Welcome to Newsletter 94!  Here in Florida we have been completely entrenched in all things “spring” – though this is easy to do since we did not experience any version of a season that resembled winter.  In reality, I cannot believe it is already March, as my “To Do” list stays perpetually filled with things I should have already completed – like NL 94!


That aside, it really has been a busy year already.  There are several HPM-related activities that have taken place or that are onging, and many of them are described or advertised in this installment of the HPM newsletter.  In my comments below, I mention two additional items which are not included in separate annoucements that you will read about in this newsletter.  As well, I would like to update you on the evolving structure of the HPM Group.


First, approximately 25 colleagues participated in the Thematic Working Group (12 TWG 12), “History in Mathematics Education,” at CERME 10 (1-5 February 2017, Dublin, Ireland).  Included in the seven ‘working sessions’ at the conference were presentations on 16 papers and 2 posters, which you can find in their pre-converence form here: https://keynote.conference-services.net/programme.asp?conferenceID=5118&language=en-uk.  Additionally, Michèle Artigue and Uffe Thomas Jankvist led participants in a discussion of the forthcoming ERME chapter on TWG 12 (http://cerme10.org/wp-content/uploads/2017/01/TWG12_ERME_Book_Chp17_History_Draft.pdf).


In reflecting on CERME 10 I was reminded that working in the field of history in / of mathematics education energizes me in two ways.  In the one sense, I enjoy coming together and seeing familiar faces and reconnecting with them about shared ideas and further following their work.  On the other, I am energized by the newcomers (not necessarily new to the field, but perhaps new to the HPM community or activities) whom I get to meet and to learn about the exciting work and scholarship taking place around the world. I believe the working group activities were well received by participants of TWG 12, and I thank Renaud Chorlay (France) and Katalin Gosztonyi (Hungary) for their leadership during the working group at CERME 10.


Secondly, I wanted to make sure that I reminded you all that the International HPM Group is an affiliated study group of the International Commission on Mathematical Instruction (ICMI), which is an official commission of the International Mathematics Union (IMU).  The ICMI leadership encourages members of the affiliated study groups to remain informed by subscribing to the ICMI News.  You can read more about the ICMI News here: http://www.mathunion.org/index.php (and at the bottom of the page you will find directions for subscribing to the ICMI News).



Finally, I would like to take this opportunity to inform you about the shape of the formal operating structure of the HPM Group.  Over the past several months I have been in contact with Advisory Board members and the previous Executive Committee (2012-2016), and after conducting a vote of the Advisory Board members I have established the Executive Committee for the 2016-2020 term and updated the Advisory Board membership.  I have also established an Honorary Advisory Board (HAdB), but at the time of this writing I am still waiting to hear back from all of the inaugural invitees.  Consequently, I hope to announce the first HAdB in the July newsletter (NL 95).


You will find the updated Advisory Board at the end of this newsletter (pp. 26), and I hope that you will join me in welcoming three new members:

Michael N. Fried (Israel),

Helder Pinto (Portugal), and

Leo Rogers (UK).


The Executive Committee (ExC) for the 2016-2020 term is:

Évelyne Barbin (France), Fulvia Furinghetti (Italy), Uffe Thomas Jankvist (Denmark), Tinne Hoff Kjeldsen (Denmark), and

Costas Tzanakis (Greece).


I should also state that for the next major HPM-related conference activities (ESU-8, HPM 2020, and ICME-14), there were will be additional ExC members who will serve as liasons to the Group (for example, Bjørn Smestad will serve in this capacity for ESU-8).



As I write this, I realize I have much to learn and to do to serve the HPM Group in the best way possible.  One of the reasons I asked the Advisory Board to vote on five members to comprise the Executive Committee was because I felt I needed additional assistance in learning about how best to serve the HPM community.  The Advisory Board is also a vital component of informing and guiding the Chair and the HPM Group, and consistent and timely participation is a critical contribution of an Advisory Board member.  There are exciting decisions that need to be made in the coming months, related to the smooth running of ESU-8, as well as to begin planning for HPM 2020.  I ask for your support in these activities, and welcome your comments and active participation.



Kathy Clark

HPM Chair

Florida State University, USA

20-24 July 2018

Oslo, Norway

Oslo & Akershus University College of Applied Sciences





  1. Aim

The ESU mainly aims

–          to provide a forum for presenting research in mathematics education and innovative teaching methods based on a historical, epistemological and cultural approach to mathematics and their teaching, with emphasis on actual implementation;

–          to give the opportunity to mathematics teachers, educators and researchers to share their teaching ideas and classroom experience related to this perspective;

–          in this way, to motivate further collaboration along these lines, among members of the mathematics education community in Europe and beyond.


  1. Focus and main themes of ESU-8

The ESU is more a collection of intensive courses than a conference for researchers. It is a place where teachers and researchers meet and work together. It is also a place where beginners, more experienced researchers and teachers present their teaching experience to the benefit of the participants and get a constructive feedback from them. It refers to all levels of education – from primary school, to tertiary education – including in-service teachers’ training.

