My latest Mathematics bookmarks

Friday, December 9, 2011

FullMarks/siyavula November 2011 Newsletter

Siyavula is very excited and proud to announce that the Department of
Basic Education <>
 is printing their openly-licensed textbooks for all learners taking
Physical Science and/or Mathematics in Grades 10-12, for the whole
country for 2012! A total of 2.5 million Siyavula textbooks (titled
"Everything Maths" and "Everything Science") will be printed
and distributed across the country!

Ensuring that this was possible became the exclusive focus of the
Siyavula team for the last 4 months, which was an all-consuming
exercise. We expanded our team and worked incredibly hard (each member
of the book team clocked almost 2 man months per calendar month since
mid-September!). We had to revamp our pipeline, develop new layouts
for the books, undergo multiple review iterations with DBE reviewers,
edit, edit, edit and then turn everyone into a translator in some
capacity. It has been incredibly hectic but worth all the effort, as
we proudly await the delivery of our open textbooks to schools across
the country.

This is a great milestone for both Siyavula and the OER movement in
South Africa, and will raise significant exposure of the issues around
access to materials and awareness of open licensing. For more
information on this please visit Mark Horner's blog
. To download our new books please visit our website by clicking here

As a result of this we had to put new developments for FullMarks
 on hold for a little while, but we will send out notification next
week on the changes that have been implemented in the last while, as
well as where we stand on future developments.

We are closing for Christmas on Thursday 15 December, with most of the
team back in the office on Tuesday 3 January.

We hope that everyone has a wonderful holiday and a good break over
the Festive season!

Wednesday, December 7, 2011

African Institute for Mathematical Sciences: Postgraduate Diploma in Mathematical Sciences

The African Institute for Mathematical Sciences (AIMS) is a centre for education and research in Cape Town, South Africa. AIMS was established in 2003 as a partnership project of the following six universities - Cambridge, Cape Town, Oxford, Paris Sud XI, Stellenbosch, and Western Cape. The goals of AIMS are to promote mathematics and science in Africa, to recruit and train talented students and teachers, and to build capacity for African initiatives in education, research, and technology.

AIMS offers an intensive graduate-level course over 10 months leading to a master's-level Postgraduate Diploma (PGD) in Mathematical Sciences, formally accredited by the Universities of Cape Town, Stellenbosch, and the Western Cape.

The programme is taught in association with the Faculty of Mathematics of the University of Cambridge, and the Division of Physical Sciences at the University of Oxford.

The course provides both a broad overview of cutting-edge sciences and strong mathematical and computing research skills. The course is unique, offering students exposure to a range of topics, thereby allowing them to make an informed choice as to their future specialisation. The goal is to develop well-rounded scientists, with excellent problem-solving skills, capable of creative thinking and genuine innovation. There is a strong grounding in end-to-end skills, from problem formulation, estimation, prioritisation, and generally applicable mathematical and computing methods, through to clear and concise scientific report writing. The aim is to equip students with the necessary tools and confidence for decision making and policy analysis. A number of modules which also make the course interesting and relevant to prospective mathematics and science teachers, have been included in the programme for South African students commencing in January 2012.

Faculties from the nearby Universities of the Western Cape, Cape Town and Stellenbosch have been intimately involved in developing the AIMS course, ensuring it is well integrated with local undergraduate and master’s courses, and with local postgraduate research opportunities. World-leading scientists and educators have volunteered to teach at AIMS. Their participation ensures an education of the highest international quality. Tutors (often including PGD alumni) provide teaching and administrative assistance, assistance to foreign language speakers, and continuity across the visiting lecturers.

Students are registered at one of the three local universities: Cape Town, Stellenbosch or Western Cape.
Prospective applicants

Completing a course of such scope and depth in just one academic year is possible only if it is highly intensive, so students must come prepared to work hard and focus. The residential nature of AIMS allows far greater contact time between lecturers and students than normally available in a university setting. Courses are student-centred but very demanding. Students study two subjects at a time every three weeks, with morning lectures and related afternoon problem solving and computing sessions. Each course consists of 30 hours contact time (10 per week). Additional tutorials and special lectures are often held in the evenings, when students complete their assignments.

