the classroom with mathematical analyses, didactic analyses and classroom experiment reports. This resources are now available on a website. Currently, the team is working on the third aim: create a progression of mathematics teaching based on research problems (example).