The programme and activities of ESU-8 are structured around the following main themes:

Theme 1: Theoretical and/or conceptual frameworks for integrating history and epistemology of mathematics in mathematics education;

Theme 2: History and epistemology in students and teachers mathematics education: Curricula, courses, textbooks, and didactical material of all kinds – their design, implementation and evaluation;

Theme 3: Original historical sources in teaching and learning of and about mathematics;

Theme 4: Mathematics and its relation to science, technology, and the arts: Historical issues and socio-cultural aspects in relation to interdisciplinary teaching and learning;

Theme 5: Topics in the history of mathematics education;

Theme 6: History of mathematics in the Nordic countries.

Emphasis is put on work and conclusions based on actual classroom experiments and/or produced teaching & learning materials, but insightful theoretical ideas and/or historical analysis with visible didactical implications are also welcome.


  1. Activities during ESU-8

All activities should refer to the ESU-8 main themes. Its scientific program will be structured along these themes, consisting of a few plenary lectures and panels, as well as, parallel sessions of oral presentations, short communications and posters, for participants, who want to speak about their own experience, or research. A major part of the programme, however, consists of workshops.


  1. Target population

The majority of the participants is expected to be (elementary or secondary) schoolteachers, who may wish to gain new ideas on how they can integrate the history of mathematics into their teaching.  Special effort will be made so that each session includes activities relevant and interesting for schoolteachers; for instance activities with focus on useful resources and didactical material available in Norwegian, or other national languages. However, there will be also university teachers and students, interested in the integration of the history and epistemology of mathematics into mathematics education, as well as, historians of mathematics, who may give a limited number of lectures to inform others about recent developments in their domain, and mathematicians with an interest in the relation between mathematics, its history and epistemology, and its role at present and in the past.


  1. Time and place

The ESU-8 will take place from 20 to 24 (Friday to Tuesday) July 2018 at the Oslo & Akershus University College of Applied Sciences, Oslo, Norway.


  1. Official Languages

The official languages of ESU-8 are English, Norwegian and French: All plenary talks and panel discussions will be in English. Other activities can be delivered in any of the official languages. However, presenters and workshop organizers should keep in mind that all activities should in principle be targeted to an international audience and that many participants will not be native speakers of any of these languages. Consequently, for activities not in English, the presenters will be asked to use two sets of transparencies, one being in English, while workshop organizers are strongly advised to prepare copies in English of their material. This will increase participation and will greatly facilitate communication among participants.


  1. Submission of proposals

31 October 2017: deadline for submitting Abstracts of proposals for all types of activities.

15 December 2017: Notification of acceptance or not of the submitted proposals.

The members of the Scientific Program Committee (SPC) will review the submitted abstracts. Acceptance of a proposal means that the proposed activity will be included in the ESU-8 Scientific Programme. Full texts for inclusion to the ESU-8 Proceedings will be submitted after ESU-8 and will be further reviewed by members of the SPC at the usual international standards.

Important: Submissions of proposals and full texts, the reviewing process, and authors’ notification will be realized online via https://esu8.edc.uoc.gr/submission and following the guidelines therewith.


8. Proceedings

Publishing the Proceedings of ESU-8 is a major task. They will appear after ESU-8, so that authors are given the opportunity to enrich their text as a result of the feedback they will gain during ESU-8. Details on the procedure and the deadline for submitting full texts, their size, the format guidelines and the expected date by which the proceedings will be available to all registered participants, will be announced in due course from the ESU-8 and HPM official websites




  1. The web site

Making known the ESU worldwide, is a major task. To this end, a web site is being developed under the URL http://esu8.edc.uoc.gr It will be regularly updated as an effective tool for providing updated practical information, allowing for online registration, submission of proposals and full texts, supporting the reviewing process, etc.


  1. For further information, contact

Constantinos Tzanakis, Dep. of Education, Univ. of Crete, 74100 Rethymnon, Greece, esu8.tzanakis@edc.uoc.gr  (chair)

Bjørn Smestad, Dep. of Primary and Secondary Teacher Education, Oslo & Akershus Univ. College of Applied Sciences, Oslo, Norway, esu8.smestad@edc.uoc.gr  (chair of Local Organizing Committee)

Evelyne Barbin, IREM et LMJL, UFR des sciences et des techniques, Univ. de Nantes, 2 rue de la Houssinière, BP 92208, 44322 Nantes Cedex, France, evelyne.barbin@wanadoo.fr (co-chair)

Uffe Thomas Jankvist, Dep. of Education, Aarhus University, Campus Emdrup. Tuborgvej 164, DK-2400 Copenhagen NV, utj@dpu.dk (co-chair)

Tinne Hoff Kjeldsen, Dep. of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, thk@math.ku.dk  (co-chair)


For more detailed and regularly updated information, visit




An Example of Using the

History of Iranian Mathematics for the Math Classroom

Dividing a right angle into five equal angles with only a straightedge and a compass is used to construct particular tiling patterns in Islamic arts, and one of these patterns is presented in figure 1 (10-petal rose construction). The methods and ideas that I explain in this paper were obtained from Iranian math history (Jazbi, S. A. (translator), Applied Geometry, appendix2. Soroush Press, ISBN 964 435 201 7, Tehran 1997). All figures have been created by the author using the Geometer’s SketchPad (GSP) software program. These samples have been used at the Isfahan Math House (IMH) in workshops for teaching math history to secondary students and mathematics teachers.

