February 2017 MATH e-NEWSLETTER


This more or less quarterly Math e-Newsletter is sent out mainly in Southern Africa, but has information that may be of interest to others from different parts of the world. Please e-mail me at profmd @ mweb. co. za (without spaces) if you'd like to be on the mailing list. (Also please say if you specifically want it sent to you as an e-mail or whether you prefer downloading/reading it from my homepage and just receiving a notification).


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Dear Colleagues & Friends


With this first Math e-Newsletter of the year 2017, I'd like to wish everyone a happy mathematical year ahead.




My 'Downloadable Articles' Homepage at http://dynamicmathematicslearning.com/homepage4.html has been updated with the following new item:

1)      Enrichment for the Gifted: Generalizing Some Geometrical Theorems & Objects (my ICME 13 paper).

2)      mathematics/science cartoon and mathematics quote (at bottom of page)


My 'Dynamic Geometry Sketches' site has been updated with a neat solution by Johan Meyer in the Explorations for Students section:

1) Japanese Circumscribed Quadrilateral Theorem


WebSketchpad: My latest Dynamic Geometry Sketches all use WebSketchpad, which are more easily accessible across a range of platforms from cellphones to tablets as well as laptops and PC's without the need to constantly update Java, or to change your security settings.




a) Entries for the SA Mathematics Olympiad (SAMO) for Grades 8-12 organized by the South African Mathematics Foundation (SAMF) is closing this Fri, 3 February 2017. Last year more than 80 000 learners participated; so please consider entering as many learners as you can.

b) The SA Mathematics Challenge (SAMC) for Grades 4-7 will also run again this year, and has had entries in excess of 70 000.

For information about entering these competitions go respectively to these 2 sites:

SAMO: http://www.samf.ac.za/Default2.aspx

SAMC: http://www.samf.ac.za/Challenge.aspx





a) The most common question students ask math teachers at every level is "When will I use math?" WeUseMath.org is a non-profit website that helps to answer this question. This website describes the importance of mathematics and many rewarding career opportunities available to students who study mathematics. Also provides some Teachers Resources and Links to Math Competitions.  Go to: http://weusemath.org/


b) Join the site https://www.academia.edu for free and read scholarly papers like "Algebraic thinking of grade 8 students in solving word problems with a spreadsheet" by Susana Carreira and "Mathematics education ideologies and globalization: Is mathematics discovered or invented?" by Paul Ernest.


c) Join the site https://www.researchgate.net/ for free and read scholarly articles about the teaching and learning of mathematics at all levels.


d) Celebrate PI day, March 14 (3.14) with these learning activities from the NCTM Illuminations website:

Grades 6–8 Unit: Apple Pi

Discover the ratio and meaning of pi.

Grades 9–12 Interactive: Pi Fight

Become comfortable using both radians and degrees with this fun game.





a) SAARMSTE Conference, Central University of Technology, Bloemfontein, Free State, South Africa, 17 - 20 January 2017; Post Conference Writing Clinic: 20 - 21 January 2017;  "Research to learn and teach for diversity in Mathematics, Science and Technology Education". URL: http://www.saarmste.org/conferences


b) 10th Congress of European Research in Mathematics Education (CERME10), 1-5 February 2017, Croke Park, Dublin. Website: http://www.cerme10.org


c) NCTM Annual Meeting and Exposition, April 5-8, 2017, "Creating Communities and Cultivating Change", San Antonio, Texas. URL: http://www.nctm.org/annual/


d) The Annual Conference of The Mathematical Association, 7 - 9 April 2017, "Common Denominators: connections within and beyond mathematics", Royal Holloway, University of London, Egham, Surrey. URL: http://www.m-a.org.uk/annual-conference


e)  The Easter Conference of the Association of Teachers of Mathematics, 10 - 13 April 2017, Holiday Inn hotel, Stratford-upon-Avon, "Mathematical Learning Journeys". URL (copy and paste into browser): https://www.atm.org.uk/Maths-teacher-conference


f) The 10th International Mathematical Creativity and Giftedness Conference (MCG10), 24-26 April 2017, University of Cyprus, Nicosia, Cyprus. URL:  http://www.cyprusconferences.org/mcg10


g) The II International Conference on Mathematics Textbook Research and Development / II Conferencia Internacional em Pesquisa e Desenvolvimento de Livros Didacticos de Matematica (ICMT2), will 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. More info at: www.im.ufrj.br/~ictm2 or email: icmt2@im.ufrj.br


