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 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


The year is already well under way and I trust all is going well mathematics educationally in your classroom, school or institution.




My homepage at has been updated with the following new items:

1)      A primary mathematics worksheet (1992) on "Order of operations"

2)      mathematical/mathematics education quote

3)      mathematics/science cartoon.


My dynamic geometry sketches Link at has been updated with the following (new & revised) sketches:

             1) Cyclic quadrilateral rectangle result (new)

             2) A (novel) generalization of the theorem of Pythagoras (new)

             3) Hierarchical quadrilateral tree (new)

             4) Octagon centroids forming parallelo-octagon (updated)

             5) Similarity of parabola (updated with additional sketch)


and the Student Explorations section  with:

             1) Bicentric quadrilateral property (new)

             2) Construct a parallel hexagon with Geo-Next (updated)

             3) Miscellaneous transformations (of figures and graphs) (updated)

             4) Pi in other geometries (new)

             5) Quadrilateral Inequality involving Perimeter & Diagonals (updated with additions)

             6) Rectangle and Rhombus angle trisection (new)



Please REFRESH pages if they don't load properly the first time.




Excellent free webinars by Key Curriculum Press on Algebra, Calculus, Geometry, Data Handling, Chemistry, etc.  are available at: Past Webinars are available at





The books below might be valuable additions to add to your university, school or personal libraries.


a) The Elements of Creativity and Giftedness in Mathematics

Editors, Bharath Sriraman, The University of Montana, USA and Kyeong Hwa Lee, Seoul National University, Korea


b) QED: Beauty in Mathematical Proof

by Burkard Polster  URL:


c) Problem Solving Strategies: Crossing the River with Dogs and Other Mathematical Adventures

by Ted Herr and Ken Johnson URL: (To order in Southern Africa, please contact )


d) EMPower Mathematics for Adult Mathematics Education URL: (To order in Southern Africa, please contact )


e) 15% Discount on all Lulu books for May 2011, URL:  


f) Expanding the science and technology learning experiences of children.

The book is specifically designed for teachers and for parents who work with PreK-8 children to help improve their science and technology education. Free download at





a) Download Einstein's 1921 address "Geometry and Experience" to the Prussian Academy of Sciences in Berlin at


b) Watch the video clip "Fibonacci Numbers - The Fingerprint of God"  which shows how much they are woven into the DNA of nature at   


c) Download for free the 1986 UNESCO Vol. 5, "Studies in Mathematics Education: The teaching of Geometry", 197 pp. at  


d) Download the Masters in Math Ed thesis of David Wagner on "Being in a Mathematical Place: Brief Immersions in Pure Mathematics Investigations" from the Univ of Alberta at  


e) Problem Solving & Logical Thinking at has free powerpoints, worksheets, and more.


f) Download FREE PDF (for developing countries like South Africa) of "Designing Mathematics or Science Curriculum Programs: A guide for using Math and Sci Education Standards" from


g) Download FREE PDF (for developing countries like South Africa) of "Helping Children Learn Mathematics" by Jeremy Kilpatrick and Jane Swafford, Eds., from  


h) Maths Masters by Burkard Polster and Marty Ross, two mathematicians from Australia, at contains articles, movie-clips, books, critiques of curricula, challenging problems, recreational math, etc.


i) Download FREE PDF of the doctoral dissertation of Ron Myers on "The Effects of Technology in mathematics Instruction on Student Achievement" at The study reports a significant increase in FCAT scores in Grade 10 students who used Sketchpad as opposed to those in a control group who didn't.


j) The 53 public use lessons collected as part of the TIMSS video studies are now available for everyone on a new website, Users must register on the site to access the videos, but registration is free. The site also provides full English-translation subtitles for each lesson, a searchable transcript, and a set of resources collected with each lesson such as scanned text materials and teacher commentaries.


k) A wikipedia for Problem Solving has been launched and is well suited to IMO preparation. It is found at   


l) View a book trailer of "Geometry Energized". The aim of this book is to bring to life GCSE mathematics topics whilst presenting some of its historical development in an energetic manner. URL:  


m) A course on "Didactics As Design Science", for doctoral students in didactics of mathematics and science, will be held in the Fall of 2011 at the University of Copenhagen (Denmark). Participation is free of charge. The course involves 3 two-day sessions in Copenhagen. More information is available here:  


n) Proceedings of the Edinburgh Mathematical Society are available at and has mathematical research articles dating back to the 1880's, many of which are freely accessible online.


o) The latest issue of the Proof Newsletter with research papers on the teaching and learning of proof is available at


p) The site was created to provide insights into the reform of mathematics teaching in the schools by making a compelling case for the rational reform of school mathematics.





a) The Mathematics & Statistics Research Unit in collaboration with the Education Research Unit of the Athens Institute for Education and Research (ATINER) will hold its 5th Annual International Conference in Athens, Greece, 13-16 June, 2011. The conference website is


b) SIEMAT III - The Third International Seminar on Mathematics Education, hosted by the Post-Graduation Programme of Mathematics Education at Bandeirante University of S‹o Paulo, Brazil, aims at promoting the interchange of ideas between research groups and researchers in the field, both nationally and worldwide, 21-25 June 2011. For more information, contact or


c) A combined conference of The Australian Association of Mathematics Teachers (AAMT) and the Mathematics Education Research Group of Australasia (MERGA) will be held in Alice-Springs, 3-7 July 2011. For more info go to:


d) The Tenth International Conference on Technology in Mathematics Teaching will be held in Portsmouth, UK between 5th-8th July 2011. Full details are available at


e) 35th Conference of the Psychology of Mathematics Education (PME), Ankara, Turkey, 10-15 July 2011 at,48,general_information