Figure 1. 10-petal rose construction (girih construction)

 1)      Task 1: Dividing a right angle into five congruent angles with only a straightedge and a compass Construct arbitrary arc  (figure 2).


Figure 2.

2)      Construct D the midpoint of OA then find D‘ as OD = OD‘ (figure 3).


Figure 3.

3)      Then construct a circle with center D‘ and radius DB. This circle cuts OA at point E (figure 4).


Figure 4.

4)      Now construct segment BE (figure 5).


Figure 5.

5)      Finally, construct a circle with center B and radius BE, and label the intersection point of the green circle and new circle (in magenta), F (figure 6).


Figure 6.


6)      Construct segment OF, and then  (figure 7). (Prove it!)


Figure 7.

7)      Now divide  into four equal angles (explain your work!). Now you have five angles.

  1. a) Task 2: Dividing a right angle into six congruent angles with only a straightedge and a compass

1)      Construct a circle with center O and radius OB (figure 8).


Figure 8.

2)      Construct a circle with center B and radius BO. Label the intersection point of the two circles, D (figure 9).


Figure 9.

3)      Construct segment OD, then . Why? (figure 10)


Figure 10.

4)      Construct the  bisector, and repeat again for created angles. Construct   bisector, then you have six  angles (figure 11).


Figure 11. Dividing a right angle into six angles.

Dividing a right angle into six equal angles can be used to construct Islamic art patterns. One of them is named a 12-petal rose pattern like the one shown in figure 12.


Figure 12. 12-petal rose pattern

Narges Assarzadegan, Math teacher, math history researcher, Isfahan Mathematics House (IMH) (Iran)

MAA Convergence is both an online journal on the history of mathematics and its use in teaching and an ever-expanding collection of online resources to help its readers teach mathematics using its history. Founded in 2004 by well-known mathematics historians and educators Victor Katz and Frank Swetz, Convergence brings you a variety of interesting articles and teaching tools. It is freely available from the Mathematical Association of America (MAA) website: http://www.maa.org/press/periodicals/convergence

We highlight here some of our newest articles and resources for use in your classroom. Many of them use interactive features to help students understand and explore historical mathematical ideas.

In “Ancient Indian Rope Geometry in the Classroom,” Cynthia Huffman and Scott Thuong offer information, activities, and applets to help you and your students explore the geometry of altar construction in ancient India. In the photograph, boys work on a model of the bird-shaped fire altar in an Agnicayana ritual in Panjal, Kerala, India in 2011. (Photo courtesy of Professor Michio Yano.)


In “Geometrical Representation of Arithmetic Series,” Gautami Bhowmik explores a geometric tradition in Sanskrit arithmetic texts from Medieval India and shares problems from these texts for your students.

“Historical Activities for the Calculus Classroom,” by Gabriela Sanchis, presents curve-sketching, tangent lines, and optimization in the context of historical problems, and is illustrated by 24 interactive applets and 10 animations.

In “Descartes’ Method for Constructing Roots of Polynomials with ‘Simple’ Curves,” Gary Rubinstein explains and derives Descartes’ methods from his 1637 Geometry and illustrates them using interactive applets. The diagram shows a step in the construction of roots of sixth degree polynomials using a ‘Cartesian parabola’ and circles (from GeoGebra applet by Gary Rubinstein).


In “Pythagorean Cuts,” Martin Bonsangue and Harris Shultz answer the question ‘Can Euclid’s proof of the Pythagorean Theorem be adapted to shapes other than squares?’ and encourage you to pose it to your students.

“Some Original Sources for Modern Tales of Thales,” by Michael Molinsky, features earliest known sources for stories about Thales, and applets illustrating methods attributed to him. The diagram shows how Thales might have measured the distance from ship to shore (from GeoGebra applet by Michael Molinsky).


“A GeoGebra Rendition of One of Omar Khayyam’s Solutions for a Cubic Equation,” by Deborah Kent and Milan Sherman, explains and illustrates how the 11th century Persian mathematician, philosopher, and poet geometrically determined a positive real solution to a cubic equation.

“Edmund Halley, 1740” is an historical poem in which Halley reflects on his role in publishing Newton’s Principia, by award-winning Oxford poet Andrew Wynn Owen.

“D’Alembert, Lagrange, and Reduction of Order,” by Sarah Cummings and Adam Parker, offers two historical approaches, one familiar and one unfamiliar, to enrich your differential equations course.

In “Euler and the Bernoullis: Learning by Teaching,” author Paul Bedard reflects on lessons he has learned about mathematics teaching and learning from these great mathematicians.

In “Can You Really Derive Conic Formulae from a Cone?” Gary Stoudt uses 17 interactive applets to explain how attempts to double the cube led ancient Greek mathematicians to discover and develop the conic sections.

Finally our “Index to Mathematical Treasures” includes hundreds of images for use in your classroom, including photographs of “The Cambodian (Khmer) Zero” (of 683 CE) by Amir and Debra Aczel.

See all of these articles and more at MAA Convergence:


Join us at the Convergence of mathematics, history, and teaching!