h) The 2017 Annual Congress of AMESA will be held at the Nelson Mandela Metropolitan University, Port Elizabeth, South Africa, 3-7 July 2017 with the theme "Restoring the dignity of mathematics learners through quality teaching and learning". Website: www.amesa.org.za/AMESA2017/index1.htm  


i) The 41st PME Annual Conference will take place in Singapore from July 17 - 22, 2017. URL: http://www.igpme.org/index.php/annual-conference 


j) The ICTMA-18 (International Conference on Mathematical Modelling and Applications will be hosted by the University of Stellenbosch, and held in Cape Town, South Africa, 23-28 July 2017. Website: http://www.ictma18.co.za Contact Prof Ndlovu Mdu at: mcn@sun.ac.za or Dr Helena Wessels at: hwessels@sun.ac.za


k) BRIDGES 2017, Mathematics, Art, Music, Architecture, Education, Culture, University of Waterloo, Ontario, Canada. Dates: 27–31 July 2017

http://bridgesmathart.org/bridges-2017 Bridges 2017 will feature talks and artworks presenting the newest ideas in mathematics and the arts from experts around the world.


l) International Symposium - Elementary Mathematics Teaching to be held in Prague, Czech Republic at the Faculty of Education of Charles University, Prague, Czech Republic, August 20-25, 2017. Contact: jarmila.novotna@pedf.cuni.cz Website address: http://www.semt.cz/


m) The 14th International Conference of the Mathematics Education for the Future Project will be held at Hotel Annabella, Balatonfured, Balaton Lake, Hungary from September 10-15, 2017. The conference title, "Mathematics Education for the next Decade: Heuristics and Challenges of P—lya and Lakatos", continues the search for innovation in mathematics, science, computing and statistics education. Email: alan@cdnalma.poznan.pl URL: http://directorymathsed.net/montenegro/AAAAHungaryFirstAnnouncementDraft.pdf


n) ICHME-5 Fifth International Conference on the History of Mathematics Education, 19-22 September, 2017, Utrecht, the Netherlands. Website:



o) The next Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics will be held in Gramado, Brazil in 26 Nov – 1 Dec 2017. Website: https://www.univates.br/evento/deltabrazil/en


p) The 22nd Asian Technology Conference in Mathematics, December 15-19, 2017, hosted by Chung Yuan Christian University, Chungli, Taiwan. Website: http://atcm.mathandtech.org





"If mathematics describes an objective world just like physics, there is no reason why inductive methods should not be applied in mathematics just the same as in physics." - Logician Kurt G̈odel (1906-1978) in 1951 Gibbs Lecture.


"The history of science, like the history of all human ideas, is a history of irresponsible dreams, of obstinacy, and of error. But science is one of the very few human activities — perhaps the only one — in which errors are systematically criticized and fairly often, in time, corrected. This is why we can say that, in science, we often learn from our mistakes, and why we can speak clearly and sensibly about making progress there."  ― Karl Popper, Conjectures and Refutations: The Growth of Scientific Knowledge


"It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He uses very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better."    - British physicist P.A.M. Dirac





Proof by deception: "Now everyone turn your backs. . ."


Proof by supplication: "Oh please, let it be true."


Proof by poor analogy: "Well, it's just like adding fruit . . . "


Proof by avoidance: "This is so easy, let's skip it ..."


Proof by design: "If it's not true in today's math, invent a new system in which it is."


Proof by authority: "Well, Wolfram Mathematica says it's true, so it must be!"


Proof by intuition: "I just have this gut feeling. . ."



Geometrically yours



"Wide acceptance of an idea is not proof of its validity. Likewise, little acceptance of an idea is not proof of its invalidity either." – own saying


Prof Dr Michael de Villiers

(Dynamic Mathematics Learning)

32 Belfry Towers

39 Beach Rd

4141 Doonside

South Africa

Tel: 027-(0)31-9035109 (h)

Fax: 0866726536 (w): Cell: 0836561396

Skype: michaeldevilliersksu

Homepage: http://dynamicmathematicslearning.com/homepage4.html

Dynamic Geometry Sketches: http://dynamicmathematicslearning.com/JavaGSPLinks.htm

Dynamic Mathematics Learning Store: http://www.lulu.com/spotlight/profmdatmwebdotcodotza


Visit the SA Mathematics Olympiad at http://www.samf.ac.za/Default2.aspx