f) 17th National Congress of AMESA, Theme: "Mathematics in a globalised world", 11-15 July 2011, Johannesburg, Congress Director: Lerato Mathenjwa, or ; Academic Coordinator:


g) TSM 3-day Residential workshop for ICT and Mathematics, Oundle school (near Cambridge) England 11-14 July 2011,


h) TIME-2012 will be held July 10-14, 2010 in Tartu in Estonia. The conference web site is:


i) The 15th ICTMA Conference (International Conference on the Teaching of Mathematical Modeling and Applications) will be hosted by the Australian Catholic University, Melbourne, 14-19 J u l y 2 0 1 1. Visit: or contact:


j) BRIDGES 2011 Conference: Connections between Mathematics, Music, Art, Architecture, Culture, Univ of Coimbra, Portugal, July 27-31, 2011. URL:


k) 11th International Conference of The Mathematics Education into the 21st Century Project: 'Turning Dreams into Reality: Transformations and Paradigm Shifts in Mathematics Education', 10-16 September 2011, Rhodes University, Grahamstown, South Africa. Download the First Announcement and Call for Papers at: E-mail, Alan Rogerson, Programme Chair at


l) The ATCM and Chinese Association of Mathematics Education is launching the ATCM-China chapter ( ) and its first meeting is to be held at Xi'an, China during August 3-6, 2011.  The ATCM local chapter is meant to promote the exchanges of students-centered projects where technological tools are being implemented creatively in solving real-life problems.


m) The 16th Asian Technology Conference in Mathematics (ATCM 2011, which is going to be hosted by the Abantzzet Baysal University, Bolu, Turkey at the beautiful five star BŸyŸk Abant hotel, September 19-23 of 2011.


n) ICMI Study 21 entitled "Mathematics Education and Language diversity". The two co-chairs are Mamokgethi Setati, University of South Africa, and Maria Do Carmo Domite, Universidade de Sao Paulo, Brazil.  The Discussion Document may be found at the study website at and the Study Conference will be held on 16 - 20 September 2011 in Sao Paulo, Brazil.


o) The 2011 International Conference on School Mathematics Textbooks (ICSMT 2011) will be held during October 12-14, 2011 in Shanghai, China and hosted by East China Normal University (ECNU). The theme of ICSMT 2011 is to explore trends and characteristics of school mathematics textbooks around the world. Official website of ICSMT 2011 at:


p) The ISTE International Conference on Mathematics, Science and Technology Education, Kruger Park, South Africa, 17-20 October 2011. Theme: "Towards Effective Teaching and Meaningful Learning in Mathematics, Science and Technology Education". URL:


q) CARN Conference 2011 (Collaborative Action Research Network) at

Bringing a different world into existence: Action research as a trigger for innovations, 4th - 6th November, 2011



r) Volcanic Delta 2011, the Eighth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics, will be held in Rotorua, NZ from 27th November to 2nd December 2011. To express your interest in the conference or find further information please visit


s) Joint Mathematics Meeting of the South African Mathematical Society (SAMS) and the American Mathematical Society (AMS) at Nelson Mandela Metropolitan University, Port Elizabeth, 29 November – 3 December 2011 at


t) The annual meeting of the Southern African Association for Research in Mathematics, Science & Technology Education (SAARMSTE), 16-19 January 2012, University of Malawi. Theme: "Mathematics, Science & Technology Education : A key to sustainable development". Go to: 1st Announcement .


u) 12th International Congress on Mathematics Education, ICME-12, July 8-15, 2012, Seoul, Korea. The 2nd Announcement has been uploaded on the ICME-12 website ( ). Calls for papers for different topic groups have also been posted.





"Intuition is the aristocratic way of discovery, rigour the plebian way." - H.V.D. Hodge, mathematician


"There are no extra pieces in the universe. Everyone is here because he or she has a place to fill, and every piece must fit itself into the big jigsaw puzzle." - Lewis Carroll, English mathematician and writer, 1832-1898.


"The saddest aspect of life right now is that science gathers knowledge faster than society gathers wisdom." - Isaac Asimov, Russian-born American author and biochemist, 1920-1992.


"Intuition comes to us much earlier and with much less outside influence than formal arguments which we cannot really understand unless we have reached a relatively high level of logical experience and sophistication. Therefore, I think that in teaching high school age youngsters we should emphasize intuitive insight more than, and long before, deductive reasoning."— George Polya (1887-1985) in (1981). Mathematical discovery: On Understanding, Learning, and Teaching Problem Solving, (Combined Edition), New York, John Wiley & Sons, p. 128.





Law of Mechanical Repair - After your hands become coated with grease, your nose will begin to itch and you'll need the toilet.


Law of the Alibi - If you tell the boss you were late for work because you had a flat tyre, the very next morning you will have a flat tyre.


Variation Law - If you change lines (or traffic lanes), the one you were in will always move faster than the one you are in now (works every time).


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


Law of Close Encounters -The probability of meeting someone you know increases dramatically when you are with someone you don't want to be seen with.





Solve the problem at:

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Infinitely yours in math




A popular legend tells of a beginning student of geometry asking Euclid, "What shall I get by learning these things?" Euclid remained silent and called his slave, saying, "Give him a coin, since he must make gain out of what he learns."


Prof Michael de Villiers

(Dynamic Math Learning)

8 Cameron Rd

3615 SARNIA (Pinetown)

South Africa

Tel: 027-(0)31-7083709 (h)

Fax: 0866726536 (w): Cell: 0836561396

Skype: michaeldevilliersksu


Dynamic Geometry Sketches:

Dynamic Mathematics Learning Online Store:


Official SA Supplier of Key Curriculum Press at


Visit the SA Mathematics Olympiad at