Janet Beery

Editor, MAA Convergence

University of Redlands


Dear colleagues and friends of HPM,


Greetings and welcome to Newsletter 93 of the HPM Group! I have assisted with the Newsletter for several years now, but this is the first time I need to address the whole group in an explicit way – so I ask for your forgiveness for my first attempt at a communication of this type.


First, I would like to thank Luis Radford for his service to the HPM community, as chair of the HPM Group for the last four years.  I also wish to thank the members of the Advisory Board, the members of the Executive Committee, the Newsletter editors and distributors (especially to Helder Pinto for formatting contributions from all over the world into such an inviting format), and the friends and colleagues of the community for all the work, interactions, and contributions made over the last four years. Being a participant in this community (for just about 12 years now) has been one of the most professionally satisfying aspects of my career, and I am grateful to be a part of it.



Since I am late in getting this message to Helder so that the November 2016 newsletter can be distributed, I will not introduce myself at great length. Here is a short summary of who I have been as a mathematics educator (broadly) and one who is interested in how history and pedagogy of mathematics belongs in mathematics education.


Many of you know me in my post-Ph.D. life; however, I lived another life in mathematics education before I became an active member in the HPM Group. I taught high school mathematics from 1987 to 2001 and in 2001 I was awarded an Albert Einstein Distinguished Educator Fellowship, and as part of that fellowship, I served on Capitol Hill in Washington, DC, advising legislators in matters of educational policy.  During that one-year fellowship, I realized that I knew very little about the education profession, and I decided that I should pursue a Ph.D. in Mathematics Education to rectify that. However, just before leaving the classroom, I became involved with The Institute for the History of Mathematics and its use in Teaching, and through that work – as a high school mathematics teacher field testing modules from what would become the Historical Modules (Katz & Michalowicz, 2004) – I met Victor Katz and the first stone in my path to a Ph.D., as well as my future academic career, was set.


I completed my Ph.D. in Curriculum and Instruction (Mathematics Education specialization) at the University of Maryland College Park, and Victor Katz continued to be a strong influence in my work there (including serving on my dissertation committee). Victor was also the first to bring such conferences as ICME and the HPM satellite meeting to my attention.  I attended my first ICME meeting in 2004 (ICME 10, Copenhagen) but due to lack of funding, I was unable to attend HPM that year. Since 2004, however, I have attended two ICMEs, three HPMs, three ESUs, and three CERMEs.


I moved to Tallahassee, Florida in 2006 and because of the pre-service teacher education program that was in place at FSU when I first began, I was able to engage in work that I am still very much interested in: investigating (problematizing?) the role that history of mathematics plays in teachers’ mathematical knowledge for teaching.


My work at FSU has changed quite a bit in the last 10 years, and as a result, I have needed to diversify and expand my interests about the role of history of mathematics in mathematics teaching and learning.  I am excited to be involved with two efforts – both since 2015. In the first, I have been working with colleagues from the University of Siegen (Ingo Witze, Gero Stoffels) and the University of Cologne (Horst Struve) on a project in which a seminar based on the historical development of a particular branch of mathematics (geometry, in one case) is used to address the transition problem faced by university students preparing to teach mathematics (the transition from school to university mathematics, in particular). In the second effort, a team of mathematicians is developing and testing primary source projects (PSPs) for use in undergraduate mathematics classrooms. One goal of the project (TRIUMPHS: Transforming Instruction in Undergraduate Mathematics via Primary Historical Sources; http://webpages.ursinus.edu/nscoville/TRIUMPHS.html) is to conduct research on the implementation of the PSPs, and the five-year project promises to contribute a variety of outcomes, perspectives, and classroom materials.


Of course, without a community like the HPM Group, many of us would not know the potential for such work and collaboration around the world.  HPM 2016 and ICME13 provided two venues in which to meet and engage others interested in the various HPM domains. Taken from the HPM Group’s website: The HPM Group seeks to [combine] the history of mathematics with the teaching and learning of mathematics, …[and] HPM is the link between the past and the future of mathematics.  Therefore, the group aims at stressing the conception of mathematics as a living science, a science with a long history, a vivid present and an as yet unforeseen future.


This is the work we engage in – along many paths and from many perspectives. It was so lovely to interact with colleagues with whom I share a “kindred spirit” in both academic work and personal interests, and to meet new friends and colleagues.  I hope to see at future HPM meetings and conferences.  If HPM 2016 or ICME 13 were the first for you: welcome to the HPM community.  If you were motivated and enthused by the people, places, and work that you met there, I sincerely hope that you will consider joining us at the European Summer University 8 (ESU8) in Oslo, Norway in 2018.  Or, perhaps you have a paper or poster you will present at CERME10 in Dublin, Ireland in February 2017; if so, I look forward to seeing you there.  Or, perhaps you are interested in the several meetings that will take place in other parts of the world (see this newsletter for details of such meetings and events).  In any and all of these cases, I hope that you will contribute just as much as you take away: this is certainly the group for which this is highly possible.


