Announcement 1:

Call for Nominations for the 2019 Felix Klein and Hans Freudenthal Awards

Dear Members of the International Mathematics Education Community,
It is at this time of the even-numbered years that calls for the ICMI Klein and Freudenthal Awards are being issued. The call for the current round, the 2019 awards, is presented below. Please read it carefully and consider coming up with a nomination. True, preparing submissions requires much thought and not a small amount of work, but such investment is not too much to ask when it comes to honoring a person whose work has had a substantial, valuable impact on us all. Within our flourishing field, there is quite a number of richly deserving candidates. Do remember, however, that without your help, they may not be honored. Indeed, ICMI Awards Committee can only choose recipients from officially submitted nominations for the current round, accompanied by full documentation, as specified in the call.

Thank you for considering this call seriously. We are looking forward to receiving your nominations.

Anna Sfard
(on behalf of the ICMI Klein and Freudenthal Awards Committee)

Since 2003, the International Commission on Mathematical Instruction (ICMI) awards biannually two medals to recognise outstanding accomplishments in mathematics education research:

• the Felix Klein Award, for lifelong achievement in mathematics education research,

• the Hans Freudenthal Award, for a major programme of research on mathematics education.

The Felix Klein medal is awarded for life-time achievement in mathematics education research. This award is aimed at acknowledging those excellent senior scholars who have made a field-defining contribution over their professional life. Past candidates have been influential and have had an impact both at the national level, within their own countries, and at the international level. We have valued in the past those candidates who not only have made substantial research contributions, but also have introduced new issues, ideas, perspectives, and critical reflections. Additional considerations have included leadership roles, mentoring, and peer recognition, as well as the actual or potential relationship between the research done and improvement of mathematics education at large, through connections between research and practice.

The Hans Freudenthal medal is aimed at acknowledging the outstanding contributions of an individual’s theoretically robust and highly coherent research programme. It honours a scholar who has initiated a new research programme and has brought it to maturation over the past 10 years. The research programme is one that has had an impact on our community. Freudenthal awardees should also be researchers whose work is ongoing and who can be expected to continue contributing to the field. In brief, the criteria for this award are depth, novelty, sustainability, and impact of the research program.

See http://www.mathunion.org/icmi/activities/awards/the-klein-and-freudenthal-medals/ for further information about the awards and for the names of past awardees (eight Freudenthal Medals and eight Klein Medals, to date).

The ICMI Klein and Freudenthal Awards Committee consists of a chair (Professor Anna Sfard) nominated by the President of ICMI, and five other members who remain anonymous until their terms have come to an end. The ICMI Klein and Freudenthal Awards Committee is at this time entering the 2019 cycle of selecting awardees and welcomes nominations for the two awards from individuals or groups of individuals in the mathematics education community.

Nominations for the Felix Klein Award should include the following:

1) a document (max. 8 pages) describing the achievements of the nominee (e.g., his or her theoretical contribution and/or empirical research, leadership roles, graduate supervision and mentoring, and peer recognition) and reasons for the nomination (including a description of the nominee’s impact on the field);
2) a one-page summarizing statement;
3) a curriculum vitae of the nominee (max. 20 pages);
4) electronic copies of three of the nominee’s key publications;
5) three letters of support (preferably from different countries); and
6) the names and e-mail addresses of two persons other than the nominee herself or himself who could provide further information, if needed.

Nominations for the Hans Freudenthal Award should include the following:
1) a document (max. 5 pages) describing the nominee’s research program and reasons for the nomination (including a description of the nominee’s impact on the field);
2) a one-page summarizing statement;
3) a curriculum vitae of the nominee (max. 10 pages);
4) electronic copies of three of the nominee’s key publications;
5) three letters of support (from different countries, if possible); and
6) the names and e-mail addresses of two persons other than the nominee herself or himself who could provide further information, if needed.

All nominations must be sent by e-mail to the Chair of the Committee (annasd@edu.haifa.ac.il, sfard@netvision.net.il) no later than 31 March 2019.

