Archive for the ‘Conference Reports’ Category
By Sebastian Schorcht
In the following, I offer my reflection about the HPM Satellite Meeting of ICME-13, which took place in Montpellier from 18 – 22 July 2016, as if it was an interview between my “past” self and the post-conference me. The past of myself is the Interviewer and the post-conference self will answer the questions.
Interviewer: Dear future-self, nice to meet you. I’m happy you have found a few minutes to answer my questions. I have many questions about the conference you attended. For example, what is your impression of the HPM Community?
Post-conference self: Overwhelming, familiar, scientifically-sound, and interested in cultural activity. The spirit in the community was overwhelming, upon first meeting each other. However, things seemed very familiar to me, when everyone discussed about the research experience. The researchers in HPM are willing to help each other in their work. They enrich their research work by comments from others. Besides this overwhelming and familiar spirit, some presentations impressed me with their carefully extracted hypotheses and logical organization, e.g., the presentation by Katz or by Fried, Jahnke, & Guillemette, or by Chorlay. Specifically, I will remember the dramatic presentation, a cultural experience about complex numbers written by Hitchcock, which provided us with a very nice afternoon.
Interviewer: It sounds to me like a fruitful conference in Montpellier. What were your scientific take-home message and/or social outcome about this conference?
Post-conference self: Perhaps there will be many scientific influences on my work. I can’t account for all of them right now, but I could make a presumption for you, my past myself:
I think there were many interesting ideas. For example, from Ewa Lakoma: she spoke about the concept of mathematical cognitive transgression (MCT) by Semadeni (2015).
The use of this concept to understand epistemological obstacles as forgotten transitions from a process to an objective view on mathematics expressions is a nice idea. Also, the ideas of Chorlay, who distinguished between mobilizable knowledge and available knowledge like Robert (2002). Chorlay enriches students’ available knowledge by meta-tasks, which requires reflection skills.
Furthermore, I obtained helpful database information. For example, the literature database Publimath in France (publimath.univ-irem.fr), the bibliographical database within the pre-conference document of ICME-13 (in Proceedings of HPM 2016) and the database within the TRIUMPHS-Project in USA (webpages.ursinus.edu/nscoville/TRIUMPHS.html), where original source projects about algebra, analysis, and topology and others are available for undergraduate mathematics instruction.
As for the social outcome, I met a lot of new friends and hopefully will keep in contact with them. My past myself, don’t hesitate to talk to them, when you arrive on Monday.
Interviewer: Which painting or photo would describe your experience at the conference?
Post-conference self: That’s a difficult question, because there are so many impressions. I can’t summarize them into one picture. If I must choose one of them, I choose the one above. It reminds me of the moment when I was asked to play the part of the renowned scholar Gert Schubring, and had to speak English in front of a big audience. Coincidentally, it reminds me of Argand, the face of the HPM 2016 Poster and Mediterranean Area. Also, I am reminded of new friends with whom I acted in this dramatic presentation.
Interviewer: What advice do you have for me?
Post-conference self (laughing): An advice for myself? Don’t miss the “swimming materials” required for the conference dinner!
Justus Liebig University Giessen,
September 29-30, 2015, Tsukuba, Japan.
The meeting was the opening event for the exhibition, “Wisdom of Mathematics: Exploration and Development,” at the Central Library of the University of Tsukuba, Japan. The exhibition featured two 15th century books: Suanxue Qimeng and Yang Hui Suanfa. These books are the oldest copies of the originally lost 13th century. The exhibition also featured 22 rare books from the 16th – 18th centuries, which have been collected by M. Isoda, with the help of HPM members such as former HPM presidents, J. van Mannen, and J. Fauvel. The exhibition shows the influence of Greek and Arabic mathematics in Europe, the mathematics that existed and developed in East Asia, and its integration into school mathematics. The exhibition showed how mathematics, since Ancient Greece, has been taught as the necessary literacy for the basic culture that can be shared and developed only through school education. The exhibition also showed how the recent Japanese secondary school textbook in 1943, as an influence of Felix Klein, has some similarities with the book by Euclid (1537 edition) and the book by van Schooten (1646).
During the meeting, the following people contributed to the theme: Luis Radford, Gert Schubring, Kenji Ueno, Yuriko Yamamoto Baldin, Wann-Sheng Horng, Shigeru Jochi, Márcia Maria Fusaro Pinto, and Masami Isoda. The lectures and discussions were very informative and fruitful according to their specialties. Firstly, L. Radford, President of HPM, introduced HPM and presented his view for Hermeneutics and significance of the collection. Then, M. Isoda explained his perspective on mathematics education (2015) as the meeting host. G. Schubring, presented his view for Hermeneutics as for research methodology on history with examples of various revisions of textbooks. K. Ueno, W. Horng, and S. Jochi explained the historical value of the books Suanxue Qimeng and Yang Hui Suanfa for the Innovation of Japanese Mathematics (Wasan). M. Pinto presented the history of mathematics education as a discipline and Y. Buldin presented necessary perspectives for integration of several presentations. The speakers also discussed the further meeting for the book project on Hermeneutics, and the future HPM meeting in 2020 in relation to ICME-14.
Isoda, M. (2015). Dialectic on the problem solving approach: Illustrating hermeneutics as the ground theory for lesson study in mathematics education. In S. J. Cho (Ed.), Selected regular lectures from the 12th international congress on mathematical education (pp. 355-381). Cham: Springer.
