Welcome to Newsletter 95!

One of the fascinating aspects of leading an “academic life” is the diversity of individuals with whom I come into contact.  Indeed, non-academics have this same experience, but I find that in meeting and engaging with so many different people that I am challenged to think differently about a range of issues – and I know that I grow because of it.  And, this notion has been on my mind quite a bit lately, as I have been living and working in Germany – whose academic system is quite different from that in my small corner of the world in Tallahassee, Florida.  Still, I would like to think that the experiences I have had and the students, colleagues, and new friends I have met this summer will inevitably help me to be a better scholar, colleague, and friend.

Why am I rambling on about this?  While working at the University of Siegen, I have had the pleasure to teach a reading course on “History of Mathematics in Mathematics Education” – and during that course I feel like many of my HPM friends have been there in the course with me and my 15 students.  We have read articles by Abraham Arcavi and his colleagues, Adriano Demattè, Michael N. Fried, Uffe Thomas Jankvist, David Pengelleny, and Man-Keung Siu.  We have accessed excerpts and materials by Michael Glaubitz, Iris Gulikers and Klaske Blom, Tinne Hoff Kjeldsen and her colleagues, Peter Ransom, and Costas Tzanakis.  Throughout the course, my students have impressed me with their struggle to learn about another aspect of their chosen profession: the potential for history of mathematics to inform their future teaching.  Yet, it is also quite clear to me that I would not be able to share this dimension of mathematics education with my students if it were not for the HPM community – of scholars and practitioners alike – and all that it affords in not just my scholarly work, but in my work with students.

It is my hope then, as you read about the numerous HPM-related activities taking place over the next year that are highlighted in this newsletter, that you consider ways in which you can add to our community.  In particular, I bring to your attention the 8th European Summer University on History and Epistemology in Mathematics Education (ESU-8), which will take place in Oslo, Norway from 20 – 24 July 2018.  One of the aims of the ESUs is “to give the opportunity to mathematics teachers, educators and researchers to share their teaching ideas and classroom experience related to this perspective.”  I highlight this aim (of the three; see the announcement of ESU-8 in this newsletter) because it is again part of my psyche this summer: sharing teaching ideas, or at least the potential for a variety of ways in which history of mathematics might be used by classroom teachers, with my students this summer would not have been possible without my own participation in meetings / conferences such as the ESUs, and all that I have learned from them over the last decade.  I encourage you to consider submitting a proposal for this important meeting, in which you can share your ideas (and, if appropriate, outcomes of research you have conducted on the implementation of those ideas in practice).

With regard to other HPM business, I hope to attend to several HPM Group matters in the coming months. (I am – as usual – woefully behind!)  These include:

  1. Contacting those of you who were involved in the research dossier work during Luis Radford’s term as Chair, to determine how we might move forward on that initiative for those who are interested.
  2. Summarizing and communicating the Advisory Board members’ discussion of a proposal to create an HPM Journal (proposed by Evelyne Barbin and David Pengelley).
  3. Creating an ad hoc committee of Advisory Board members interested in helping me to facilitate a “Practitioner’s Corner” feature of the HPM Newsletter (see NL 94 for an example).

Also, please join me in recognizing the inaugural members of the newly-established Honorary Advisory Board (HAdB):

Abraham Arcavi Abdellah El Idrissi

Hans Niels Jahnke

Manfred Kronfellner

Chris Weeks

I thank these colleagues for their service to the HPM community, and for their time on the HPM Advisory Board!

In closing, I ask for your support and active participation in the activities of HPM.  If you have questions, concerns, or suggestions, please let me know (kclark@fsu.edu).

Kathy Clark

HPM Chair

Florida State University

Tallahassee, Florida, USA

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, the Mathematical Association of America’s Convergence brings you a variety of interesting articles and teaching tools.

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.

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In “Exploring Liu Hui’s Cube Puzzle: From Paper Folding to 3-D Design,” author Lingguo Bu offers history, classroom activities, and interactive applets to help you and your students explore Liu Hui’s 3rd century dissection of the cube into three pieces with volumes 1/2, 1/3, and 1/6 of the volume of the cube. The three puzzle pieces are shown above and below. The pieces in the image below were made using a 3-D printer.

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For a different kind of puzzle, try “Mathematicians from A to Z,” a New York Times-style crossword puzzle created by mathematics instructor Sid Kolpas and a crossword puzzle creator Stu Ockman.

