November 2016 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).


For the PREVIOUS two e-Newsletters go to:

and the one before that from:   






(To unsubscribe from this e-Newsletter, please reply with the word 'remove' in the subject box of the email.)

(If you prefer to just receive a notice with a URL link to this newsletter online, please reply with the word 'internet read' in the subject box of the e-mail)




Dear Colleagues & Friends


With this last Math e-Newsletter of the year 2016, I'd like to wish everyone a joyous and restful festive holiday season ahead.




My 'Downloadable Articles' Homepage at has been updated with the following new item:

1)      Order of Operations: The Math and the Myth.

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


My 'Dynamic Geometry Sketches' site available at: has been updated with a dynamic WebSketchpad sketch for Pirate Treasure Hunt and a Generalization, as well as the following new dynamic, interactive sketches in the Explorations for Students section:

1) Japanese Circumscribed Quadrilateral Theorem
2) SA Mathematics Olympiad Problem 2016, Round 1, Question 20
3) Three Circle Geometry Theorem Proofs by Transformations


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) In August 2016, Jonathan Borwein passed away at the age of 65. Apart from being a prolific researcher in mathematics, he was well-known for his advocacy of the value of experimentation in mathematical research and was a co-founder of the journal ‘Experimental Mathematics’. More info (copy and paste into browser): 

b) The co-developer of the programming language LOGO and Turtle Geometry, Seymour Papert, passed away in July 2016. He was a student at the University of Witwatersrand, South Africa, completing a PhD in mathematics in 1952. More info (copy and paste into browser):

c) Mathematics educator and colleague of many years, Dexter Luthuli, passed away in July 2016. He was a staff member of CASME and UKZN ,as well as an active AMESA member for many years. Over the years he positively contributed to the mathematical development of numerous mathematics education students and mathematics teachers.




a) Congratulations to Jill Adler, Wits University, who over and above been awarded the Freudenthal Award at the ICME-13 Congress for her contributions to mathematics education, was appointed president of The International Commission on Mathematical Instruction (ICMI) during the congress in Hamburg.


b) Chris Pritchard’s new book “A Square Peg in a Round Hole: Adventures in the Mathematics of Area” contains a wonderfully rich collection of problems of various levels related to the concept of area, and will be especially useful to a wide range of classroom teachers for lesson planning and enrichment. It is available through The Mathematical Association. Website:


c) Two FREE Massive Open Online Courses for Educators (MOOC-ED) for in-service and pre-service middle and high school mathematics teachers' professional development, namely, “Teaching Mathematics with Technology”, and “Teaching Statistics Through Data Investigation” has been running since September, but registration is still open until 1 December 2016. More info (copy and paste into browser):


d) The International Society for Design and Development in Education (ISDDE) has awarded the prestigious 2016 ISDDE Prize for Excellence in Educational Design to Uri Wilensky, professor of Learning Sciences, Computer Science and Complex Systems at Northwestern University for NetLogo ( is a computer-based modeling environment that enables learners to both explore and build computer models of natural and social phenomena.


e) The past year more than 80 000 learners participated in the SA Mathematics Olympiad. Congratulations to all learners who made it to the Third Round, especially to the top 10 learners, and to Nicholas Kroon from St. Andrews who emerged as the eventual winner.




a) Listen to the Podcast of my Interview by Michelle Cirillo (University of Missouri) at ICME 13 in Hamburg in July 2016 about my career in Mathematics Education.  Go to: (If problems are experienced playing it through completely in your browser, ensure that you have 'Allowed Flash Player' in your settings and preferences).


b) The Journal of Humanistic Mathematics, an online-only, open-access, peer-reviewed journal is available at: 


c) Access the complete digital archive of the Humanistic Mathematics Network Journal (1987-2004) at: 


d) The Springer open access journal, International Journal of STEM Education contains a variety of papers that could be of use to both mathematics teachers and researchers of mathematics education.