University of Tsukuba (Japan)
November 4-6, 2015, Bogotá, Colombia.
The Fifth National School of History and Mathematics Education (Quinta Escuela Nacional de Historia y Educación Matemática, or, ENHEM 5) took place on the campus of Universidad Externado de Colombia in Bogotá, on 4-6 November 2015.
The conference themes were:
History and Philosophy of Mathematics;
- History of Mathematics in Latin American countries;
- The history of mathematics teaching;
- History of Mathematics in cultural contexts;
- History of Mathematics in teacher training;
- History of Mathematics in the teaching and learning of mathematics; and
- History in mathematics education research.
There were several activities of ENHEM5, including conference plenaries and short courses given by international guests (Gert Schubring, Alejandro Garcíadiego, Sergio Nobre, Kathleen Clark, Analia Bergé, and Carlos Augusto Di Prisco), some 30 lectures by Latin American specialists, 50 short oral communications, and a panel session.
The conference was expertly organized by the committee consisting of:
Luis Recalde, Guillermo Ortiz, Luis Carlos Arboleda, Luz Victoria De la Pava, Ligia Torres, Maribel Anacona, Fernando Gálvez (Universidad de Valle);
Fabio Ortiz (Universidad Externado de Colombia);
Clara Helena Sánchez (Universidad Nacional de Colombia);
Edgar Alberto Guacaneme, Johana Andrea Torres (Universidad Pedagógica Nacional);
Gabriela Arbeláez, Martha Bobadilla (Universidad del Cauca); and
Armando Aroca (Red Latinoamericana de Etnomatemáticas).
The National School of History and Mathematics (ENHEM) takes place every two years; the next takes place in 2017.
Florida State University, USA
September 20-25, 2014
Zhejiang University of Science and Technology，Hangzhou; Department of Mathematics, Northwest University, Xi’an
In Association with
REHSEIS (SPHERE), CNRS & University Paris Diderot; Dept of Mathematics, Simon Fraser University
Chinese Society for the History of Mathematics
Organization Scientific Committee
* Qu Anjing (Northwest University, Xi’an, China, Co-Chair)
* Tom Archibald (Simon Fraser University, Vancouver, Canada, Co-Chair)
* Karine Chemla (REHSEIS—SPHERE, CNRS & University Paris Diderot, Paris, France)
* Niccolò Guiccardini (University of Bergamo, Italy)
* Tinne Hoff Kjeldsen (Roskilde University, Copenhagen, Denmark)
* Norbert Schappacher (Université de Strasbourg, France)
* Ueno Kenji (Seki Kowa Institute of Mathematics, Japan)
Local Organizing Committee
Zheng Youqu (Chair), Cen Gang, Tao Xiangxing, Ruan Shiping, Xue Youcai, Qiu Binqiang, Yin Weidong, Wang Wenbin (Zhejiang University of Science and technology, Zhejiang China), Yuan Min (Northwest University, Xi’an, China)
Four days of scientific sessions are planned.
1. Plenary Invited Lectures
Invited lectures will be announced later.
2. Scientific Sessions for Contributed Papers
Parallel sessions will be organized on specific topics.
3. One day sight-seeing
4. Language: English
5. Tentative Schedule
Sept 20, arrival, registration, getting together
Sept 21-24, Scientific program
Sept 25 Sightseeing
Contemporary Research in the History of Modern Mathematics and Applications to Pedagogy
Research in both the history of mathematics and the applications of history of mathematics to pedagogy have in recent years been enriched by new directions. The results have included new emphases in both disciplines, with diverse and far-reaching consequences. On the side of history, we see a renewed interest in the philosophical issues of various kinds, on the transmission of mathematical knowledge from local settings to global norms, on networks of scholars and networks of texts, on the nature and importance of application in mathematics, and on a reassessment of the importance of computation in all its forms. On the side of education, we see an expansion of the strategic use of history as a tool, going beyond cross-cultural comparison to being an ingredient in various theoretical approaches.
The purpose of the meeting proposed is to assemble senior scholars active in these fields, junior scholars whose work promises to be transformative, and scholars who are ambitious to acquire new approaches while presenting contributed papers on work of their own for comment by their peers.
With a broadly inclusive scope we hope to build on the positive experiences of earlier meeting to continue to build a Chinese and international research community and to build links for the future.
We are deeply convinced that the better understanding of modern mathematical activity that such an approach can yield will be helpful for mathematics education at all levels, and that the presence of researchers with education as a primary focus will enhance this aim.
Registration Fees (Registration covers the book of abstracts, all the conference sessions, including the banquet and all meals. It does not cover accommodation).
|Before June 30||
|After June 30||
Modalities of payment, to be announced later.
Rooms will be available on campus or near the campus. Precise information will be given in the second circular.
Title and Abstract
Please send title of your talk to Dr. Wang Chang: email@example.com, before 15 April 2014.
We expect that you send the abstract of your paper by email to Dr. Wang Chang: firstname.lastname@example.org, before 30 June 2014. We accept *.doc and *.txt files.
Webpage and Contact persons
Official webpage will be announced.
Dr. Wang Chang, Northwest University, email@example.com
Prof. Xue Youcai, Zhejiang University of Science and Technology, firstname.lastname@example.org
About the WG on history in mathematics education
2013 was the third time that the history working group was part of the CERME program. This time the group had about twenty participants, presenting twelve papers and three posters.