In the next Newsletter, I will revisit initiatives that have carried over from Luis’ Chairship, including revisiting the “research dossiers.”  Additionally, I will be working with the existing Advisory Board to establish the Executive Committee for this term (2016-2020).  In the meantime, please contact me if you have questions, concerns, ideas, etc. – and I will try to address them to the best of my ability (and if I am unable, then the Executive Committee and Advisory Board can certainly assist me in doing so).  Finally, I thank the Newsletter distributors for their work in disseminating the Newsletters to interested folks around the globe.  We may be in need of folks to help us in this work, so please stay tuned for invitations in this regard!


Kathy Clark

HPM Chair

Florida State University, USA

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!


Sebastian Schorcht

Justus Liebig University Giessen,


19-22 September, 2017

Utrecht, the Netherlands


ICHME-5 First Announcement

We are calling for papers for this fifth conference, as a continuation of the successful work of the first four conferences, in Iceland (2009), Portugal (2011), Sweden (2013) and Italy (2015). Abstracts of proposed contributions must be submitted before April 1, 2017. The decision about acceptance of proposals will be communicated by May 15, 2017.


Submission of abstracts, and later of papers, is only possible via the conference website: http://www.ichme-5.nl. Abstracts should be in English and about one page (500 words). References must be included. Please briefly describe (one or two sentences) why your proposed presentation is a relevant addition to the body of knowledge of the History of Mathematics Education. Once submitted, there will be no possibility for a revision of abstracts.


The conference

First becoming visible internationally at ICME 10 in 2004 (in Copenhagen) as Topic Study Group 29, the history of mathematics education has since become a well-established area of research. It has been a subject of interest in various international meetings, e.g., ICME, HPM, CERME and ESU conferences.


The first specialized research conference, entitled “Ongoing Research in the History of Mathematics Education,” held in Garðabær near Reykjavík (Iceland) in 2009, led to a series of such specialized conferences. This will be the fifth international conference, this time held in Utrecht, the Netherlands.


During previous conferences themes discussed included:

– The Development of Mathematics Education in Specific Countries;

– Practices of Teaching, Mathematics Textbooks, Teacher Education, Transmission and Reception of Ideas;

– Geometry Teaching;

– Algebra Teaching;

– Teaching of Calculus;

– Interdisciplinarity and Contexts;

– The Modern Mathematics Movements; and

– History of Curricula.


Those proposing abstracts will have wide freedom of choice, but in order to stimulate research in areas that are less explored, new topics such as teacher journals and mathematics education prior to 1800 are suggested. A publication of the proceedings is planned. Papers will be peer-reviewed.


The conference is organized by the Dutch Association of Mathematics Teachers in cooperation with the Freudenthal Institute and the Descartes Centre of the University of Utrecht.




International program committee:

  • Kristín Bjarnadóttir (Iceland)
  • Jan Hogendijk (the Netherlands
  • Jenneke Krüger (the Netherlands)
  • Johan Prytz (Sweden)
  • Gert Schubring (Brazil/Germany)
  • Bert Theunissen (the Netherlands)


Advisor: Fulvia Furinghetti (Italy)


Further information about the conference and practical information is available on the conference website: http://www.ichme-5.nl.


Registration and conference fee:  until 15 June 2017, the fee is € 195; thereafter the fee will be € 230. Last day of registration and payment is 31 August 2017. Registration will take place via the conference website.



Schubring, G. (Ed.) (2006). Special issue: History of teaching and learning mathematics. Paedagogica Historica, 42(5-6). [Proceedings of TSG 29 at ICME 10] http://www.tandfonline.com/loi/cpdh20

Bjarnadóttir, K., Furinghetti, F., & Schubring, G. (Eds.) (2009). “Dig where you stand.” Proceedings of the conference on on-going research in the history of mathematics education. Reykjavik, Iceland: University of Iceland – School of Education.

Bjarnadóttir, K., Furinghetti, F., Matos, J., & Schubring, G. (Eds.) (2012). “Dig where you stand” 2. Proceedings of the second conference on the history of mathematics education. Lisbon, Portugal: Universidade Nova.

Bjarnadóttir, K., Furinghetti, F., Prytz, J., & Schubring, G. (Eds.) (2015). “Dig where you stand” 3. Proceedings of the third conference on the history of mathematics education. Uppsala, Sweden: Department of Education, Uppsala University. https://uu.diva-portal.org/smash/get/diva2:794222/FULLTEXT03.pdf

Karp, A., & Furinghetti, F. (2016). History of mathematics teaching and learning: Achievements, problems, prospects (ICME-13 Topical Surveys, G. Kaiser (Ed.). Switzerland: Springer Open.

Karp, A., & Schubring, G. (Eds.) (2014). Handbook on the history of mathematics education. (2014). New York, NY: Springer.

Jenneke Krüger

Freudenthal Institute

University of Utrecht

The Netherlands


Fritz Schweiger

 This book is about the history of f-expansions, their theory, their application, and their connection to other parts of mathematics. Sketches of proofs of some of the theorems about f-expansions–particularly theorems from historical sources–are included not to convince the reader of the truth of the theorem but rather as a way to demonstrate why the theorem is true. These sketches should give a clearer and more easily understood description of the working of the theorem than a hand-waving literary flourish.