Prof. Anna Sfard
Department of Mathematics Education, The University of Haifa
Mount Carmel, Haifa 31905, Israel

—–
Announcement 2:

The Emma Castelnuovo Award (Second Call – deadline March 31, 2019)

The Emma Castelnuovo Award recognizes outstanding achievements in the practice of mathematics education in order to reflect a main aspect of the ICMI ‘essence’ not previously recognized in the form of an award. The award was named after Emma Castelnuovo, an Italian mathematics educator born in 1913, in celebration of her 100th birthday and honoring her pioneer work. The first Emma Castelnuovo medal was awarded to Hugh Burkhardt and Malcolm Swan in 2016 during the 13th International Congress on Mathematical Education (ICME-13) in Hamburg, Germany.

The Emma Castelnuovo Award for outstanding achievements in the practice of mathematics education honors persons, groups, projects, institutions or organizations engaged in the development and implementation of exceptionally excellent and influential work in the practice of mathematics education, such as: classroom teaching, curriculum development, instructional design (of materials or pedagogical models), teacher education programs and/or field projects with a demonstrated influence on schools, districts, regions or countries.

The Emma Castelnuovo Award seeks to recognize and to encourage efforts, ideas and their successful implementation in the field, as well as to showcase models and exemplars of inspirational practices from which to learn. The recipient of the award will be announced late in 2019 or early in 2020, and the award will be conferred at ICME-14 in July 2020 in Shanghai, China. The awardee (or its representative in the case of a group, institution, project, or organization) will be invited to present a special lecture at the Congress. The Emma Castelnuovo Award Committee consists of a Chair (Professor Konrad Krainer) nominated by the President of ICMI, and five other members who remain anonymous until their terms have come to an end.

The six members come from six different countries, representing different continents (Africa, Asia, Australia, Europe, North America and South America). The Committee is completely autonomous, its work and records will be kept internal and confidential, except for the obvious process of soliciting advice and information from the professional community, which is done by the Committee Chair. The Committee is at this time entering the 2020 cycle of selecting awardees and welcomes nominations for the award from persons, groups, projects, institutions or organizations in the mathematics education community.

For information about the other ICMI awards and the names of past awardees, see https://www.mathunion.org/icmi/awards/icmi-awards

Nominees for the award will be evaluated in light of the following criteria:

• the educational rationale for the candidate’s work and what served as a catalyst for that work;
• the problems addressed by the candidate;
• the candidate’s role in addressing the problems, whether they involve curriculum development, teacher education, professional development, design of instruction, or other areas of mathematics education practice;
• the conditions under which the work has taken place (the cultural and political context, infrastructure, funding, and people involved);
• the originality and creativity involved in how the candidate has addressed problems and overcome obstacles;
• the quality of networking with other key stakeholders (e.g., bridging theory and practice);
• external or internal evaluations of the work, if available;
• the extent of the influence of the work on educational practice, including quantitative or qualitative evidence of that influence; and
• the potential of the work to serve as a model (either for inspiring others addressing similar problems or because of taking an approach that could be applied elsewhere with appropriate modifications).

Nominations for the Emma Castelnuovo Award should include the following documents in the English language (exceptions for 4. – see below):

1. a document (max. 5 pages) describing the nominee’s program and reasons for the nomination (including the nominee’s impact on the field);
2. a one-page summary statement;
3. an account of the genesis and dissemination of the nominee’s work and the roles of the people involved, with brief curricula vitae of the key persons (max. 10 pages);
4. electronic copies of three publications that reflect the nominee’s work related to the practice of mathematics education (e.g., journal articles, textbooks, other instructional materials, or CD-ROMs); (if a publication is not written in English, an English translation of a key part – e.g. an abstract – and an independent statement on the publication’s quality written in English – e.g. a review – should be provided)
5. three letters of support (from different stakeholders and, if possible, from different countries); and
6. the names and e-mail addresses of two persons who could provide further information, if needed.