The educational scope of the contributions ranges from the use of history in kindergarten over primary and secondary school, upper secondary school, tertiary level, and teacher education. In addition to this, the group also has studies on the history of mathematics education as long as they have relevance for mathematical practices of today, as seen from the main themes in the call for papers:
1. Theoretical, conceptual and/or methodological frameworks for including history in mathematics education;
2. Relationships between (frameworks for and empirical studies on) history in mathematics education and theories and frameworks in other parts of mathematics education;
3. The role of history of mathematics at primary, secondary, and tertiary level, both from the cognitive and affective points of view;
4. The role of history of mathematics in pre- and in-service teacher education, from cognitive, pedagogical, and/or affective points of view;
5. Possible parallelism between the historical development and the cognitive development of mathematical ideas;
6. Ways of integrating original sources in classrooms, and their educational effects, preferably with conclusions based on classroom experiments;
7. Surveys on the existing uses of history in curricula, textbooks, and/or classrooms in primary, secondary, and tertiary levels;
8. Design and/or assessment of teaching/learning materials on the history of mathematics;
9. The possible role of history of mathematics/mathematical practices in relation to more general problems and issues in mathematics education and mathematics education research.
Papers presented in WG12
|Alpaslan, M. &Güner, Z.||Teaching modules in history of mathematics to enhance young children’s number sense|
|Bayam, S. B.||Students’ views about activities for history of mathematics included in mathematics curriculum|
|Bjarnadóttir, K.||Arithmetic textbooks and 19th century values|
|Clark, K. &Phillips, L. G.||“I was amazed at how many refused to give up”: Describing one teacher’s first experience with including history|
|Jankvist, U. T.||The use of original sources and its possible relation to the recruitment problem|
|Kaenders, R., Kvasz, L. & Weiss-Pidstrygach, Y.||History of mathematics as an inspiration for educational design|
|Kotarinou, P. &Stathopoulou, C.||The history of 5th postulate: Linking mathematics with other disciplines through drama techniques|
|Krüger, J.||The power of mathematics education in the 18th century|
|Krüger, J. &van Maanen, J.||Evaluation and design of mathematics curricula: Lessons from three historical cases|
|Lawrence, S.||Making sense of Newton’s mathematics|
|Mota, C., Ralda, M. E. &Estrada, M. F.||The teaching of the concept of tangent line using original sources|
|Tsiapou, V. &Nikolantonakis, K.||The development of place value concepts to sixth grade students via the study of the Chinese abacus|
Posters presented in WG12
|Moeller, R. D. &Collignon, P.||Calculus and applications – Learning from history in teacher education|
|Monteiro, T. M.||Ideas about modern mathematics and teacher trainees at Liceu Normal de Pedro Nunes (1957-1971)|
|Navarro, M. &Puig, L.||Facets of the presentation of the Cartesian coordinate system in Euler’s Introductio in Analysin Infinitorum and Lacroix’s textbooks|
Themes and questions discussed during the WG sessions
The presentation of papers and following group discussions were ordered according to five general themes deemed important for history in and of mathematics education:
ii. Theoretical frameworks in history of mathematics education
iii. History in pre-high school mathematics education
iv. History in high school mathematics education
v. History of mathematics in teacher education and design
In the following, we list the questions that initiated and/or formed the subgroup discussions of the five themes.
Theme I: Interdisciplinarity
• What is true interdisciplinarity? (e.g., the principles, techniques, frameworks, etc. from one discipline that are used to gain new insights within another discipline.)
• How do we ‘measure’ the level of interdisciplinarity obtained in a given context?
• To what extent does interdisciplinarity (need to) go hand in hand with cooperation between researchers?
• What is a good example of interdisciplinary research; and what is a non-example?
• Do we consider a study about mathematics education as interdisciplinary (i.e., between mathematics and the social sciences)?
Theme II: Theoretical frameworks in history of mathematics education
• What is the difference between story and history?
• What theoretical frameworks are available already?
• To what extent does history of mathematics education require the study of primary sources?
Theme III: History in pre high school mathematics education
• What are the special challenges when using history in primary school, kindergarten, etc.?
• How do we stay true to history, i.e., non-Whig, when applying history of mathematics at pre high school levels? (Briefly, ‘Whig’ history may be explained as an interpretation of the past through the eyes of the present.)
• How do we determine the effect of history, as opposed to the use of physical materials/resources or other interventions (e.g., drama, poetry, posters, and presentations)?
Theme IV: History in high school mathematics education
• How far can you ‘push’ the use of primary sources when using history of mathematics at high school level? What are techniques for doing so?
• If one of the aims of using history of mathematics at high school level is to develop students’ mathematical awareness (beliefs, images, etc.) about mathematics as a (scientific) discipline, what is then the best way(s) to describe or maybe even ‘measure’ such development?
• How do we appreciate the principle of ‘authentic practice’ (i.e., to have the students act as if they were a 17th century surveyor, or a Roman treasurer?)
• What role can history in mathematics education play in building new mathematical concepts with the students? Are there other specific domains in which history in mathematics education was useful, or can be useful?
Theme V: History of mathematics in teacher education
• In the UK there is an increasing public opinion that the universities should get out of teacher training and that teachers should be employed by schools where they will train on the job. If this is the case, what role would or could academic research in the history of mathematics have in teacher training?
• What is the role (from a policy/institutional point of view) of history of mathematics in teacher/mathematics teacher education?