The article, “Misseri-Calendar: A Calendar Embedded in Icelandic Nature, Society, and Culture,” by Kristín Bjarnadóttir, reviews the calendar’s long history from Viking times to the present, and offers animations and ideas for your classroom.

In “A Translation of Evangelista Torricelli’s ‘The Quadrature of the Parabola, solved by many methods through the new geometry of indivisibles,’” authors Andrew Leahy and Kasandra Sullivan provide plenty of history and helpful diagrams along with their translation.

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In “A Series of Mini-projects from TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources” the TRIUMPHS team introduces the first of a collection of mini-Primary Source Projects (mini-PSPs), “The Derivatives of the Sine and Cosine Functions” (by Dominic Klyve), a classroom assignment in which Calculus I students learn how Leonhard Euler (1707-1783) obtained these derivatives via differentials. Above, students work on a Primary Source Project under the supervision of Janet Barnett at a TRIUMPHS Site Tester Workshop in Denver, Colorado, in September of 2016.

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In “Illustrating The Nine Chapters on the Mathematical Art: Their Use in a College Mathematics History Classroom,” author Joel Haack shares how he used his experiences on an MAA Mathematical Study Tour to China to enrich his teaching. The photo above is of a statue in the National Museum of China of a civil servant from the Sui Dynasty (581-618), an intended user of the Nine Chapters.

“Moses ibn Tibbon’s Hebrew Translation of al-Hassar’s Kitab al Bayan,” by Jeremy I. Pfeffer (Hebrew University of Jerusalem) features the arithmetic of fractions as you’ve (possibly) never seen it before!

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See fractions in the context of problem-solving using the method of double false position in the Arabic manuscript Kitab al-nuzah in “Mathematical Treasure: The Method of Scales in ibn al-Ha’im’s Book of Delights,” by Randy Schwartz and Frank Swetz. Above: This diagram is used in this and other manuscripts to illustrate and carry out the “method of scales.”

In “Mathematical Treasures at the Linda Hall Library,” author Cynthia Huffman highlights the mathematics collections available at this rare book library in Kansas City, Missouri. See images of mathematics books by Euclid, Pacioli, Cardano, Torricelli, Maria Agnesi, and Emilie du Chatelet.

Our “Index to Mathematical Treasures” includes hundreds of images for use in your classroom from dozens of libraries and sources.

See all of these articles and more at MAA Convergence:

http://www.maa.org/press/periodicals/convergence

 

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

 

Janet Beery

Editor, MAA Convergence

University of Redlands, California

USA

 

 

 

20-24 July 2018

Oslo, Norway

ESU – 8

Oslo & Akershus University College of Applied Sciences

 

https://esu8.edc.uoc.gr  

 

ANNOUNCEMENT

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.

 

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.

More detailed information:

Visit the regularly updated website of ESU-8 http://esu8.edc.uoc.gr

See the First Announcement at https://esu8.edc.uoc.gr/1st-announcement/ &

The HPM Newsletter issue No 94 pp.10-12 at http://www.clab.edc.uoc.gr/HPM/HPMNews94_final.pdf

 

 

 

Important dates:

  • Submission of abstracts of proposals for all types of activities:

1 September 31 October 2017.

  • Authors’ notification of acceptance: 15 December 2017
  • Launch of the Second Announcement: By 31 December 2017
  • Deadline for early registration: 31 January 2018

Submission procedure: The submissions of proposals and full texts for the proceedings, the reviewing process, and authors’ notification will be realized online via https://esu8.edc.uoc.gr/submission and following the guidelines therewith.

Reviewing & Proceedings: Abstracts of proposals will be reviewed by the members of the Scientific Program Committee (SPC). 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.

Reviewing procedure: Each proposal and full text will be reviewed by two independent referees. In case of conflicting reports, the paper will be adjudicated by a third referee. The final decision will be made by the chair and co-chairs of ESU-8, on the basis of all three reports. Any proposal or full text receiving two negative reports will not be accepted. All other proposals and full texts should be revised satisfactorily according to the referees’ suggestions and comments before they are finally accepted for inclusion in the ESU-8 scientific program.

For more detailed information on the reviewing procedure, and the evaluation criteria, see https://esu8.edc.uoc.gr/submission/

Second Announcement: The Second Announcement will be launched by 31 December 2017 at the latest. It will include all necessary information on the registration fees, the ESU-8 timeline and its overall time schedule, information on the publication of its proceedings after ESU-8, information on the registration procedure, accommodation, the social program and other practical issues.

