September 5-6, 2013
Dublin, Ireland
Dear Friends in the HPM Community,
I am pleased to let you know that the first call for papers has been announced on the MEI 5 web page, www.spd.dcu.ie/mei.
This is the fifth in the series of “Mathematics Education Ireland” biennial conferences. International keynote speakers are: Tinne Hoff Kjeldsen (Roskilde), John Monaghan (Leeds) and Jennifer Young-Loveridge (Waikato).
Research reports, reviews and posters relating to work done in mathematics education across the educational spectrum are invited. The conference proceedings will be published. Papers should be submitted by 8th April 2013. For further details, see the conference web page.
Although MEI 5 does not specialise in HPM, the theme of the conference, “Mathematics Education: Crossing Boundaries”, is amenable to HPM contributions – to dépaysement in all its manifestations! If you would like to send this announcement to others, I encourage you to do so.
Maurice OReilly
July 22-28, 2013
Manchester, UK
Information from http://www.ichstm2013.com/
The International Congress of History of Science, Technology and Medicine takes place every four years. Recent meetings have been held in Mexico City (2001), Beijing (2005) and Budapest (2009). The 2013 International Congress theme is Knowledge at Work.
Disciplines:
-Mathematics
S005. Mathematics and machines: explorations of machine-assisted mathematics since 1800
S010. The introduction of mathematics in Iberoamerica (part II)
S011. Les sciences mathématiques 1750-1850: continuityés et ruptures
S045. Mathematical facets of measurement, measuring units, measured quantities and their uses
S107. Poincaré’s Méthodes nouvelles de la mécanique céleste in historical context: bridging the frontiers of knowledge in mathematics, astronomy and wireless tech
S114. Mathematics and patronage
S115. Mathematical knowledge at work in Ancient China
S116. The history and philosophy of mathematical optimization
S117. The institutionalization of mathematics and the founding of national societies
-Astronomy
S092. Astronomy and its applications in ancient and medieval societies
S095. Using modern computing power to analyse and explicate ancient astronomical sources: opportunities and challenges
S107. Poincaré’s Méthodes nouvelles de la mécanique céleste in historical context: bridging the frontiers of knowledge in mathematics, astronomy and wireless tech
S129. Islamic astronomy in its cultural context
-Technology and communications
-Systems, data, automation, computation
-Measurement
-Physics and natural philosophy
-Chemistry and alchemy
-Earth, geology, climate, oceans
-Life sciences and natural history
-Medical and human sciences
-Ecology and environment
-Social sciences
-Philosophy and logic
For the complete programme, see:
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:
- İnterdisciplinarity
- 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)
http://www.google.pt/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CCwQFjAA&url=http%3A%2F%2Fwww.rematec.net.br%2Farquivos%2Frevista_rematec_09.pdf&ei=a6cjUcbDMsWChQfC4ICYDg&usg=AFQjCNHzQhasjvQYVCQtv_29NaoUFMk7Tg&bvm=bv.42553238,d.ZG4
Congresso: I ENAPHEM 2012, Vitória da Conquista (Brasil)
http://www.google.pt/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0CDMQFjAB&url=http%3A%2F%2Fenaphem.galoa.com.br%2Fsites%2Fenaphem.galoa.com.br%2Ffiles%2FResumo-ENAPHEM-metodologia-doc.doc&ei=L6gjUfTCKMqphAfn5YHgCA&usg=AFQjCNG9d7X8xcnvxPj6HANYAKQaVOqNOw&bvm=bv.42553238,d.ZG4 <http://www.google.pt/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0CDMQFjAB&url=http%3A%2F%2Fenaphem.galoa.com.br%2Fsites%2Fenaphem.galoa.com.br%2Ffiles%2FResumo-ENAPHEM-metodologia-doc.doc&ei=L6gjUfTCKMqphAfn5YHgCA&usg=AFQjCNG9d7X8xcnvxPj6HANYAKQaVOqNOw&b>
Congresso: SPCE 2011, Guarda (Portugal)
http://www.google.pt/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0CDMQFjAB&url=http%3A%2F%2Fwww.ipg.pt%2F11congresso-spce%2Fatas_SPCE2011_volume3.pdf&ei=SKkjUc_LDsiEhQedrYDgDQ&usg=AFQjCNFrGL4_TppXb9kV1cuIGniJQPPfQA&bvm=bv.42553238,d.ZG4
Seminário Temático – Casa da Cerca, Almada (Portugal):