• What lessons can we learn about the engagement of teachers with the history of mathematics and their professional progression for the teacher training?
• What part of cultural/historical/heritage implications does the history of mathematics have in teacher training?
Selected outcome of the group discussions
In the final session, every subgroup gave a report of its discussion of the five themes and the related questions. Providing a full account of all these subgroup discussions is beyond the possible scope of this introductory report, but in order to illustrate what went on in the WG we shall focus on a few of the themes and questions by drawing in viewpoints and arguments on these from all subgroup reports.
The first is theme II. The reason for including this as one of the general themes has to do with our experiences of sometimes receiving manuscripts (e.g., when reviewing for journals) that seem to report more of a story related to mathematics education, than to report on an actual historical research study. We are delighted to report that this was not the case of the participants of WG12, which was also reflected in the discussions. For example, there was a consensus about story being something narrative, whereas history, although it may contain narratives (or stories), is structured by theoretical frameworks, the purpose of which includes being able to see benefits or limitations, to communicate results, and to enable the researchers to organize and present findings, assertions, etc. As examples of such frameworks, the participants pointed to sample constructs from history research, e.g., those of more externalistic historiography of studying factors crucial to the development of institutions, etc. But in the light of main theme 9, frameworks from mathematics education research of course also play an important role in creating a scene for pointing at possible consequences for modern day practice. As to the role of primary sources, all participants consider these practically a necessity for conducting history of mathematics education. But one important aspect regarding this is that primary sources in this context can be of various different kinds, including written documents, oral records, textbooks, conference proceedings, etc. This is different from when discussing, for example, theme IV, where the reference to primary sources usually refers to original mathematical texts.
The use of history at high school level (theme IV) is something that has been extensively discussed within the context of using history in mathematics education, not least because students at this level to some degree can be successfully exposed to original sources, even if it is still a challenging task for them. But what about using history in pre-high school education, such as primary school, kindergarten, and other early childhood education contexts? An actual reading of original texts at this level is often far beyond pupils’ reach. The participants point to the fact that in practice when using history at younger age levels there is a need for compromise, also in order to make the mathematics itself more accessible to children. In particular with very young children there may be the need for narratives in the form of telling stories of mathematics, rather than confronting them with the actual history of mathematics. But as one of the subgroups state in their report: “You have to tell stories, but the knowledge of history enables you to tell true stories.” To the question of why one would even bother to go to all the efforts of bringing in history of mathematics to younger aged pupils, another subgroup refers to the discussion of providing context in the teaching of mathematics stating that lack of context can have a negative influence on learning and that “history provides that context” which is often needed and welcome.
The above naturally links in with theme V, illustrating that sound knowledge of history of mathematics can act as a valuable resource for teacher practice. But equally important is that history of mathematics has a role to play in mathematics teachers’ professional development – something that was illustrated through a few empirical studies issued in the late 1970s and early 1980s. Nevertheless, the frequency with which we come across examples from practice of using history of mathematics in mathematics teacher training is still fairly low. Why is this so? It is an open question. But it is clear that it is related to the matter, as one subgroup mentions, of showing teachers, mathematics educators, curriculum designers, and politicians the benefits and potential of using history of mathematics in mathematics education. How to possibly, and partly, do so is addressed next.
A permeating question of frameworks and constructs
One topic or question which permeated many of the other discussions and to which we found ourselves returning again and again, is that of which frameworks, theories, or theoretical constructs from mathematics education research may apply best to the various uses of history of mathematics in the teaching and learning of mathematics. The challenge of conducting studies within the scope of WG12 is to find a balance between the three fields: that of the history of mathematics, mathematics, and mathematics education (research). This requires knowledge of all three disciplines, often making such studies a relatively demanding task to undertake. For ‘outsiders’, e.g., math educators who are not as familiar with the history of mathematics, we need to be able to provide convincing arguments for wanting to resort to history in the teaching and learning of mathematics. A sensible way of doing so is to argue by means of theoretical constructs from mathematics education research and to rely on suitable mathematics education frameworks for analyzing data, presenting and discussing results, etc. For ‘insiders’, who are familiar with history of mathematics, it is important not to be unintentionally anachronistic (or ‘Whig’) when including history in the teaching and learning of mathematics. From an educational point of view, this is important if having as a goal to foster historical awareness with students. From a research community point of view, it is important if we want to maintain our integrity and strengthen the connections with research historians of mathematics.
Evaluation and Aspects to consider for the next WG
In accordance with decisions made at CERME-7, more time was allocated to poster presenters during the WG sessions of CERME-8. More precisely poster presenters gave short presentations of their posters in the WG before they presented their posters in general. This initiative seemed to function well, and we plan to repeat it again. As always, the history group at CERME works to maintain very close connections to the HPM group, not least within the leading team. As new initiatives for CERME-9, we have in mind to broaden the ‘bullets’ in the call for papers to also encompass studies related to epistemology of mathematics in relation to mathematics education and the use of philosophy of mathematics in the teaching and learning of mathematics.
The next CERME will be held in Prague, Czech Republic, 4 – 8 February 2015. The Local Chair is Nada Vondrova and the Program Chair is Konrad Krainer. Please check http://www.mathematik.uni-dortmund.de/~erme/ in the future for information.