All nominations must be sent by e-mail to the Chair of the Committee (konrad.krainer@aau.at) no later than March 31, 2019.

Konrad Krainer, Chair of the ICMI Emma Castelnuovo Award Committee
University of Klagenfurt, Department of Instructional and School Development
Sterneckstraße 15
9010 Klagenfurt, Austria

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The most recent Newsletter is now posted:

http://www.clab.edc.uoc.gr/hpm/HPMNews99_final.pdf

 

Researching the History of Mathematics Education: An International Overview
Editors: Furinghetti, Fulvia, Karp, Alexander (Eds.)
https://www.springer.com/gp/book/9783319682938

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Mathematics, Education and History: Towards a harmonious partnership
Editors: Clark, Kathleen M., Kjeldsen, Tine Hoff, Schorcht, Sebastian, Tzanakis, Constantinos
https://www.springer.com/gp/book/9783319739236

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The HPM Newsletter 97 (March) is now posted on the website:

 http://www.clab.edc.uoc.gr/HPM/HPMNews97.pdf

 

All recent newsletters are at

http://www.clab.edc.uoc.gr/HPM/NewsLetters.htm

 

“Concrete numbers” versus “abstract numbers”: an anthropological, historical, historiographical and didactical approach

Edited by Christine Proust & Eric Vandendriessche (Laboratory SPHERE, CNRS & University Paris-Diderot)

This special issue would be an incentive to interconnect several disciplinary perspectives: history, anthropology, philosophy, didactics and ethnomathematics, in order to critically analyze the opposition between “concrete numbers” and “abstract numbers”. Some historians, philosophers, and anthropologists have theorized a separation between “numbers” and the entities enumerated or counted with these numbers, and more particularly, between numbers and measurement units attached to them in the expression of measurement values. This perception gave rise to a linear history of oral and written numerations rooted in evolutionary theories and classifications (Smith, Guitel, and many others). To what extent does this separation reflect the practices carried out in societies or social groups under scrutiny by these scholars? How has the notion of “abstract numbers”-as opposed to those described as “concrete numbers” shaped the history of numerations? This issue’s goal is to confront common historiography with the great diversity of numeration and measurement systems (and their interrelations), attested to by the various textual and ethnographic sources available to us (Murdoch, Thomas, Lean, etc.).

Contributors are invited to expose different case studies, from distinct times and in various contexts, highlighting the way in which mathematical work on measurement units is an integral-and sometimes essential-part of the mathematical elaborations of numbers. How the inclusion of units of measurement shape our understanding of numerical systems and fractions, in past or present treaties and textbooks? How focusing on often neglected mathematical elements such as measurement units could open up new prospects for discussion on mathematical practices? Of particular interest are the cases studies which enable the analysis of various methods of quantification involved in administrative tasks, trade, craft-making, as well as those developed in oral tradition societies, and furthermore in the way mathematics are currently taught. Anthropological, historical, historiographical and didactical approaches are encouraged.

This special issue will include selected articles-as well as a general introduction by the editors-which will be submitted to the Historia Mathematica Journal. The journal’s editorial staff has expressed a keen interest in this project.

Contributors to this issue are invited to submit a title and an outline of the projected article of about 500 words in English, and a short bibliography, including their publications on the subject or related subjects.

 

Proposals should be sent before January 31, 2018 to Christine Proust <christine.proust@univ-paris-diderot.fr> and Eric Vandendriessche <eric.vandendriessche@univ-paris-diderot.fr>.

Approvals will be sent to the authors by March 5, 2018. Subsequently, the first version of the articles (written preferably in English, approximately 60 000 characters including spaces, references, as well as a 100 word abstract) should be sent to the editors by September 30, 2018. 2

Short indicative bibliography

 

Bernard, Alain, Grégory Chambon, and Caroline Ehrhardt. 2010. Le sens des nombres.

 

Mesure, valeur et informations chiffrées: une approche historique. Paris : Vuibert. Cajori, Florian. 1928-1929. A history of mathematical notations. Chicago: The Open Court Publishing Company.