Publication Date: May 2, 2016

ISBN/EAN13: 1942795939 / 9781942795933

Language: English

Related Categories: Mathematics / History & Philosophy

Information send it by Manfred Kronfellner

Doctoral Dissertation (2016)


Title:  Formative potential of the history of the Euclidean theory of proportion in the constitution of mathematics teacher knowledge

Author: Edgar Alberto Guacaneme Suárez



The general research context in which this thesis is placed is the role of the History of Mathematics [HM] in the constitution of mathematical knowledge for teaching [MKT]. And the specific research question addressed by the thesis is what is the educational potential of the history of Euclidean theory of reason and proportion, contained in Book V of Elements, in the constitution of MKT.

In pursuit of an answer, the need for an approach to the state of the art in the reflection and the research on the relationship between Mathematics Education and History of Mathematics is established. From such a state of the art one seeks to explore the relationship “HM – MKT” guided by questions related to 1) the arguments used in favor of the integration of HM in such processes, 2) the aims pursued with such integration, 3) the characteristics of HM that have been linked to the mathematics teachers educational processes, and 4) the methodological strategies that have been designed and implemented for teachers of mathematics to appropriate and use historical discourses. A framework for the relationship mentioned is thus constructed.

Euclidean theory of reason and proportion of Book V of The Elements is then studied to gain insight into this theory. Documents related to the history of reason and proportion are also studied. Based on these studies, the history of Euclidean theory of proportion is analyzed using the analysis categories for the questions “what HM” and “for what HM”. The overall result shows that the set of documents covers almost all categories of analysis.

Finally, the educational potential that the documents concerning the Euclidean theory of proportion have in favor of the MKT is established.


Master’s Theses


Title: Categories of Uses of History of Mathematics in Mathematics Education






Title: Contributions of History of Mathematics to Pedagogical Content Knowledge on Trigonometric Equations of a Mathematics Teacher Studying for the Master’s or Doctorate (in Mathematics Education)






Title: The Philosophy of Mathematics in Mathematical Knowledge for Teaching





In the original Spanish:


Tesis de Doctorado en Educacion (2016)


Potencial formativo de la historia de la teorí a euclidiana de la proporcio n en la constitucio n del conocimiento del profesor de Matema ticas


Edgar Alberto Guacaneme Suárez


La tesis ubica el papel de la Historia de las Matemáticas [HM] en la constitución del conocimiento del profesor de Matemáticas [CPM] como contexto general de investigación y dentro de este la pregunta ¿cuál es el potencial formativo de la historia de la teoría euclidiana de la razón y la proporción, contenida en el Libro V de Elementos, en la constitución del CPM?

En procura de una respuesta, se establece la necesidad de lograr una aproximación al estado del arte de la reflexión e investigación en torno a la relación “Historia de las Matemáticas – Educación Matemática”. A partir de tal estado del arte se procura explorar la relación “HM – CPM”, guiado por las preguntas relacionadas con los argumentos que se esgrimen a favor de la integración de la HM en tales procesos, las intenciones que se persiguen con dicha integración, las características de la HM que se vincula a los procesos educativos de los profesores de Matemáticas y las estrategias metodológicas que se han diseñado e implementado para que los profesores de Matemáticas se apropien y usen los discursos históricos. Se construye así un marco de referencia para la relación mencionada.

Se estudian entonces la teoría euclidiana de la razón y la proporción del Libro V de Elementos para obtener una perspectiva de esta. Asimismo se estudian los documentos que versan sobre la historia de la razón y proporción. A partir de esto se analiza la historia de la teoría euclidiana de la proporción a través de las categorías de análisis para las pregunta qué HM y para qué la HM. El resultado global muestra que el conjunto de documentos cubre la casi totalidad de las categorías de análisis.

Finalmente, se establece el potencial formativo que los documentos que versan sobre la teoría euclidiana de la proporción tienen a favor del CPM.


Master’s Theses



















Content provided by

Edgar Alberto Guacaneme Suárez;

translation by Luis Puig;

submitted by Kathy Clark

 II International Conference on Mathematics Textbook Research and Development

II Conferência Internacional em Pesquisa e Desenvolvimento de Livros Didáticos de Matemática




Research focused on the analysis and development of textbooks (in conventional format or digital media) has recently gained great prominence in the international arena of research in mathematics education. This prominence is reflected, for example, in the International Conference on School Mathematics Textbooks (ICSMT), held in Shanghai in 2011, and in the ZDM special issue (Volume 45, Issue 5, September 2013), on textbooks research in mathematics education.

Also reflecting this trend, the first International Conference on Mathematics Textbook Research and Development (ICMT-2014) took place at the University of Southampton (UK), from 29 to 31 July 2014. About 180 participants, from 30 different countries, attended ICMT-2014. ICMT-2014 proceedings are available on http://eprints.soton.ac.uk/374809/. Visit also ICMT-2014’s official website on: http://blog.soton.ac.uk/icmtrd2014/.

It is our pleasure to announce the II International Conference on Mathematics Textbook Research and Development / II Conferência Internacional em Pesquisa e Desenvolvimento de Livros Didáticos de Matemática (ICMT2), to be held from 7 to 11 May 2017, at the Federal University of Rio de Janeiro (UFRJ) and at the Federal University of the State of Rio de Janeiro (UNIRIO), Brasil.

