February 2011 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 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


Wishing you all a very Happy New Math Year!




My homepage at http://mysite.mweb.co.za/residents/profmd/homepage4.html has been updated with the following new items:

1)      PME (1989) paper "A comparative study of two Van Hiele testing instruments"

2)      mathematical/mathematics education quote

3)      mathematics/science cartoon.


My dynamic geometry sketches Link at http://math.kennesaw.edu/~mdevilli/JavaGSPLinks.htm has been updated with the following (new & revised) sketches:

             1) De Villiers points & Hyperbola of a triangle (updated)

             2) A generalization of Neuberg & Simson line (updated)

             3) Interior Angle Sum of Polygons: A general formula (new)

             4) Some unproved conjectures (updated)


and the Student Explorations section  with:

             1) Cyclic quadrilateral rectangle result (new)

             2) Interior Angle Sum of Polygons: A general formula - with introductory activity using LOGO (turtle geometry) (new)

             3) Quadrilateral Inequality involving Perimeter & Diagonals (updated)

             4) Added links to 'Mathematical Digest' and 'School Maths'



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




Please remember the dates for this year's Olympiad:

Closing date for entries: 4 Feb

1st round: 16 March

2nd round: 17 May

3rd round: 7 Sep


For more info about entering this prestige competition, past papers and answers, go to:



Download the free e-Book, "Geometry Unbound" at http://www.scribd.com/doc/18935265/Geometry-Unbound


It provides great training and reference for students to prepare for the Senior 3rd Round of SA Mathematics Olympiad (SAMO) and the International Mathematical Olympiad (IMO)




Please note the change of dates to 11-15 July 2011 (see more info further down).




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


a) The Computer as Crucible: An Introduction to Experimental Mathematics

Jonathan Borwein; Keith Devlin, ISBN 9781568813431 URL: http://www.crcpress.com/ecommerce_product/product_detail.jsf?isbn=9781568813431

(Also available in German now)


b) Interdisciplinarity for the 21st Century: Proceedings of the 3rd International Symposium on Mathematics and its connections to the Arts and Sciences, Moncton 2009. Edited by Bharath Sriraman; Viktor Freiman, Paperback 978-1-61735-218-8, Hardcover 978-1-61735-219-5, URL: http://infoagepub.com/products/Interdisciplinarity-for-the-21st-Century


c) Creativity in mathematics and the education of gifted students, Edited by Roza Leikin, Abraham Berman and Boris Koichu URL: https://www.sensepublishers.com/product_info.php?products_id=853&osCsid=f66cb52b2eb4f1f5e196160ff0ebf18b


d) Proof in Mathematics Education: Research, Learning and Teaching by David Reid and Christine Knipping, URL: https://www.sensepublishers.com/product_info.php?products_id=1094&osCsid=f66cb52b2eb4f1f5e196160ff0ebf18b


e) Republished Boolean Algebra at School, Vol. 1 & Vol. 2 by Michael de Villiers, available as PDF or printed book, URLÕs: http://www.lulu.com/product/paperback/boolean-algebra-at-school-vol-1/14244188 and http://www.lulu.com/product/paperback/boolean-algebra-at-school-vol-2/14244227





With sadness, three friends & colleagues I personally knew passed away.


Pierre van Hiele on 1 November 2010 at the age of 101. He is famous for the Van Hiele theory of learning geometry, which is used in many countries. He was given a Honorary Award at UNISA in 2001 for his influential work.


Tom O'Brien on 6 December 2010.  He worked with Polya and Freudenthal. His websites at http://www.mathplace.net/ and http://www.professortobbs.com/ contain several of his books and papers, including a Personal Memory of George Polya at http://www.professortobbs.com/articles/Memories_of_George_Polya.pdf


Peter Hilton, renowned algebraic topologist, on 6 November 2010. Worked on the Enigma project during World War II and visited South Africa several times together with Jean Pedersen. Go to http://www.guardian.co.uk/science/2010/dec/02/peter-hilton-obituary He also had harsh, critical views about the traditional one-sided emphasis on 'computational expertise' at school – see for example: http://www.guardian.co.uk/theguardian/2010/dec/07/letter-peter-hilton-obituary