Chrisomalis, Stephen. 2010. Numerical Notation: A Comparative History. Cambridge University Press.

Conant, Levi. 1896. The Number Concept. New York/London, MacMillan & Co.

Crump, Thomas.1992. The Anthropology of Numbers. Cambridge University Press. Dehouve, Danièle. 2011. L’imaginaire des nombres chez les anciens Mexicains. Rennes : Presses Universitaires de Rennes.

Guitel, Geneviève. 1966. “Classification hiérarchisée des numérations écrites.” Annales. Économies, Sociétés, Civilisations 21e année, n°5: 959-981.

Guitel, Geneviève. 1975. Histoire comparée des numérations écrites. Paris: Flammarion. Lean, Glen.1992. Counting systems of Papua New Guinea and Oceania. Unpublished PhD thesis. Lae: Papua New Guinea University of Technology.

Lévy-Bruhl, Lucien. 1910. Les fonctions mentales dans les sociétés inférieures. Paris : F. Alcan.

Malinowski, Bronislaw. 1920. “Classificatory Particles in the Language of Kiriwina”. Bulletin of the School of Oriental Studies, University of London, 1(4): 33-78.

Murdoch, John. 1890. “Counting and Measuring among the Eskimo of Point Barrow”. American Anthropologist, 3 (1): 37-44.

Owens, Kay, Glen Lean, Patricia Paraide, and Charly Muke. 2018. History of Number. Evidence from Papua New Guinea and Oceania. Springer International Publishing.

Neugebauer, Otto. 1933. “Sexagesimalsystem und babylonische Bruchrechnung”. Quellen und Studien zur Geschichte der Mathematik B 2: 199-210.

Nissen, Hans J., Peter Damerow, and Robert Englund. 1993. Archaic Bookkeeping. Writing and Techniques of Economic Administration in the Ancient Near East. Chicago: University of Chicago Press.

Peacock, George. 1826 (ed. 1845). “Arithmetic”. In Encyclopaedia Metropolitana, vol. I: Pure Sciences. London: Smedley & Rose, pp. 369-523.

Proust, Christine. 2008. “Quantifier et calculer: usages des nombres à Nippur”. Revue d’Histoire des Mathématiques 14:143-209.

Smith, David Eugene and Jekuthiel Ginsburg. 1937. “Numbers and numerals”. National Council of Teachers of Mathematics.

Thureau-Dangin, François. 1930. “Nombres concrets et nombres abstraits dans la numération babylonienne”. Revue d’Assyriologie, 27: 116-119.

Thomas, Cyrus 1900. “Numeral Systems of Mexico and Central America”. Smithsonian Institution, Bureau of American Ethnology, 19th Annual Report, Part 2. Washington DC: 853-955. Troure, Kalifa and Nadine Bednarz. 2006. “Une étude ethnomathématique au Burkina Faso : l’arithmétique au quotidien”. Canadian journal of science, mathematics and technology education, 10 (4): 307-320.

Urton, Gary, 2003. Signs of the Inka Khipu: Binary Coding in the Andean Knotted-String Records. Austin: University of Texas Press.

Tylor, Edward.1871. “The Art of Counting”. In Primitive Culture: Researches Into the Development of Mythology, Philosophy, Religion, Languages, Art and Customs, Vol. 1, chap. VII. London : John Murray, Albemarle Street, pp. 239-272.

Vandendriessche, Eric. 2016. “Variabilité culturelle de la numératie : quelques points d’entrée dans la littérature ethno-mathématique”. Statistique et Société, 4 (1): 51-55.

Vellard, Dominique. 1988. “Anthropologie et sciences cognitives : une étude des procédures de calcul mental utilisées par une population analphabète”. Intellectica, 2: 169-209.

Welcome to Newsletter 96!

Dear friends,

Happy November!