 

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)

30 March – 1 April 2018

Tunis, Tunisia

 Second announcement

The 13th Colloquium on the History of Arabic Mathematics (COMHISMA 13) shall take place on Friday 30th March, Saturday 31st March and April 1st , 2018 in Tunis City (CIFFIP – Lac II).

Themes of the Colloquium:

A.  Theoretical mathematics, Astronomy, Applied mathematics, Recreational mathematics in Arabic and Islamic traditions.  

B.  History of teaching Arabic mathematics and its circulation.

C.  Mathematics and Society. 

 

Languages of the meeting: Abstracts, papers and communications can be presented in the Arabic, English or French languages.

 

Important deadlines

          Deadline for abstract submission

15 September, 2017

          Deadline for acceptation of papers

15 November, 2017

          Deadline for receiving full text of communication        

15 February, 2018

          Deadline for registration

15 January, 2018

Registration Fees

Professor : 120 DT (± 50 Euros)

Student :      50 DT (± 25 Euros)      

Accomodations

All activities planned for COMHISMA 13 will be held at CIFFIP – Lac II.

Participants can use some lodging facilities on the premises or they can also lodge at one of the Hotels in the center of Tunis.

Accomodations fees at the CIFFIP : 180 DT (± 75 Euros) for three days.

For center city hotels, 73 DT to 200 DT for each night with breakfast.

          Arrival of the participants

29 March, 2018, after noon.

          Departure of the participants

01 April, 2018, after noon.

 Cultural activities and tourist tour

No work is planned for Saturday after noon, March 31st . We shall offer several activities for participants to choose.

The International scientific committee of COMHISMA 13 is chaired by Professor Ahmed Djebbar.Institutional Partners

                     Centre International de Formation des Formateurs et de l’Innovation Pédagogique (CIFFIP)

                     Institut Supérieur de l’Education et de la Formation Continue (ISEFC)

                     Laboratoire du Monde Arabo-Islamique Médiéval (LMAIM)

 Organizing Associations

                     Association des Femmes Tunisiennes Mathématiciennes

                     Association Tunisienne des Sciences Mathématiques

                     Association Tunisienne de Didactique des Mathématiques

                     The Mediterranean Institute for the Mathematical Sciences (MIMS-Tunisia).

                     Société Mathématique de Tunisie

Local Organizing Committee

Honorary Chairman:       Béchir Kachoukh

Members:       

                     Mahdi Abdeljaouad – Faouzi Chaabane – Marouane Ben Miled – Hmida Hedfi

                     Taoufik Charrada et Salma Elaoud (ATSM)

                     Mounir Dhieb et Rahim Kouki (ATDM)

                     Makkia Dammak (AFTM)

                     Salwa Aouadi (MIMS)

                     Nedra Belhaj Rhouma (SMT)

 

Contact : mahdi.abdeljaouad@gmail.com

The fourth Irish conference on the History of Mathematics (IHoM4) will be held in the Edward Worth Library, Dublin, on Friday 9th June 2017.

The themes of the conference will be:

  • Significant people in the History of Mathematics
  • Using original sources in History of Mathematics
  • History of Mathematics as revealed in significant books
  • History of Mathematics in Mathematics Education
  • History of Mathematics Education
  • General topics from the History of Mathematics

It will be of particular interest to situate any of these themes in an Irish context.

Abstracts (of no more than 150 words) are invited for presentation at IHoM4, on or before 7th May. It is envisaged that each presentation will be allocated 40 minutes (including 10 minutes for questions). The programme for IHoM4 will be posted here.

Organizing committee:

For further information contact maurice.oreilly[AT]dcu.ie (with IHoM4 in the subject field).

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

 

https://esu8.edc.uoc.gr  

94_esu8

 ANNOUNCEMENT

  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

https://esu8.edc.uoc.gr 

http://www.clab.edc.uoc.gr/hpm/meetings  

 

  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

https://esu8.edc.uoc.gr 

http://www.clab.edc.uoc.gr/hpm/meetings

 

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.

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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).

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Figure 2.

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

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Figure 3.

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

94_pc_4

Figure 4.

4)      Now construct segment BE (figure 5).

94_pc_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).

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Figure 6.

 

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

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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).

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Figure 8.

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

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Figure 9.

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

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Figure 10.

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

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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.

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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.)

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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).

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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).

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“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:

http://www.maa.org/press/periodicals/convergence

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

Janet Beery

Editor, MAA Convergence

University of Redlands

(USA)

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

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