The History of the Teaching and Learning of Mathematics
Abstract
History of mathematics teaching and learning is a subject that concerns two domains of research and may generate fruitful synergies between them. In 2000, during the International Symposium celebrating the centenary of the first international journal on mathematics teaching ( L’Enseignement Mathématique ), the interplay between the present educational problems in mathematics and their historical evolution through the twentieth century brought to the fore the potentialities of the field of research, “History of mathematics teaching and learning,” not only for historians, but also for educators.
Keywords
Mathematics Education Teacher Professional Development Reform Movement Junior High School Student Topic Study GroupHistory of Mathematics Teaching and Learning
History of mathematics teaching and learning is a subject that concerns two domains of research and may generate fruitful synergies between them. In 2000, during the International Symposium celebrating the centenary of the first international journal on mathematics teaching ( L’Enseignement Mathématique ), the interplay between the present educational problems in mathematics and their historical evolution through the twentieth century brought to the fore the potentialities of the field of research, “History of mathematics teaching and learning,” not only for historians, but also for educators, see Coray et al. ( 2003 ). This field of research became particularly visible at ICME10 in 2004 at Copenhagen, where a Topic Study Group (TSG 29) was dedicated to it, see Special issue ( 2006 ), Schubring and Sekiguchi ( 2008 ). History of mathematics education then became a subject of talks and workshops in various international meetings, for instance at the European Summer Universities (ESU4 in Uppsala in 2004, ESU5 in Prague in 2007, ESU6 in Vienna in 2010), and at the Congresses of European Research in Mathematics Education (CERMEs). During the TSG 38 at ICME11 in 2008 in Monterrey, research into this topic again proved its productivity, with papers presented on the history of the reform movements, on the analysis of classical textbooks, and on historical practice (inside and outside institutions), see Special issue ( 2009 ). In 2008 the celebration of the centenary of International Commission on Mathematical Instruction (ICMI), also emphasized the importance of the dialogue between the present and the past in mathematics education, see Menghini et al. ( 2008 ). In 2006 the first international journal devoted to this field of study, the International Journal for the History of Mathematics Education , was launched. Recently, specialized international research symposia took place in Iceland (2009) and in Portugal (2011), see Bjarnadóttir et al. ( 2009 , 2012 ).
On the occasion of ICME10, a first international bibliography of research in the field was prepared. The bibliography is now retrievable at the following address: http://www.icmeorganisers.dk/tsg29/BiblTSG.pdf .
This bibliography outlined streams in research: transmission and sociocultural reform movements; aspects of teaching practice (textbooks, methods, teacher professional development); cultural, social and political functions of mathematics instruction; and comparative studies.
History of Mathematics Teaching and Learning at ICME12

changes and roles of teachers’ associations

changes of curricula in the various countries

changes of mathematics education as a professional independent discipline

general trends in the organizing of the lesson

interdisciplinarity and contexts

methods

policies in teacher education

reforms movements

the cultural and social role of mathematics

the overall impact of digital technologies in the learning and teaching of mathematics

the role of textbooks in the teaching and learning of mathematics

the situation of journals on mathematics education

treatment of particular topics (geometry, algebra, etc.)

Amy AckerbergHastings (UMUC and NMAH, US). Teaching Mathematics with Objects: The Case of Protractors

Senthil Babu (French Institute of Pondicherry, India). Learning of Mathematics in Nineteenth Century South India

Kristín Bjarnadóttir (University of Iceland, Iceland). The Implementation of the ‘New Math’ and its Consequences in Iceland. Comparison to its Neighbouring Countries

McKenzie (Ken) A. Clements, and Nerida F. Ellerton, (Illinois State University, US). Early History of School Mathematics in North America, 1607–1861

Gregg DeYoung (The American University in Cairo, Egypt). Evangelism, Empire, Empowerment: Uses of Geometry Textbooks in 19th Century Asia