Uffe Thomas Jankvist,
Jan van Maanen
Reported by Snezana Lawrence, Bath Spa University, Bath, England
The CERME-8, which took place in Antalya Manavgat-Side in February this year, had, for the third time, the Working Group on the history of mathematics. This time it was given the title History in Mathematics Education. The leader, as last time was Uffe Thomas Jankvist, who is now also on the Council of the European Society for the Research in Mathematics Education: a timely recognition for his contribution to CERME and also almost coinciding with his new permanent position as associate professor of mathematics education at Aarhus University (Campus Emdrup).
The group was very lively, bringing experienced and new researchers together. Whilst the experienced may not be ‘old’ the new are certainly young – and so here are their recollections of the CERME-8.
Reflections from Mustafa Alpaslan, Middle East Technical University, Turkey
This was my second participation in the group for the history of mathematics at CERME, the first being CERME-7 in Rzeszow. I strive to incorporate the historical connections into my teaching of mathematics, and base this on studying experts in the field. My paper, “Teaching Modules in History of Mathematics to Enhance Young Children’s Number Sense” was reviewed before the congress, and I found the comments by U. T. Jankvist, T. H. Kjeldsen and K. Clark very useful. After the presentation, I got some other feedback and this made me believe that the quality of my paper would increase. I also had a chance to further discuss the paper and how to use history of mathematics with younger children with K. Clark. Considering these experiences, I think that we had a group that supported the development of young researchers in their own fields of interest.
Before coming to Antalya, the group leaders determined five hot topics about using history in mathematics education (for example one was ‘interdisciplinarity’). Knowing that these five topics would be discussed made me review the related literature about each of these topics. During this preparatory study, I believe I broadened my perspective in the field: I noticed that I came across valuable sources on the topics set for discussion, like for instance, the ICMI Study edited by J. Fauvel and J. van Maanen. This aspect of the Working Study Group gave me inspiration for my future research and gave me some indication where I may go to search for further resources.
Another issue I wanted to address is about the learning that took place in the group. The papers covered a full range of mathematics education, from early childhood to university level. During the presentations, I noticed how the use of history differs across various levels of education. For example, it seemed more possible to use the original sources in the upper levels. As for the lower grades, adopting the original sources and/or getting inspired from the historical artefacts appeared to work when the lesson focus was practical work involving some historical artefacts. Secondly, I learnt possible difficulties with using original sources (e.g., the problems of recruiting, transition, retention, as discussed in U. T. Jankvist’s paper). This was important for me since I also plan to consult and use some of these original sources in my PhD thesis. Lastly, I learnt more about some arguments and theoretical frameworks (e.g., M. Niss’ fundamental reasons for mathematics education) for studying the history of mathematics education. This latter, I hope will be helpful to me to as I start researching for my paper on the first journal in mathematical sciences which began to be published in the 19th century Ottoman Turkey.
Finally, the 12th group in CERME-8 had a great atmosphere. The critiques were quite kind and only aimed at increasing the quality of work done in the name of the HPM spirit. I also believe that the group eminently reflected the CERME spirit as that of communication, collaboration and cooperation.
Here a link for my contributions to the HPM community since 2011: http://metu.academia.edu/MustafaAlpaslan
Catarina Mota, Didáxis – Cooperativa de Ensino & CMAT – Universidade do Minho, Portugal
About 15 years ago I started learning about the history of mathematics. Ever since, I use the history of mathematics to learn more mathematics itself and to use this in my teaching. Being able to discuss and interact with colleagues that share my enthusiasm for this subject is always a pleasure and a source of knowledge – that is exactly what I found during the CERME-8.
For five days we learnt about mathematics education in different countries and contexts, in particular how the history of mathematics can be used in the classroom. We heard oral presentations, discussed papers previously given to us, and above all shared ideas about our practice.
CERME 8 was my second CERME experience. The main reason for me to attend CERME again this year was that I found the environment, and the learning experience in this group meant that I can present my work knowing that all the criticisms are going to be made to help me improve. Being a congress in mathematics education, CERME also allows all participants to interact with researchers in different fields within mathematics: algebra, geometry, statistics, teacher training, etc.
As I am a PhD student, CERME provided to me the complete experience in academic research, from writing the paper, to reviewing process, to making oral presentation and listening and critiquing others’. It allowed me make the contact with more experience researches, in a friendly environment where everyone is available and willing to help.
In Antalya, during the Work Group 12 – History in mathematics education – I learned several very important things that I believe will help me improve my own practice:
- how the history of mathematics can be an inspiration for interdisciplinary activities
- that even in the earlier years in school the history of mathematics can help improve students’ knowledge and enthusiasm for mathematics
- I became aware of how original sources can be used for the teaching of mathematics
- I realized the importance of history of mathematics in teacher training and how the history of mathematics education can help us today with present difficulties in the teaching of mathematics.
All the experience was fruitful thanks to a wonderful organization, an interesting scientific program and an excellent WG chair (Uffe Thomas Jankvist) and co-chairs (Kathy Clark, Snezana Lawrence and Jan van Maanen). They prepared a program divided into different themes, and this allowed everyone’s work to be discussed, and promoted the friendly environment that made us receptive to others opinion, and at the same time available to make contribution with our own expertise.
When I left Antalya I was exhausted but full of energy and ideas, eager to start working and to share the experience with all of those who had not attended. For me, CERME and WG 12 is an experience to repeat.
Teresa Maria Monteiro, Portugal
This CERME is my second, I also attended the CERME in Poland two years ago. My fluency in English is not good enough for discussing more the ideas that I would like to talk about, so that is why I presented a poster rather than a paper.