e) Use Alfinio Flores' excellent site in your classroom to help learners dynamically visualize and derive the area formulae for some basic geometric figures like rectangles, parallelograms, trapeziums, and regular polygons. Go to: 


f) The European Union Comenius Continuation Project: DQME II  (Developing Quality in Mathematics Education) (2007-2010) has an enormous amount of practical classroom materials, as well as many new ideas for learning and teaching mathematics. These materials are freely available at:


g) Challenge your mathematically talented learners with the interesting problems of the Junior Balkan Mathematical Olympiad (JBMO 2016) at:


h) Visit Math Camps at: for various teaching ideas and links to other useful websites.


i) Challenge your primary school learners with ATM Problems of the week at (copy and paste into browser):


j) Watch the short, inspirational video clip "Good Morning, Miss Tolliver" about mathematics teaching at (copy and paste into browser): 





a) There will be a Special session for Mathematics Education at the Southern Africa Mathematical Sciences Association (SAMSA 2016) Annual Conference, November 21 – 24, 2016,University of Pretoria, Pretoria, South Africa. More info:   


b) The 21st Asian Technology Conference in Mathematics, December 14-18, 2016. Host: Suan Sunandha Rajabhat University Bangkok. Conference Venue: NongNooch Pattaya Garden & Resort, Pattaya, Thailand. Website:


c) 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:


d) 10th Congress of European Research in Mathematics Education (CERME10), 1-5 February 2017, Croke Park, Dublin. Website:


e) NCTM Annual Meeting and Exposition, April 5-8, 2017, “Creating Communities and Cultivating Change”, San Antonio, Texas. URL:


f) 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:


g)  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):


h) The 10th International Mathematical Creativity and Giftedness Conference (MCG10), 24-26 April 2017, University of Cyprus, Nicosia, Cyprus. URL:


i) 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: or email:


j) The 2017 Annual Congress of AMESA will be held in the Eastern Cape, South Africa, July 2017. More details to follow in the next e-newsletter.


k) The 41st PME Annual Conference will take place in Singapore from July 17 - 22, 2017. URL: 


l) 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: Contact Prof Ndlovu Mdu at: or Dr Helena Wessels at:


m) 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: Website address:


n) 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 Pólya and Lakatos’, continues the search for innovation in mathematics, science, computing and statistics education. Email: URL:


o) The next Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics will be held in Gramado, Brazil in late November in 2017. Details to follow in next e-newsletter.





"If the breadth of our knowledge of plane geometry can be compared with the surface of the ocean, then the yet unknown knowledge of spatial geometry is comparable with its depths." – Heinz Schumann, University of Weingarten, October 2016


“If the proof starts from axioms, distinguishes several cases, and takes thirteen lines in the text book … it may give the youngsters the impression that mathematics consists in proving the most obvious things in the least obvious way.”

– George Polya. Mathematical Discovery: on Understanding, Learning, and Teaching Problem Solving (1981), 129.


"Believe nothing,

Merely because you have been told it.

Or because it is traditional.

Or because you yourself have imagined it.

Do not believe what your teacher tells you,

Merely out of respect for the teacher.

But whatever, after due examination

and analysis,

You find conducive to the good,

The benefit, the welfare of all beings,

That doctrine believe and cling to, and take it as your guide."   – Gautam Buddha





The Coffee Law - As soon as you sit down to a cup of hot coffee, your boss will ask you to do something, which will last until the coffee is cold.


Murphy's Law of Lockers - If there are only 2 people in a locker room, they will have adjacent lockers.


Law of Physical Surfaces - The chances of an open-faced jelly sandwich landing face down on a floor are directly correlated to the newness and cost of the carpet or rug.


Law of Logical Argument - Anything is possible if you don't know what you are talking about.


Brown's Law of Physical Appearance - If the clothes fit, they're ugly.


Oliver's Law of Public Speaking - A closed mouth gathers no feet.


Wilson's Law of Commercial Marketing Strategy - As soon as you find a product that you really like, they will stop making it.


Doctors' Law - If you don't feel well, make an appointment to go to the doctor, by the time you get there you'll feel better.  But don't make an appointment, and you'll stay sick.



Mathematically yours



The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.”  Andrew Wiles From interview for PBS website on the NOVA program, 'The Proof'.


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


Dynamic Geometry Sketches:

Dynamic Mathematics Learning Store:


Visit the SA Mathematics Olympiad at