 I’ve decided to use my “Welcome” message in Newsletter 96 as a way to revisit one of the discussion group sessions from HPM 2016 (Montpellier, France). In Discussion Group 2, Sebastian Schorcht (Germany) and I facilitated a discussion of the topic, “History of Mathematics in Teacher Education.” During the group exchange we discussed several topics, including ways in which we might be able to build a community of interested teachers, scholars, and researchers to address responses to and develop work based upon the work from four prompts that guided a similar discussion at HPM 2012:

Prompt 1: Identify one or two beneficial aspect(s) of a “History of Mathematics” course (from either the perspective of having taken or taught such a course before).

Prompt 2: Identify one or two obstacles that may arise in implementing a “History of Mathematics” course. Describe ways in which the obstacles can be addressed.

Prompt 3: Describe the benefits to teacher candidates (teacher students) that requiring a “History of Mathematics” course may provide (again, based on actual experience or what you believe).

Prompt 4: With regard to the potential content and pedagogy of such a course, what are examples of tasks that should be required?

The discussion group in Montpellier was engaging (at least from my perspective!), but I would like to generate further discussion based on what began there. To begin that continued work I invite you to visit the link below and to contribute your thoughts and experiences via a brief survey.

I will leave the survey open for a few weeks, and I will compile the results to inform the next step. When we proposed the Discussion Group for Montpellier 2016, we stated that we wanted to:

focus on sharing and discussing specific tasks or activities, which may serve as examples for contexts that do not currently possess a strong history of mathematics dimension within mathematics teacher education programs, or which may provide new examples for those who do. A key product of the DG is to produce a document that contains a description of examples, notation of potential uses, and contact information for persons who either devised or implemented the sample task or activity. (Clark & Schorcht, 2016, emphasis added)

It’s important to me to continue to build and connect a broader community of persons engaged in thinking deeply about the ways in which history of mathematics informs the education of future and current mathematics of teachers. I believe the reach of this Newsletter will enable us to compile examples from around the world, and moving forward, we can provide a space to share resources and to propose additional collaboration, including those with other researchers outside the HPM, which will continue to open the door for new ideas and new areas in which we can contribute.

Please share your examples and experiences on the short survey here: https://fsu.qualtrics.com/jfe/form/SV_25KWFeGg5Rxjd5j

And, if you have any questions, please don’t hesitate to contact me!

If you have not already done so, I hope that you will consider submitting a proposal for ESU-8 (the proposal deadline has been extended to 15 November 2017!). And, I would like to extend my gratitude to the International Scientific Program Committee and the work that they have completed thus far in preparation for the event in Oslo in July 2018. Thank you, Evelyne, Uffe, Tinne, Bjørn, and Costas, for all of your hard work!

Finally, I wish you a productive close to 2017 and a lovely start to 2018!

Kathy

(kclark@fsu.edu)

Reference:

Clark, K., & Schorcht, S. (2016). History of mathematics in teachers’ education: Motivation for and of Discussion Group 2. In L. Radford, F. Furinghetti, & T. Hausberger (Eds.), Proceedings of the 2016 ICME Satellite Meeting of the International Study Group on the Relations Between the History and Pedagogy of Mathematics (HPM 2016, 18-22 July 2016) (pp. 203-204). Montpellier, France: IREM de Montpellier.

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: In the regularly updated ESU-8 website http://esu8.edc.uoc.gr. See also the First Announcement at https://esu8.edc.uoc.gr/1st-announcement/ & the HPM Newsletter issues No 94 & No 95
Important dates:
New deadline for abstract submission of proposals for all types of activities: 15 November 2017 (original 31/10/17)
• Authors’ notification: 15 December 2017
• Second Announcement: By early December 2017
• Deadline for early registration: 31 January 2018

Submission procedure: Submission of proposals and full texts for the proceedings, the reviewing process, and authors’ notification is being realized online via https://esu8.edc.uoc.gr/submission where more detailed information on the reviewing procedure and the evaluation criteria can be found.

Proceedings: They will be published in digital form after ESU-8, so that the authors are given the opportunity to enrich their text as a result of the feedback they will gain during ESU-8.

