Source:University of Western Macedonia - Faculty of Education, Florina, Greece, p.158 (2016)
Keywords:2016, menon, Thematic issue
INTRODUCTION TO THEMATIC ISSUE
“The Use of History of Mathematics in Mathematics Education”
The question of the integration of the History of Mathematics in Mathematics Education has been discussed since the 20th century by Educators (Barwell, Brousseau, Freudental, Piaget), Philosophers (Bachelard), Mathematicians (Klein, Poincare), and Historians of Mathematics (Loria, Smith), who have supported the proposal and have given arguments on the interest and challenges in school Mathematics courses.
Since the 1960s the use of the history of mathematics in mathematics education has become more popular and many papers in scientific journals, books, proceedings of conferences and groups of researchers have focused on this in contrast to the paradigm of the “modern mathematics” reform. We can find many didactical situations, mathematical problems, teaching series but also empirical and theoretical studies, Master and Phd level dissertations on the role and the ways of using historical, social and cultural elements in the teaching of mathematics. During the 2nd International Congress on Mathematics Education (ICME) in 1972 we have the creation of an International research group (International study group on the relation between the History and Pedagogy of Mathematics (HPM)) which organizes a congress every 4 years. The idea of a European Summer University (ESU) on the Epistemology and History in Mathematics Education started from the Instituts Universitaires de Formation de Maîtres (IUFM) in France, and an ESU is organized every three years in different European countries. Since 2009 in the context of the Congress of the European Society for Mathematics Education (CERME) we have also the appearance of a discussion group on The Role of History of Mathematics in Mathematics Education: Theory and Research (WG 12). This group also concentrates on empirical research. We should also mention the publication of the ICMI study History in mathematics education: the ICMI study (Fauvel & van Maanen, 2000) which presents the state of the art until this period.
Since the publication of this study, researchers address in a more demanding way questions about the efficacy and pertinence of many efforts (examples) of applications in classrooms. They are also wondering about the transferability of positive experiences from educators on different levels of education. They are considering questions on the capacity of students but also of educators when they were in front of the difficulties of studying the historical aspect of many notions.
Recently researchers΄ activities are moving to investigations in terms of didactic and educational foundations from which they believe that it could be possible to think better about the role of the history of mathematics in the teaching and learning of mathematics and the development of theoretical and conceptual frameworks which could provide the required equipment for the production of finer and more focus investigations.
These issues include, among others, the educational and teaching foundations of a cultural-historical perspective in the classroom, the need to give voice to community stakeholders about the introduction and more broadly, the nature and the terms of the empirical investigation prevailing in the research environment.
Parallel to these advancements in research, an attempt to humanize Mathematics is increasingly present in the mathematics curricula worldwide.
For over 20 years, the presence of the history of mathematics in training teachers’ environments has increased considerably in many countries. However, despite the different objectives associated with the introduction of the history of mathematics in training mathematics teachers, this presence, implicit or explicit, took the form of specific initiatives for each establishment of teacher training.
By browsing through the literature since 1990, it is possible to classify the empirical studies on the use of history in the mathematics classroom into two categories: studies that relate to the narrative of grounded experiences and quantitative studies on a larger scale.
Overall, it appears necessary to restore the research field on the introduction of History in the teaching and learning of mathematics within Didactics of mathematics and more generally with the educational sciences. This repositioning should enable research to get inspired from the contexts of the exploratory work from Humanities as well as theoretical, conceptual and methodological issues from the Didactics of mathematics and educational sciences.
This issue includes eight invited papers. Six papers are written in English and two in French. Each text is accompanied by an abstract in English. The following papers discuss specific issues in the domain of Using History of Mathematics in Mathematics Education and are ordered according to the instructional level; from elementary school to the university and in service teachers training.
- Evelyne Barbin suggests a new thinking on technique, proposed in the texts of Simondon and Rabardel. Her purpose, in introducing an historical instrumental approach of geometrical teaching for students aged 11-14 years, is to show how an instrument can be conceived both as an invention to solve problems and as a knowledge or theorem in action. In particular, she stresses the links between different varieties of instruments and different kinds of knowledge and shows the consequences of an instrumental failure for the construction of new knowledge. Her goal is a coherent using where teaching is based on families of instruments.
- Matthaios Anastasiadis and Konstantinos Nikolantonakis describe the context of an instructional intervention focused on isoperimetric figures and area-perimeter relationships with the use of one historical note and two primary sources, from Pappus’ Collection and from Polybius’ Histories. Their findings are based on classroom observations, worksheets and interviews with sixth grade Greek students.
- Vasiliki Tsiapou and Konstantinos Nikolantonakis present part of a research study that intended to use the Chinese abacus for the development of place value concepts and the notion of carried number with sixth grade Greek students.
- Ingo Witzke, Horst Struve, Kathleen Clark and Gero Stoffels describe how the concepts of empirical and formalistic belief systems can be used to give an explanation for the transition from school to university mathematics during an intensive Seminar. They stress the usefulness of this approach by outlining the historical sources and the participants’ activities with the sources on which the seminar is based, as well as some results of the qualitative data gathered during and after the seminar.
- David Guillemette tries to highlight some difficulties that have been encountered during the implementation of reading activities of historical texts in the preservice teachers training context. He describes a history of mathematics course offered at the Université du Québec à Montréal, with reading activities that have been constructed and implemented in class and the efforts made by the students and the trainer to articulate both synchronic and diachronic reading, in order to not uproot the text and his author from their socio-historical and mathematical context.
- Michael Kourkoulos and Constantinos Tzanakis present and analyze a teaching work on Pascal’s wager realized with Greek students, prospective elementary school teachers, in the context of a probability and statistics course. They focus on classroom discussion concerning mathematical modeling activities, connecting elements of probability theory and decision theory with elements of philosophical discussions.
- Areti Panaoura examines in-service teachers’ beliefs and knowledge about the use of the history of mathematics in the framework of the inquiry-based teaching approach at the educational system of Cyprus, and the difficulties teachers face in adopting and implementing this specific innovation in primary education.
- Snezana Lawrence offers ideas for teachers to engage with mathematics through the historical ‘journeys’ and relationship with art and cultural and intellectual history. She treats the question of how teachers could find their own ‘mathematical’ voice through series of historical investigations and what impact that may have on their teaching and pupils’ progress.
Firstly, I would like to express my warmest thanks to Christina Gkonou for her precious efforts to read and ameliorate the English texts.
Secondly, I would also like to express my thanks to the Editorial Committee of Menon Journal for giving me the chance to work this Thematic Issue on the field of Using History in Mathematics Education.
Finally, I would like to express my grateful thanks to my Colleagues who sustain with their papers this publication.
The Editor of the 2nd Thematic Issue of
MENON: Journal for Educational Research
Konstantinos Nikolantonakis, Associate Professor
University of Western Macedonia, Greece
Download the 2nd Thematic Issue from here.
 Christina Gkonou is Lecturer in Teaching English as a Foreign Language in the Department of Language and Linguistics at the University of Essex, UK. She received her BA from Aristotle University and her MA and PhD from the University of Essex. Her research interests are in foreign language pedagogy and the psychology of language learning and teaching.