The conference is organized by the Federal University of Rio de Janeiro (Universidade Federal do Rio de Janeiro, UFRJ), the Federal University of the State of Rio de Janeiro (Universidade Federal do Estado do Rio de Janeiro, UNIRIO), the State University of São Paulo (Universidade Estadual Paulista, UNESP) and the Federal University of Pernambuco (UFPE). It is supported by the Brazilian Mathematics Education Society (SBEM), the Brazilian Society of Mathematics (SBM), and the Brazilian Society of Applied and Computational Mathematics (SBMAC).

ICMT2 will feature different activities, including plenary lectures, symposia, workshops, oral presentations, posters and special activities addressed to teachers. Accepted and presented papers will be published after a peer-review process in Proceedings following the Conference.



International Programme Committee (IPC)

  • Rúbia Amaral (UNESP, Brazil) – Secretary
  • Ubiratan d’Ambrosio (UNIAN, Brazil) – Honorary President
  • Marcelo Borba (UNESP, Brazil)
  • Rute Borba (Universidade Federal de Pernambuco, Brazil)
  • Marcos Cherinda (Universidade Pedagógica de Moçambique)
  • Lianghuo Fan (University of Southampton, UK) – Co-chair
  • Victor Giraldo (Universidade Federal do Rio de Janeiro, Brazil) – Local Chair
  • Patricio Herbst (University of Michigan, USA)
  • Marja van den Heuvel-Panhuizen (Universiteit Utrecht, Netherlands)
  • Abdellah El Idrissi (École Normale Supérieure de Marrakech, Morocco)
  • Diana Jaramillo Quiceno (Universidad de Antioquia, Colombia)
  • Cyril Julie (University of the Western Cape, South Africa)
  • Gabriele Kaiser (Universität Hamburg, Germany)
  • Alexander Karp          (Teachers College, Columbia University, USA)
  • Jeremy Kilpatrick (University of Georgia, USA)
  • Jian Liu           (Beijing Normal University, China)
  • Eizo Nagasaki (National Institute for Educational Policy Research, Japan)
  • Michael Otte (UNIAN, Brazil)
  • Johan Prytz (Uppsala Universitet, Sweden)
  • Sebastian Rezat (Universität Paderborn, Germany)
  • Angel Ruiz (Universidad de Costa Rica, Costa Rica)
  • Kenneth Ruthven (University of Cambridge, UK)
  • Gert Schubring (UFRJ, Brazil/Universität Bielefeld, Germany) – Chair

Local Orgnization Committe (LOC)

  • Lourdes Werle de Almeida (UEL)
  • Rúbia Amaral (UNESP) – Co-chair
  • Franck Bellemain (UFPE)
  • Marilena Bittar (UFMS)
  • Victor Giraldo (UFRJ) – Chair
  • Verônica Gitirana (UFPE)
  • Carmen Mathias (UFSM)
  • João Frederico Meyer (UNICAMP)
  • Cydara Ripoll (UFRGS)
  • Walcy Santos (UFRJ)
  • Fábio Simas (UNIRIO)
  • Ralph Teixeira (UFF)

Plenary speakers


  • Kay O’Halloran (Curtin University, Bentley, Australia)
  • João Bosco Pitombeira (Universidade Federal de Mato Grosso do Sul, Campo Grande, Brazil)
  • Ken Saito (Department of Human Sciences, School of Humanities and Social Sciences, Osaka Prefecture University, Osaka, Japan)
  • Zalman Usiskin (University of Chicago, Chicago, USA)
  • Jianpan Wang (Jianpan Wang, East China Normal University, Shanghai, China)

Conference themes

  • Textbook research (concepts, issues, methods, directions, etc.)
  • Textbook analysis (characteristics, treatment of contents and/or pedagogy, etc.)
  • Analysis of historical textbooks
  • Textbook use (by teachers, by students, and/or by other parties)
  • Textbooks and student achievement
  • Textbook development (domain/competence analyses, teaching trajectories, task design, format of presenting the “content” to the student, format of presenting the “content” to the teacher (teacher guides)
  • Textbook policies (governmental educational policy about textbooks, distribution, market strategies)
  • Evolution of textbooks in the light of new digital technologies (including integration of ICT tools and innovation, e-textbook)
  • Other disciplines in mathematics textbooks & mathematics in textbooks of other disciplines
  • Other major relevant issues about mathematics textbooks

Modalities of contributions (besides invited lectures)

ICMT 2 will receive contributions, related with the Conference Themes described above, on the following modalities:

  • symposium (in English, 180 minutes)
  • workshop (in English, 120 minutes)
  • workshop for teachers (in Portuguese, 120 minutes)
  • oral presentation (in English, 30 minute presentation)
  • poster presentation (in English, one time slot, 60 minutes)

A symposium is organised by one or more researchers to discuss jointly, based on submitted papers, a specific issue of the thematic spectrum of the conference.

A workshop is a kind of activity that allows participants to work (in small teams) around prepared documents, guided by specific questions.



Anyone (including university lecturers, school teachers, and graduate and undergraduate students) can submit a proposal for any modality of contribution. In general, each applicant can submit at most two proposals (symposia, workshops, oral presentations, posters) with his/her name as presenting author. All submissions will be peer reviewed. In order to be included in the Conference Programme, at least the presenting author must be registered and have paid the registration fee by January 3rd 2017.


