### CERME-8 Reflections of our Young Researchers

**Reported by Snezana Lawrence, Bath Spa University, Bath, England**

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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 19^{th} century Ottoman Turkey.

Finally, the 12^{th} 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>

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