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November 2018 MATH e-NEWSLETTER

This more or less twice a year 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 summer holidays looming for those in the southern hemisphere, and winter holidays in the northern hemisphere, I wish everyone a festive season ahead! Please note I am sending this Math e-Newsletter from my g-mail account(s), which I don't check daily.


My Downloadable Articles Homepage has been updated with the following new items:
1) An Example of Constructive Defining: From a Golden Rectangle to Golden Quadrilaterals and beyond At Right Angles, March 2017.
2) Reflecting on a 2nd Round 2013 SA Mathematics Olympiad Problem Learning & Teaching Mathematics, Dec 2013.
3) A Merry-Go-Round the Triangle Learning & Teaching Mathematics, June 2018. 4) mathematics/science cartoon and mathematics quote (at bottom of page)

My Dynamic Mathematics Sketches site has been updated with the following new sketch (as well as some updates to older sketches):
1) A Merry-Go-Round the Triangle

My Student Explorations site has been updated with the following new sketches (as well as some updates to older sketches):
1) Constant perimeter triangle formed by tangents to circle
2) Diagonal Division Ratios in a Quadrilateral
3) Japanese Circumscribed Quadrilateral Theorem (Updated with more solutions and generalizations)
Similar Parallelograms: A Generalization of a Golden Rectangle property

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.


All parents, teachers and students please note that the closing date for SA Mathematics Olympiad (SAMO) entries is 1 Feb 2019. Download the entry form here. Currently about 100 000 high school learners participate, but we'd like to see more learners involved and stimulated.


1) Long time colleague and friend, Alan Bell, from Nottingham, UK, passed away on 5 April this year. He was very influential in my thinking around the role and function of proof, as well as its teaching. More information about Alan is at: "Tribute by Hugh Burkhardt".
2) Tom Carpenter from from Wisconsin-Madison, USA passed away on 8 August. He was very involved with Cognitively Guided Instruction. More information regarding Tom is given at "Remembering Tom Carpenter".


a) The latest History and Pedagogy of Mathematics (HPM) Newsletter 98 (July 2018) is now posted at: "HPM July 2018 Newsletter".
b) Enjoy some beautiful and challenging geometry problems at: "Sangaku (Japanese Temple Geometry) Journal of Mathematics".
c) Download the following interesting, provocative paper by Whitney George appeared in the Journal of Humanistic Mathematics (January 2017) at: Bringing van Hiele and Piaget Together: A Case for Topology in Early Mathematics Learning.
d) Jo Boaler's video The importance of Struggling encourages learners to persist and struggle to develop their mathematical skills.
e) Read Athina Thoma and Elena Nardi's paper in the International Journal of Research in Undergraduate Mathematics Education, Nov 2017 for free Transition from School to University Mathematics: Manifestations of Unresolved Commognitive Conflict in First Year Students' Examination Scripts.
f) The latest issues of Paul Ernest's Philosophy of Maths Ed Journal are available.
g) Douglas Clements and Julie Sarama's paper "Myths of Early Math" in Educ. Sci. 2018, 8(2), challenges many popular myths around early childhood math education.
h) Read about Islamic Science's India Connection.
i) Mathematics in the news from The New York Times, August 1, 2018 at: Fields Medals Awarded to 4 Mathematicians.


a) SAARMSTE (Southern African Association for Research in Mathematics, Science and Technology Education) Conference, 15-17 January 2019. Website:

b) 10th International Mathematics Education and Society Conference (MES10), Jan 28 - Feb 2, 2019, Hyderabad, India. URL:

c) Eleventh Congress of the European Society for Research in Mathematics Education (CERME11), Utrecht, Netherlands, 6-10 February, 2019. URL:

d) The Fourth Interdisciplinary Scientific Conference Mathematical Transgressions (ISCMT), 13-16 March 2019, Cracow, Poland. Organized by Institute of Mathematics of the Pedagogical University of Cracow. URL:

e) PME & Yandex Russian Conference Technology and Psychology for Mathematics Education, March 18-21, 2019, Moscow. URL:

f) NCTM Annual Meeting and Exposition, April 3-6, 2019, "Empowering the mathematics community", San Diego, CA. URL:

g) Joint Annual Conference Mathematical Association (MA)/Association of Teachers of Mathematics (ATM), 15 - 18 April 2018, Chesford Grange, Warwick. URL:

h) The Mathematics and its Connections with the Arts and Sciences (MACAS) symposium, McGill University, Montreal, June 18-21, 2019. Website:

i) The 2019 Annual Congress of AMESA will be held at the University of KwaZulu-Natal, Edgewood, South Africa, 25-29 June 2018 with the theme "Developing deep mathematical thinking through mathematics teaching". Website: 

j) The 43st PME Annual Conference will be in Pretoria, South Africa, from July 7-12, 2019. URL: 

k) The 15th International Conference of the Mathematics Education for the Future Project, "Theory and Practice: An Interface or A Great Divide?", 4-9 August 2019, Maynooth University, Kildare, Ireland. Email: URL:

l) The 15th Bi-annual Conference on Elementary Mathematics Teaching, SEMT '19, August 18-22, 2019, Prague, Theme: 'Opportunities in Learning and Teaching Elementary Mathematics'. Website address:

m) The 11th International Conference on Mathematical Creativity and Giftedness, August 22-24, 2019 in Hamburg, Universitat Hamburg. URL:

n) Sixth International Conference on the History of Mathematics Education (ICHME-6) CIRM, Marseille (France), September 16-20, 2019. Website:

o) Third International Conference on Mathematics Textbook Research and Development (ICMT3), 16-19 September 2019, Paderborn, Germany. URL:

p) The 14th International Congress on Mathematical Education (ICME-14), Shanghai, China, July 12-19, 2020. URL:


"Perhaps, though, there is another purpose to proof - as a testing ground for the stamina and ingenuity of the mathematician. We admire the conqueror of Everest, not because the top of Everest is a place we want to be, but just because it is so hard to get there.." - Davis & Hersh (1983:369). The Mathematical Experience. Birkhauser, Boston.

"Were all proofs in mathematics routine, there would be a machine that could solve any problem; press a button and wait until the machine presents its answer. But it can be proved that no such machine can ever exist. Your first reaction to this fact of life might be despair, but do not be discouraged. Mathematics is not the realm of a few "magicians"; you are not expected to compete with Archimedes, Gauss, Hilbert, and Poincaré. Each of us is inventive to some degree; and the more one learns, the more proficient one becomes. In music, we can listen and thrill to the beauty of Bach, Mozart, and Beethoven. Even though we cannot compose the sonatas for unaccompanied violin, Don Giovanni, or the late quartets, we can still sing." - Joseph Rotman (1998: 15). Journey into Mathematics. London: Prentice-Hall.


Law of Random Numbers - If you dial a wrong number, you never get a busy signal and someone always answers.

Law of the Bath - When the body is fully immersed in water, the telephone rings.

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.

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

Proof by lack of interest - "Does anyone really want to see a proof of this?"


Mathematically yours


Prof Dr Michael de Villiers
(Dynamic Mathematics Learning)
South Africa
Dynamic Geometry Sketches:
Dynamic Mathematics Learning Store:


Visit the SA Mathematics Olympiad at