I wanted to participate in this group because the themes of the group are near to my area of interest. We were able to work together and in small groups (4 or 5 people), which I found very good in terms of clarifying ideas and getting to really know colleagues in the group.
This year, I went back home before the end of the congress, so I did not assist the last two days and I know now that they were very intense. I heard from other colleagues that these two days were also full of good discussion, so I am awaiting eagerly the report of the group.
During the three days that I participated in CERME 8, I learned and reflected a little more about:
- examples of what and how can we use the history of mathematics in our classrooms
- examples of how to use historical drama in mathematics classroom
- that there is a similarity of the history of mathematics education in different countries, even between the countries that have different systems and structures of mathematics education now
I would like to share some links on the research I have done related to the poster I presented at CERME-8:
Revista: REMATEC 2012 (Brasil)
Congresso: I ENAPHEM 2012, Vitória da Conquista (Brasil)
Congresso: SPCE 2011, Guarda (Portugal)
Seminário Temático – Casa da Cerca, Almada (Portugal):
We were there
The HPM Group celebrated its 40th anniversary with HPM 2012 – the 8th quadrennial Satellite Meeting of ICME. It took place in Daejeon, Korea from 16 – 20 July, 2012, where more than 100 participants gathered for an interesting week with 7 plenary lectures, 60 oral presentations, 7 workshops, 2 panel discussions, a poster session, several exhibitions, and a special focus on Asian HPM and insights into Eastern Asia Mathematics History.
The seven plenary lectures concerned the seven themes of the meeting. The first one concerned history and epistemology implemented in mathematics education and was given by Tsang-Yi Lin from Taiwan. He gave three examples of projects, on ancient Greek geometry, on Brigg’s tables of Logarithm and on Cramer’s Rule. He concluded on the necessity for teachers to acquire knowledge on history. The second lecture, given by Tinne Hoff Kjeldsen from Denmark, was interested by the theoretical framework for integrating history of mathematics in mathematics education. It dealt with the difficult question of the results of history for and about the learning of mathematics. For this purpose, she analyzed two examples: Bernoulli’s catenary and Egyptian mathematics. The third lecture, given by Janette Barnett from USA, considered the use of original sources in the classroom and their educational effects. She described her own experiences with using papers of Boole and Cayley. These three lectures indicated that the purpose and ideas of HPM now has entered a new mature period.
Three other plenary lectures were interesting for seeing history of mathematics as an interdisciplinary and cultural tool for the teaching and learning of mathematics. Dominique Tournès from France gave a very complete panorama of mathematics for 19th century engineers, and especially on their methods and instruments, which can be used in classrooms. Michel-Pajus from France proposed a historical voyage into the literary-mathematical Universe. Her very living voyage had five stops: a Greek theatre, the world of Romans, a castle in Middle Ages, Parisian salons of the 17th and 18th centuries and the machinist world of 19th century. The last lecture of the meeting was devoted to mathematics from Eastern Asia, with the theory of equations in the history of Chosun mathematics presented by Sung Sa Hong from Korea.
For many years now, history of mathematics education has been a theme of International meetings of HPM. The number of oral presentations given in Daejeon on this theme shows the increasing interest among teachers and researchers. The plenary lecture of this theme concerned the social structures in mathematics education, more precisely the research on mathematics education with theories and methods from sociology of education. Johan Prytz, from Sweden, began to give motives for studying the history of mathematics education and argued for the use of a sociological perspective for this endeavor.
The oral presentations, workshops, and the poster session taken together showed the richness of on-going HPM related activities and research. From examples of how to teach history of mathematics to teaching mathematics through historical sources over a “journey to a proof”, issues about “trends on mathematics in novels”, “the ladder and the box problem”, “historical problems and mathematical knowledge for teachers” and “research on the Muk Sa Jib San Beob” we got a glimpse of the diversity of HPM activities and the multi-faceted perspectives through which History and Pedagogy of Mathematics is perceived and treated around the world in research, classrooms, art, culture, literature.
It is impossible to summarize and do justice to all the presentations in this short Newsletter contribution; for that we refer to the program and the papers that were submitted, all of which are available at the web site: http://www.hpm2012.org/?mid=announce_05. Instead we will make a few comments about the two panel sessions. Their themes were addressed towards practices: the first panel dealt with the problem of justification: Why do we require a “history of mathematics” course for mathematics teacher candidates? The second panel dealt with how we can get insights into effects of history in mathematics education through empirical research.
The intentions of the first panel session were twofold: to share experiences with ways in which history of mathematics is part of elementary and/or secondary mathematics teacher candidates’ education, and to provide a synthesis of group discussions during the panel session – this second part is going to be post-panel work based on records of the group discussions which were produced during the session. The presentations by the five panelists showed two things: 1) The status of history of mathematics in the curriculum in their different countries varies a lot from being explicit to being implicit at different levels, and 2) reflections about why history of mathematics should be part of teacher training and how that reflects back on the content and teaching of such a course for teacher candidates do not seem to be clearly developed. However, the two questions that were raised by the panel of why history of mathematics should be part of mathematics teacher training programs and (in case of a positive outcome of the why question) what it should look like, are key questions to be dealt with in the HPM-community.