Key Curriculum Press has been honored with two 2010 BESSIE Awards for The Geometer's Sketchpad¨ and Tinkerplots¨ Dynamic Data Exploration. For 16 years, the Best Educational Software (BESSIE) Awards have been presented by ComputED Learning Center, targeting content-rich programs and Web sites that provide teachers with the technology to foster educational excellence. For more info about these programmes or to order in Southern Africa, please contact: dynamiclearn@mweb.co.za





a) Join Sketchpad Exchange for free at http://sketchexchange.keypress.com/, a new online community where you can share ideas and connect with your peers: share & download Sketchpad sketches and activities for use in your classroom, post links to your website and videos, participate in the community forum, browse the site by grade levels, topics, and tags, etc.


b) The online group MathFuture have been holding a series of "forward-thinking" discussions using Elluminate, an online conferencing software program. Here's a link to the group wiki page that shows the past and future online discussions:



c) The full 2010 Psychology of Mathematics Education of North America (PME-NA) Proceedings in Columbus, Ohio, of 1600 pages of research papers on mathematics education is available at the website http://pmena.org/2010/ This is a valuable resource for students, teachers & researchers.


d) Worksheets to experimentally explore the Triangle & Parallelogram Law of Forces at http://www.tutornext.com/help/triangle-law-of-forces


e) Virtual Mathematics Marathon at http://www8.umoncton.ca/umcm-mmv/index.php


f) Free   online access to the journal Creative Education at: http://www.scirp.org/journal/ce  Contains some math papers, for example, Vol 1, no 3 Dec 2010 has a nice, downloadable article on  'Language and Mathematics: Bridging between Natural Language and Mathematical Language in Solving Problems in Mathematics' by Bat-Sheva Ilany, Bruria Margolin


g) Bernhard Kutzler has retired, but has generously made available a summary of his research work on technology in mathematics education in a free e-book Technology and the Yin & Yang of Teaching and Learning at: http://b.kutzler.com/downloads/YinYang_E.pdf


h) 'Calculus Lectures' in Videos at http://www.onlinemathlearning.com/calculus.html

A series of free, short Calculus Video Lessons from UMKC - The University of Missouri-Kansas City.


i) Gerrit Stols' website http://school-maths.com/  has interactive applets, links, books and other materials directly related to the South African mathematics curriculum.


j) TenMarks has launched a math practice and learning program for grades 3 - High School and as of today, it's FREE for teachers to use in class or for their students to use at home. Check it out at http://www.tenmarks.com/teachers 


k) For all mathematics-teacher educators, an article "Mathematics for Teaching" by Al Cuoco, Notices of the AMS 48 #2 (February 2001), 168-174 at:



l) For a variety of Mathematical Challenges on probability and statistics, conic sections, secondary geometry, middle-school and elementary mathematics visit: http://www.odysseys2sense.com


m) Problem-based Learning: PBL is any learning environment in which the problem drives the learning. That is, before students learn some knowledge they are given a problem. The problem is posed so that the students discover that they need to learn some new knowledge before they can solve the problem. This site has some valuable resources and materials to promote problem-based learning: http://www.chemeng.mcmaster.ca/pbl/PBL.HTM 


n) Apple iTunes U - http://www.apple.com/education/itunes-u/whats-on.html  There are over 600 universities with active iTunes U sites. About half of these institutions — including Stanford, Yale, MIT, Oxford, and UC Berkeley — distribute their content publicly and for FREE on the iTunes - including Mathematics & Science - click on the links for movies, mp3's, pdf's, etc.


o) Jeff Weeks' free Topology & Geometry Games for Win, Mac at: http://www.geometrygames.org/


p) Learning Theory: Constructivism website at: http://carbon.cudenver.edu/~mryder/itc_data/constructivism.html 


q) This site http://homepage.mac.com/efithian/geometry.html has nice geometry worksheets and ideas for teaching on topics like tangrams, tilings, the golden ratio, symmetry, etc.





a) The 7th Congress of CERME, the European Society for Research in Mathematics Education will be held in Rzesz—ow, Poland, from 9-13 February 2011. Papers and poster proposals should use the CERME7 WORD template, and conform to the guidelines at www.cerme7.univ.rzeszow.pl/?id=cerme-guidelines-for-authors


b) The 14th Connected Mathematics Project (CMP) Users' Conference, February 25-26, 2011, Kellogg Center on the Campus of Michigan State University in East Lansing, MI.