Viktor Freiman (Université de Moncton, Canada) and Alexei Volkov (National Tsing Hua University, Taiwan). Common Fractions in L.F. Magnitskii’s Arithmetic (1703): Interplay of Tradition and Didactical Innovations

María Teresa González (University of Salamanca, Spain). Notebooks as a Teaching Methodology: A Glance through the Practice of Professor Cuesta (1907–1989)

Alexander Karp (Teachers College, US). Russian Mathematics Teachers: Beginnings

Kongxiu Kuang (Southwest University, China), Yimin Xie (Jinan University, China), Qinqiong Zhang (Wenzhou University, China), Naiqing Song (Southwest University, China) Development, Problems and Thoughts of New China (PRC)’s Mathematics Education

Snezana Lawrence (Bath Spa University, UK). The Fortunes—Development of Mathematics Education in the Balkan Societies in the 19th Century (Distributed paper)

Lucieli M. Trivizoli (Universidade Estadual de Maringa, Brazil). Some Aspects of Scientific Exchanges in Mathematics between USA and Brazil

Alexei Volkov (National Tsing Hua University, Taiwan). Scholarly Treatises or School Textbooks? Mathematical Didactics in Traditional China and Vietnam
Alexander Karp presented the Handbook on the History of Mathematics Education , edited together with Gert Schubring (University of Bielefeld, Germany and U.F.R.J., Brazil). About 40 distinguished scholars from all over the world have agreed to participate in this major project. The publisher of the book is SpringerVerlag. This Handbook is a real landmark in the development of the theme in question.
It is worth mentioning other activities related to the theme of TSG 35 that enriched the panorama of the themes treated.
Regular Lecture
RL5–9, Marta Menghini (University of Rome La Sapienza, Italy). From Practical Geometry to the Laboratory Method: The Search for an Alternative to Euclid in the History of Teaching Geometry. See the text in ICME  12 Pre  Proceedings .
Posters and Oral Presentations

Tanja Hamann and Barbara SchmidtThieme (Germany). “Macht Mengenlehre Krank?”: New Math at German Primary Schools

Sanae Fujii (Japan). Mathematics Teaching Using “Sanpou shojyo (Algorithm Girl)” for Junior High School Students

Sung Sook Kim (Korea). SeokJeong Choi and Magic Squares

Shinya Itoh (Japan). Structure of Didactical Principles in Hans Freudenthal’s Didactics of Mathematics, Oral Presentation.
The abstracts are in ICME  12 Pre  Proceedings . The contributions cover important subjects of mathematics education:

physical devices for teaching mathematics

teacher professional development

systems of instruction

exchanges between countries

reforms

textbooks

treatment of parts of mathematics

eminent people in mathematics education.
Both specificity of national contexts and internationality of themes inherent in mathematics education were treated in the presentations and the discussions.
Final Remarks
We know that the vision and mission that inspired the journal L’Enseignement Mathématique and afterwards ICMI enhanced internationalization and communication in the world of mathematics education, see Furinghetti ( 2003 ). These goals were pursued throughout the ICMI’s existence and, in particular, ICME conferences have been a powerful means for realizing them, see Furinghetti and Giacardi ( 2008 ). TSG 35 and the related activities are an example of internationalization and communication among researchers. All five inhabited continents have presented contributions to the history of mathematics education: Africa (Egypt), Asia (China, India, Japan, Korea, Taiwan), Europe (Germany, Iceland, Italy, Spain, UK), North America (Canada, US), and South America (Brazil).
In spite of the limitation of the scheduled time, the contributions at ICME12 on the history of mathematics teaching and learning have allowed reflection on the double aspect of this topic. On the historical side, they showed that the present situation of mathematical education does not come out of the blue but has old roots and accompanied the growth of civilizations and societies. On the educational side, history offers to educators a different point of view for looking at educational problems and provides insights into possible solutions. Then, really, we may see the history of mathematics education as a bridge between the past and the future.
References
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