The second panel discussed the question of empirical research on history in mathematics education through four lenses: 1) Lesson studies and the use of technology, 2) Original sources and recruitment, transition, retention, 3) Integrating history and teacher training, and 4) Mathematics education research frameworks and theoretical constructs in HPM. Several of these lenses were also addressed in some of the plenary lectures and the panelists managed to draw on these presentations and in doing so, they provided a sort of a common ground that initiated a very lively discussion in the audience. One of the suggestions for measuring the effects of history in mathematics education has come out of the New Mexico State University & Colorado State University – Pueblo programs of using primary sources for the teaching of mathematics. Their results show that maybe the use of primary sources can do more than function as a tool for teaching and learning of mathematics. They suggest addressing the specific aspect on student success consisting of recruitment, transition and retention – topics that educators, curriculum designers, and policy makers care about and pay attention to. Hereby linking to a group of people the HPM community needs to address, if we want to promote the explicit inclusion of history of mathematics in mathematics education curricula.
We would like to mention also that the meeting was very well organized, in a very agreeable and friendly atmosphere. We thank Sunwook Hwang, his colleagues, and students for all they did for the success of HPM 2012.
IREM and Laboratory LMJL, University of Nantes, email@example.com
Tinne Hoff Kjeldsen,
IMFUFA, NSM, Roskilde University, Denmark, firstname.lastname@example.org
On the first day evening of HPM 2012, we had “Preparation Session for Asia HPM.”
Chaired by Sung Sa Hong (Korea), there were three speeches given by Chang-Koo Lee (Korea), Mitsuo Morimoto (Japan), and Anjing Qu (China).
During the dinner after this special session, three countries agreed on the collaboration through Asia HPM.
I believe Asia HPM will play a very important role in helping Asian colleagues work together internationally and open their vision to research in Mathematics History.
What is a new-comer to HPM? In my case, I had met two inspirational figures in the HPM family, Costas Tzanakis and Fulvia Furingetti, at the ICTM conferences in Samos (1998), Crete (2002) and Istanbul (2006). Yet it was not until ICME 11 (Monterrey, 2008) that my meeting Costas and Fulvia came to fruition – there I met Jan van Maanen and Snezana Lawrence also. It took some more years and experiences (ESU-6 Vienna, 2010, CERME 7 Rzeszów, 2011 and BSHM in Greenwich and Dublin) before I was ready for the full immersion in HPM itself at ICME 12 in Seoul and HPM 2012 in Daejeon. The process of changing lens from that of a mathematician and ‘arriving’ at HPM is indeed a dépaysement; an internal adjustment is required to become comfortable with the external ‘paysage’.
It was at CERME 7 when I first presented my own work and enjoyed interaction with Mustafa Alpaslan, Kristín Bjarnadóttir, Kathy Clark, Uffe Janqvist, Tinne Kjeldsen and Peter Ransom, amongst others. It was good to meet all of these established HPM friends again in Daejeon; on the other hand, I regretted that Costas, Fulvia, Jan and Snezana could not be there. There were others I had met at ESU-6, some of whom came to Daejeon. I would like to mention Evelyne Barbin, Sunwook Hwang, and Manfred Kronfellner in their respective chairing roles of HPM and of the organizing committees for Daejeon and Vienna. These thirteen, along with several others whose company I enjoyed in Greenwich, Vienna, Rzeszów, and Dublin were the ones who inspired me to consider coming to the HPM conference in Daejeon – and I was not disappointed!
Of course it is the job of the scientific programme committee of any conference to give the conference a coherent shape and to ensure faithfulness to the chosen form. The structure afforded by the seven themes achieved this in the case of HPM 2012. However, the themes contributed much more than coherence, they underpinned the rich variety of endeavour that is the essence of HPM in the breadth and depth of the work carried out by researchers in a great many countries. Attention was paid, to good effect, to theoretical frameworks, on the one hand, and to the use of history (including original sources) in teaching mathematics, on the other. I appreciated how I might draw from most of the 27 presentations I attended to enhance my own professional work in teaching not only the history of mathematics (HoM), but also mathematics itself. The importance of the role of history in motivating seminal questions relating mathematics to science, technology and the arts was emphasised, as was the key position of mathematics in the cultures of Europe, Asia and the Americas. A variety of topics in the history of mathematics education (HoME) was explored. It seems that an emphasis on this area of research is relatively new; I suspect it will become more and more important as we try to understand deeply trajectories of curricular reform. Of the seven themes, it was the last one, namely mathematics from Eastern Asia, with which I had most difficulty engaging; I hasten to add that this was due to my own lack of familiarity with the area, rather than the quality of the presentations!
The conference embodied the rich interaction between the H, the P and the M of HPM. In the discussion, concern was expressed about the perceived peripheral position of HPM within the broader corpus of research in mathematics education. To address this concern, it may be important to be more explicit in employing established mathematics education research frameworks in HPM research. On the other hand, HoM plays its own distinctive role in mathematics education – this may need to be articulated more clearly outside the HPM community. There appeared to be diverse views on what were the appropriate grounds to persuade ‘others’ of the importance of HoM and HPM research.
The entire experience of HPM 2012 in Daejeon was extremely enriching: the presentations, the discussions, the interactions at the venue and later ‘into the evening’, the excursion (to historic Gongju) and the overall organization. For all of these, I am very grateful to all those who prepared so carefully for this excellent conference. I am confident I will draw on the experience of Daejeon for a long time to come.