For more information please visit: http://www.connectedmath.msu.edu/conferences/overview.shtml


c) Conference on Creative Education (CCE 2011) will be held from April 8-10, 2011 in Wuhan, China. For more info go to: http://www.creativedu.org/2011/


d) The Annual Conference of the Mathematical Association, 14-16 April 2011, Univ. of Loughborough at http://www.m-a.org.uk/jsp/index.jsp?lnk=100


e) ATM Conference 2011, 'Celebrating Gattegno', 18 - 21 Apr 2011, Univ. of Wolverhampton, Telford Campus at http://www.atm.org.uk/events/conferences/


f) NCTM 2011 Annual Meeting & Exposition, Indianapolis, IN, April 13-16, 2011 - Geometry: Constructing and Transforming Perspectives – more info at http://www.nctm.org/conferences/content.aspx?id=25947


g) 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 www.atiner.gr/mathematics.htm


h) 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: http://www.aamt.edu.au/Conferences/AAMT-MERGA-conference


i) 35th Conference of the Psychology of Mathematics Education (PME), Ankara, Turkey, 10-15 July 2011 at http://www.arber.com.tr/pme35.org/index.php/page,48,general_information


j) 17th National Congress of AMESA, Theme: "Mathematics in a globalised world", 11-15 July 2011, Johannesburg, Congress Director: Lerato Mathenjwa, leratojd@yahoo.com or lerato@amesa.org.za ; Academic Coordinator: Hamsa.Venkatakrishnan@wits.ac.za


k) TSM 3-day Residential workshop for ICT and Mathematics, Oundle school (near Cambridge) England 11-14 July 2011, www.tsm-resources.com


l) TIME-2012 will be held July 10-14, 2010 in Tartu in Estonia. The conference web site is: http://time2012.ut.ee/


m) 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: http://dlibrary.acu.edu.au/staffhome/jibrown/ictma.html or contact: Gloria.Stillman@acu.edu.au


n) BRIDGES 2011 Conference: Connections between Mathematics, Music, Art, Architecture, Culture, Univ of Coimbra, Portugal, July 27-31, 2011. URL: http://bridgesmathart.org/bridges-2011/


o) 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: http://math.unipa.it/~grim/21project.htm E-mail, Alan Rogerson, Programme Chair at alan@rogerson.pol.pl


p) 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 http://www.icmi-21.com/index.php?page_id=140 and the Study Conference will be held on 16 - 20 September 2011 in Sao Paulo, Brazil.


q) 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 www.delta2011.co.nz





"Zu glauben, es gŠbe nur eine Wahrheit, ist von allen Illusionen die gefŠhrtlichste."

                      - Paul Watzlawick, Austrian-American psychologist and philosopher

Translation: "To believe that only one truth exists, is the most dangerous of all illusions."


"The only thing that interferes with my learning is my education." - Albert Einstein


'I invent nothing, I rediscover.' - Famous artist, Auguste Rodin




"The shortest distance between two points is under construction." - Bill Sanderson


"Geometry is just plane fun."


Math Joke:  An infinite crowd of mathematicians enters a bar.  The first one orders a pint, the second one a half pint, the third one a quarter pint ... . "I understand", says the bartender - and pours two pints.


Math Joke:  Teacher: What is 2k + k?   Student: 3000.


An internet user's signature seen recently:

'Integrate me. Differentiate me.

You can't hurt me. I'm e^x. Ha ha ha!'




Solve the cyclic quadrilateral problem at: http://math.kennesaw.edu/~mdevilli/cyclic-quad-rectangle-result.html

(Use a free, Java enabled web browser like Firefox or Safari or download & install Java for Internet Explorer).


Mathematically yours




"Pablo Picasso once said that 'every child is an artist - the problem is how to have him/her remain an artist once s/he grows up'. Mathematics is no different from art in this respect."


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

Homepage: http://mysite.mweb.co.za/residents/profmd/homepage.html

Dynamic Geometry Sketches: http://math.kennesaw.edu/~mdevilli/JavaGSPLinks.htm

Dynamic Mathematics Learning Online Store: http://www.FreeWebStore.org/DynamicMathematicsLearning


Official SA Supplier of Key Curriculum Press at http://www.keypress.com


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