http://www.google.pt/url?sa=t&rct=j&q=&esrc=s&source=web&cd=5&ved=0CEsQFjAE&url=http%3A%2F%2Fwww.uied.fct.unl.pt%2Fmoodle%2Ffile.php%2F28%2FX_Semina_rio_Tema_tico-programa-livro.pdf&ei=SKkjUc_LDsiEhQedrYDgDQ&usg=AFQjCNEKGyh7CUyNHyik0ysich5ZY8gb7w&bvm=bv.42553238,d.ZG4 <http://www.google.pt/url?sa=t&rct=j&q=&esrc=s&source=web&cd=5&ved=0CEsQFjAE&url=http%3A%2F%2Fwww.uied.fct.unl.pt%2Fmoodle%2Ffile.php%2F28%2FX_Semina_rio_Tema_tico-programa-livro.pdf&ei=SKkjUc_LDsiEhQedrYDgDQ&usg=AFQjCNEKGyh7CUyNHyik0ysich5ZY8gb7w&bvm=bv.42>
September 25-28, 2013
Uppsala, Sweden
1st Announcement
Organizer: Department of Education, Uppsala University
We are calling for papers for this third conference continuing the successful works initiated in Iceland (June 2009) and continued in Portugal (October 2011). Abstracts of proposed contributions (length: about one page) should be submitted by March 31, 2013. The decision about acceptance will be communicated by May 15, 2013. Submission of abstracts, and later on papers, is done via the conference website:
http://www.blasenhus.uu.se/3ICHME
The conference
History of mathematics education, since it became first visible internationally at ICME 10 in 2004 in Copenhagen as the TSG 29, is meanwhile a well-established research area. The first international journal devoted to this field of study, the International Journal for the History of Mathematics Education, is published since 2006. History of mathematics education became a subject in various international meetings, for instance at the ESU-5 (Prague, 2007) and ESU-6 (Vienna, 2010), at the CERME meetings, and at ICME 11 (Monterrey, 2008, TSG 38), ICME 12 (Seoul, 2012, TSG 35) and HPM2012 (Daejong, 2012)
The first specialized research conference, entitled “On-going Research in the History of Mathematics Education”, held in Garðabær near Reykjavík (the capital of Iceland) in 2009, turned meanwhile to a series of such specialized conferences. We are now organizing the third international conference, this time in Uppsala, Sweden. Uppsala University has longstanding traditions in studies of the history of education and more recently also the history of mathematics and mathematics education.
The themes treated in the former conferences were in particular (see also the Proceedings): Geometry teaching, Algebra teaching, Teaching of calculus, Interdisciplinarity and contexts, The modern mathematics movements, Curriculum history, Development of mathematics education in specific countries, Practices of teaching, Mathematics textbooks and Transmission and reception of ideas.
We are projecting to publish peer reviewed proceedings.
Organizing committee:
- Kristín Bjarnadóttir
- Fulvia Furinghetti
- Johan Prytz
- Gert Schubring
Further information about the conference, accommodation and Uppsala is or will be available on the conference website.
Registration and conference fee
Before June 15, 2013, the fee is 160 Euros, after that the fee is 190 Euros. Last day of registration and payment is August 28, 2013. Registration is done via the conference website.
References
Paedagogica Historica, Special Issue: History of Teaching and Learning Mathematics, ed. by Gert Schubring, 2006, XLII: IV&V. [Proceedings of TSG 29 at ICME 10]
Bjarnadóttir, Kristín; Furinghetti, Fulvia & Schubring, Gert (Eds.) (2009). “Dig where you stand”. Proceedings of the conference on On-going research in the History of Mathematics Education. Reykjavik: University of Iceland – School of Education.
Bjarnadóttir, Kristín; Furinghetti, Fulvia; Matos, José & Schubring, Gert (Eds.) (2012). “Dig where you stand” 2. Proceedings of the conference on the History of Mathematics Education. Lisbon, Universidade Nova. (Forthcoming)
Information sent by
Johan Prytz
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.
Evelyne Barbin,
IREM and Laboratory LMJL, University of Nantes, evelyne.barbin@wanadoo.fr
Tinne Hoff Kjeldsen,
IMFUFA, NSM, Roskilde University, Denmark, thk@ruc.dk
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.
Sunwook Hwang
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.
Maurice OReilly,
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.