CASTeL, Dublin, Ireland
SEOUL, KOREA, JULY 8TH TO 15TH
The premise of Discussion Group 5 at ICME 12 was that research on history of mathematics in education tends to have older pupils and students in mind, and that there is a lack of both research and resources on how to include a historical perspective when teaching younger pupils. Thus, we proposed a discussion group focusing on pupils aged 6-13. The organizers of the group were “co-chairs” Bjørn Smestad (Norway) and Funda Gonulates (USA/Turkey), with “team members” Narges Assarzadegan (Iran), Kathy Clark (USA), and Konstantinos Nikolantonakis (Greece). Of these, Kathy, Narges, and Bjørn made it to the conference and led the discussions in Seoul.
There were three key questions provided out in the invitation to the discussion group:
- Which ideas from HPM can be used with children (aged 6-13) in such a way that produces good results (e.g. improved student engagement, positively impacted student learning)?
- What would be criteria for finding, developing and selecting materials to be used with children (aged 6-13)?
- How does the HPM community in particular (and mathematics education community more broadly) assure that high-quality material that cover a variety of topic are produced and shared?
Discussion groups were allotted two 90-minute sessions at the conference. Question 1 was discussed in the first session and questions 2 and 3 were discussed in the second session.
In the first session, after everybody introduced themselves, there was a short introduction mentioning different ideas from the literature about how to include history of mathematics in teaching. Thereafter, Narges Assarzadegan gave a short talk on how she has been working with her students in Iran on the topic. Kathy Clark subdivided question 1 into further sub-questions:
- What are the ideas for which HPM contributes meaningfully to the mathematical experience of pupils aged 6-13?
- What are the forms of good results we wish to happen?
- How do we know when good results occur?
- What are some of the obstacles that teachers using HPM with pupils of this age may encounter – and what are ways to address or minimize the obstacles?
These questions were discussed in groups, and then the group discussions were summarized for the whole group. A wealth of ideas were discussed in the groups: incorporating historical instruments, finding good problems from history to engage children of this age range, using concrete materials to visualize mathematics, working with words instead of symbols, exploring cross-curricular themes, for instance historical measuring units, using source material from the middle ages, studying materials from the cultures of children’s parents and grandparents, and studying positive/negative numbers through history, to mention a few. More generally, it was discussed that although “storytelling” was in our introduction described as just one of many ways of working with history of mathematics to kids, storytelling is indeed particularly important at this age level and should not be disparaged. Teachers who are able to fascinate their pupils with great (and meaningful) stories from the history of mathematics have a wonderful gift.
The good results we wish to happen at this age level mostly has to do with the attitudes of the children: we want them to see mathematics as a fascinating cultural and human activity and make them connect to it in new ways. We will probably never be able to prove beyond doubt that using history of mathematics with children do have positive effects, as history of mathematics will always be just one of several elements a teacher uses simultaneously to engage his students. For the teacher, however, such proofs are not necessary – just seeing the pupils engaged is good enough.
Of course, there are obstacles – both in terms of resources and in teachers’ opinion that history of mathematics will take time from mathematics. Moreover, as work on history of mathematics is not mandated in curricula in most countries, there is the ever-present need to justify it to colleagues who are not interested. This can also be lonely work. Some of these issues can partly be remedied by working on what we discussed in session 2, however.
For the second session, discussing questions 2 and 3, Bjørn Smestad had an introduction giving some good examples of use of history of mathematics (see link below), and Kathy Clark showed some examples from online resources. Then, after a summary of the discussion in part 2, there was more group work, which was then shared.
On which criteria should be used, a whole range of issues were mentioned, but not every resource need to fit every criterion. The resource should:
- Include significant mathematics (and be curriculum-related)
- Include activity/task/problem/something for pupils to “do”
- Fire-up the imagination; inspire pupils to do mathematics
- Tell a story
- Have multiple representations (pictures, text, sound, video, interactivity)
- Show mathematics as a human endeavor (e.g., have a cultural aspect)
- Be doable in a “reasonable amount of time”
- Generate discussion, debate among the pupils
- Be authoritative and accurate
The groups mentioned that there are lots of materials on the internet, and at first you feel lost as it is difficult to see what is of good quality. After a while, you start being able to determine what “makes sense”, but still you need to sort through a lot of bad stuff while looking for the gems. (But to get even there, you will probably need experience in using the materials – and where do you get that?) Thus, there is a need for a “clearing house” for keeping materials in one location. This was made more concrete later in the discussion: what we need is a “Kantor project” (named after Moritz Kantor), mimicking the “Klein Project” in providing high-quality resources to teachers, for instance with comments both from historians of mathematics and from teachers who have used the resources with pupils (including information on how it was used and the perceived outcomes). In addition, the need for History of Mathematics courses and better resources at libraries, were mentioned.
For the organizers, this was the first attempt at organizing a discussion group at such a conference. Part of the difficulty of planning it was that there was no way of knowing if there would be five or fifty participants. As it turned out, there were about 25 people from around the world participating, with a good mix of well-known faces in the HPM community and newcomers, which led to good discussions where everybody took part. In that respect, we view the discussion group as a successful experience, and hope that the discussions here will inspire further work on teaching with history of mathematics for young pupils.
Bjørn Smestad: Examples of “Good” Use of History of Mathematics in School. http://hioa.academia.edu/Bj%C3%B8rnSmestad/Papers/1769606/Examples_of_Good_Use_of_History_of_Mathematics_in_School
based partly on the notes of Kathy Clark