Registration and Conference fees:
Registration is being done online via https://esu8.edc.uoc.gr/registration/
Early registration (before January 31, 2018): 2100 NOK (1600 NOK for students and school teachers)
Late registration (before 31 May 2018): 2600 NOK (2100 NOK for students and school teachers)
(Current equivalence of Norwegian Krone (NOK): 1NOK  0,106€  0,127 US$)

Plenary Lectures
Theme 1: Hans Niels Jahnke (Germany), Hermeneutics, and the Question of “How is Science Possible?”

Theme 2: Ingo Witzke (Germany), Epistemological beliefs about mathematics – Challenges and chances for mathematical learning: Back to the future.

Theme 3: Frédéric Métin (France), Implementing history in the math class, from kindergarten to teacher training: words and artifacts

Theme 4: Snezana Lawrence (UK), The art and architecture of mathematics education – a study in metaphors

Theme 5: Marta Menghini (Italy), The fusion of plane and solid geometry in the teaching of geometry: textbooks, aims, discussions

Theme 6: Andreas Christiansen (Norway), The first Norwegian textbooks in mathematics — A story of independence and controversy
Plenary Panel Discussion:
Theme 2: Caterina Vicentini (Italy) coordinator, panelists still to be decided: History, Epistemology and Teaching Mathematics: A challenging partnership?

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

For further information, contact
Constantinos Tzanakis, Dept. 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, Dept. of Education, Aarhus University, Campus Emdrup. Tuborgvej 164, DK-2400 Copenhagen NV, utj@dpu.dk (co-chair)
Tinne Hoff Kjeldsen, Dept. of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, thk@math.ku.dk (co-chair)

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 Victor Katz and Frank Swetz and published by the Mathematical Association of America, 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 high school or college classroom.

“Trisecting an Angle Using Mechanical Means” is one of our many articles with interactive features. You and your students can use author Keith Dreiling’s interactive applets to trisect angles using the methods of Hippias, Archimedes, and Nicomedes.

nl 96_3

Above: Spiral of Archimedes for trisecting angles

 

In “The Mathematics of Levi ben Gershon in the Classroom,” author Shai Simonson shares his translations of work by Levi (1288-1344) on the value of pi, calculating square roots, and a selection of word problems. Learn how you and your students can compute your personal estimates of pi!

In “Impacts of a Unique Course on the History of Mathematics in the Islamic World,” author Nuh Aydin shares his motivation for developing such a course, its structure and content, its community service component, and its impacts on students, community members, and his own scholarship.

nl 96_2

Above: From the title page of a 1648 manuscript of John Speidell’s 1648 Spherical Trigonometry. See more in MAA Convergence’s “Mathematical Treasures,” where this image appears courtesy of the University of Pennsylvania Libraries.

 

We continue our series of mini-Primary Source Projects (mini-PSPs) from the TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources (TRIUMPHS) team with two new projects:

  • “Why be so Critical? Nineteenth Century Mathematics and the Origins of Analysis,” by Janet Barnett, in which introductory analysis students read criticisms by Bolzano, Cauchy, Dedekind, and Abel that helped motivate the development of formal proof via precise inequalities in analysis.
  • “Connecting Connectedness,” by Nicholas Scoville, in which introductory topology students see how mathematical ideas and definitions evolve over time by reading contributions to the concept and definition of connectedness from Cantor, Jordan, Schoenflies, and Lennes.

“The Totient Function” is the first article in a new series titled “Math Origins,” in which Euler Archive Director Erik Tou answers the question, “How were concepts, definitions, tools, and theorems familiar to today’s students of mathematics developed over time?” In this first installment, Tou explains how the totient function, also known as the Euler phi-function, was shaped by Euler, Gauss, and Sylvester.

nl 96_1

Above: Proposal of Charles Dodgson (Lewis Carroll) for symbols for trigonometric functions (1861). From MAA Convergence’s “Mathematical Treasures”

 

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

 

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

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