Formats and deadlines

  • symposium: 2 pages proposal, in English, submitted until 15 August 2016;
  • workshop: 2 pages proposal, in English, submitted until 31 October 2016;
  • workshop for teachers: 2 pages proposal, in Portuguese, submitted until 31 October 2016;
  • oral presentation: 1 page abstract, in English, submitted until 31 October 2016;
  • poster presentation: 1 page abstract, in English, submitted until 31 October 2016.


All submissions must comply with the following format guidelines:

  • A4 paper (size 21 cm x 29.7 cm);
  • margins set at 2.5 cm top and 2.5 cm bottom, 2 cm left and 2 cm right;
  • 12pt Times New Roman, single space between lines, and 6pt space after paragraphs.


Templates with format details for each modality of submission is also available on the website.

All submissions must be made through the system available on the Conference website.

For a full list of deadlines, see Key dates (below).


Workshops, oral presentations, and posters

Submissions for workshops, workshop for teachers, oral presentations, and posters will go through two stages:

  1. Abstract submission. Applicants will be first invited to submit abstracts. If accepted, contributions will be included in the Conference Programme, accordingly to the respective modality.
  2. Full paper submission. After the Conference, authors of accepted contributions will be invited to submit a full paper for publications on the electronic Proceedings. In order to submission a full version, the corresponding contributions must fulfil the following conditions:
    1. have abstract accepted;
    2. at least the presenting author have registered and paid registration fee;
    3. have been presented at the Conference.


Researchers interested in proposing a symposium, must first submit a proposal.

Then, submissions for oral presentations within the accepted symposium will be opened. Such submissions will then follow the two stages, as described above.


Registration fees (in euros)

Until January 31st, 2017, registration fees will have the following values. After that date, the fees will suffer an increase. New values will be informed in due course. Registration must be made through the system that will be available on the Conference website.


Category Withconference dinner Withoutconference dinner
Standard  160 € 110 €
graduate student/ school teacher  120 € 670€
One day rate 30 €
Accompanying person 75 € 50 €


Payments with credit card will be possible via paypal.


Key dates

  • submission of proposals for symposia: August 15th, 2016
  • information about acceptance of proposals for symposia: September 15th, 2016
  • submission of paper abstracts within symposia: October 31st, 2016
  • submission of paper abstracts for oral presentation, workshop and poster: October 31st, 2016
  • information about acceptance of such submissions: December 15th, 2016
  • registration deadline (for presenting authors9: January 3rd, 2017
  • conference: May, 7th to 11th, 2017



Rio de Janeiro, also known as Cidade Maravilhosa (Wonderful City), was recently named a World Heritage Site by UNESCO. Despite the city is among the largest urban areas on the planet, it is well known worldwide for its landscapes of exceptional scenic beauty. Its unique geographical location gathers tropical beaches, dramatic mountain ranges, luxuriant rain forest, rivers and waterfalls – all within the urban area.

The area today occupied by the city of Rio de Janeiro was inhabited by different native ethnic groups, including Tamoios, Tupinambás e Maracajás. The city of Rio de Janeiro was officially founded by Portu- guese colonisers in March 1st, 1565. In 1808, with the arrival of the Portuguese royal family, who fled from Napoleon’s troops, Rio becomes the seat of the Portuguese government. With independence in 1822, Rio becomes the capital of Brazil, position occupied until 1960, with the foundation to the current capital – Brasilia.

The beaches of Rio de Janeiro – being Copacabana, Ipanema and Barra da Tijuca the most famous ones – extend along an over 30 km long coastline, on south and west sides of the city. Tijuca Forest – a protect area since nineteenth century, and a National Park (see http://www.parquedatijuca.com.br) since 1961 – keeps valuable remnants of their original ecosystems, native flora and fauna. Lying inside the urban area of Rio de Janeiro, Tijuca National Park is regarded as the largest urban forest in the planet. Other not-to-miss touristic spots are: Corcovado Mountain with Christ the Redeemer Statue (www.corcovado.com.br); Sugar Loaf and its cable car (www.bondinho.com.br); the Botanical Garden (www.jbrj.gov.br) with a remarkable collection including rain forest native and rare species; São Cristóvão Market (www.feiradesaocristovao.org.br), an open market with typical food, art craft and music from the northeastern region of Brazil.

Rio de Janeiro offers a wide hotel network, with accommodation options suitable for all budgets. The city has also a rich range of restaurants of different trends, from traditional Brazilian food to international contemporary cuisine. Lapa district, in the central area of the city, is probably the most vivid nightlife spot, with several restaurants, bars, and places for live music, especially samba and typical Brazilian rhythms. Rio de Janeiro has a population of around 6 million, and is currently the most visited city in Latin America. It receives 4.5 million tourists each year.

For further information, visit: http://www.rio.rj.gov.br/web/riotur/.

Visa Information

Citizens from most of Latin American and European countries do not need to apply to visas to short- term visits to Brazil. Visas are required for US citizens, as well as citizens from some African and Asian countries.

Vaccinations may also be required.

For further information, please consult Brazilian consulates in your country of origin, and see: http://www.portalconsular.mre.gov.br/.


Further Information





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