See also:
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
Bjørn Smestad,
based partly on the notes of Kathy Clark
At the ICME 2012 Conference, history of mathematics (HM) in maths education was specifically discussed in several contexts: one of the 37 Topic Study Groups (chaired by W.S. Horng and R. Chorlay); one discussion group on “Uses of History of Mathematics in School (Pupils aged 6-13)” (organized by B. Smestad, Kathy Clark, and Narges Assarzadegan); one regular lecture on “History, Application, and Philosophy of Mathematics in Mathematics Education: Accessing and Assessing Student’s Overview & Judgment” (by U. Jankvist); and one general presentation of The HPM international study group, among the organizations affiliated with the ICMI. A parallel TSG dealt with the history of mathematics teaching and learning (chaired by K. Bjarnadóttir and F. Furinghetti).
Eleven talks and fourteen posters were presented in the context of TSG 20, with participants from (nearly) all continents; unfortunately, the African continent was not represented. The TSG was a great success if success is to be measured by attendance; due to the size of the room, many had to sit on the floor, or stay in the lobby. We are sorry our attempts to remedy this situation failed.
Being of a multi-faceted nature, the topic was addressed from a great variety of viewpoints, which testifies to the richness of our field. Our goal here is not to summarize the talks (which are still available on-line at http://www.icme12.org/) but to stress this variety of viewpoints and research perspectives.
Research in the history of mathematics was represented by A. Cauty’s talk on Aztec calendars, providing the rest of the community with fresh material for future, more teaching-oriented work. At the other end of the spectrum, several innovative teaching or training experiments were presented and discussed: a course for undergrad students, with a focus on the role of mathematics in European culture (J. Wanko); an undergraduate course on propositional logic and the meaning of “if-then” statements, emphasizing student work on original sources (J. Lodder); a course designed for newly qualified teachers, with an emphasis on the role of HM as a means to foster mathematical content knowledge (S. Lawrence, presented by P. Ransom); a course on the history of mathematics for pre-service teachers in Norway, with a focus on the interactions between historical content knowledge, image of mathematics, and attitude toward the inclusion of HM in teaching (B. Smestad).
Finding the right tools (be they conceptual, or quantitative) to describe, analyze and assess teaching practices is another endeavour that calls for further research. These questions are by no means specific to the HPM community, and it is well-worth investigating the extent to which shared tools are relevant in an HPM context. Along this line of research, M. Alpaslan presented his on-going doctoral work on the assessment of a pre-service teacher-training course in HM in Turkey, with a view to improving its design in a context of institutional reform. U. Jankvist presented a joint work (with R. Mosvold, J. Fauskanger, and A. Jakobsen) on the MKT framework (Mathematical Knowledge for Teaching), and argued for its usefulness both as an analytical tool and as a means of communication with the math-ed community at large.
Four case-studies were presented, which used specific historical texts to address didactical/epistemological research questions. The role of visualization in proofs was studied on the base of Archimedes’ “mechanical proof” of the theorem on the volume of the sphere (M. del Carmen Bonilla); CABRI 3D was used as a visualization tool. S. Xuhua argued that several justifications for algorithms in the multiplicative theory of fractions that can be found in the Chinese classic The Nine Chapters could improve students’ understanding of the standard rules, and help fight well-known systematic errors. T. Kjeldsen reported on an experiment conducted at high-school level, in which students were asked to make sense and compare two historical texts bearing on the notion of function (Euler, Dirichlet); among other effects, this unusual task was shown to help make “meta discursive rules” more explicit. Finally, A. Michel-Pajus presented a collection of algorithmic texts – some well-known, some less well-known – and studied them from an epistemological and comparative perspective; the algorithms were studied both in terms of expression (algorithmic texts, in a semiotic and instrumental context), and justification.
It should be stressed that in the ICME context, the TSG on HM in mathematics education attracts many newcomers to the field of HPM, thus challenging us to make our “common culture” and our quality requirements more explicit. For instance, the fact that we lay the emphasis on the use of original sources may have come as a surprise to some; even without considering use in the classroom, the fact that original sources are available (availability being highly dependent on language) is not always so well known. When original sources are considered, working with them does require some know-how. We hope this TSG was instrumental in raising awareness on these aspects; we were pleased to see that many participants, including newcomers, could attend the HPM meeting in Daejeon.
The chairpersons would very much like to thank all those who helped organize this TSG, in particular the members of the “team”: Hyewon Chang, Kathy Clark, Abdellah El Idrissi, and Manfred Kronfellner; and, Evelyne Barbin, who acted as liaison with the IPC.
Renaud Chorlay
IUFM de Paris (Uni. Paris Sorbonne) & IREM de Paris (Uni. Paris Diderot)
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