No special preparation for the course is needed on a student's part. However, the working language is English and foreign students are advised to take an English language course before arrival. The course also carries a large component of scientific computing, and many hours are spent in the computer laboratory; students who have improved their touch typing skills before the programme will have a distinct advantage.

To apply for admission go to the Apply section for the required forms.

Students are strongly advised to apply by 31 March 2012 to qualify for the first round selection which takes place during March. Applicants who are accepted on to the programme will be notified by the end of March 2012. Late applications received may be considered in exceptional cases and where places are still vacant.

For more about the Postgraduate Diploma in Mathematical Sciences, refer to

For more about the African Institute for Mathematical Sciences, refer to

Saturday, December 3, 2011

Weekly maths bookmarks (weekly)

Posted from Diigo. The rest of my favorite links are here.

Saturday, November 19, 2011

Weekly maths bookmarks (weekly)

  • This article deals with an intervention unit which focused on the positive effect of integrating poems, stories and fables (the literary genre) for improving mathematical language, fostering the teaching of mathematics language, increasing satisfaction with the process and strengthening the relationship between use of daily language and mathematics language. The study was conducted amongst pre-service mathematics teachers, specialising in literacy activities designed to foster mathematics language.

    tags: mathematics

Posted from Diigo. The rest of my favorite links are here.

Saturday, November 5, 2011

Weekly maths bookmarks (weekly)

Posted from Diigo. The rest of my favorite links are here.

Saturday, October 22, 2011

Weekly maths bookmarks (weekly)

Posted from Diigo. The rest of my favorite links are here.

Thursday, October 20, 2011

Invitation to a Russian professor's talk on Olympiads

Dear colleagues


You are kindly invited to attend a lecture by a visiting Mathematics and Statistics professor from Russia.

Professor Ivan Vysotski

He will give us an insight into the Mathematics Olympiads conducted in Russian schools.


Date: Monday: 24 October 2011

Venue: AJH van der Walt Building, Muckleneuk Campus, UNISA, Room 6-36

Time: 12:30 for 13:00 to 14:00


Please RSVP for catering purposes (by Friday, 21 October):


Monday, October 17, 2011

Calling South African teachers to start twittering: Online un-workshop

Twitter has great potential as a creative and collaborative learning and teaching tool in the classroom. It has been chosen as the number 1 learning & teaching tool for the last 4 (going on 5) years globally, which shows that it is tool that has to be taken seriously.

Some of the reasons for using twitter as a teacher and in your classroom:
  • You can create a personal learning network on the fly
  • You can learn from others and get instant support
  • You can use this tool to teach your learners how to use social media responsibly
  • You can share resources, events, thoughts, lesson ideas... quick as lightning!
  • You can have discussions on topical issues in your classroom and in education in general.
  • You can use it to connect your class to other global classrooms and experts
  • .................
Obviously it is just a tool and learning and teaching only takes place if we use a tool effectively! My mission is to get at least 500 South African teachers to do just that! So this online un-workshop will guide newbie twitter teachers or those wanting to learn about how to use twitter for teaching and learning through some of the steps- from getting started, to creating a learning networks- to using the tool more effectively- to using it as a classroom tool- to sharing resources- to embedding it your school website, LMS, or your blog- to managing it -to using it as an on demand assessment and feedback tool-to......

The (.....) parts is where the UN part of the un-workshop comes in. Even though I, and hopefully others, will be providing structure as far as making sure that everybody will be getting some of the basic information and providing learning objects and references along the way, this workshop will be dependent on the input, direction and needs of all who participate. I will also invite my learning network to interact, support and share best practices with you and I am sure we will ALL be able to add value and direction to this unworkshop. So if you are part of my amazing twitter PLN, please let me know if you will be able to mentor a few new teacher twits and get them to understand why we are a-twitter about twitter!
It will also entail some online ad hoc webinars (which will be hosted by Schoolnet) to help you connect and we even may want to meet face to face and have edu-tweetups all around the country?!!

The whole workshop will be run via Facebook ( and my blog ( for those without faces ;-). So, you can either RSVP as a comment on the event blogpost here, or on my Facebook events page.

Looking forward to interacting with you all! If you are a South African teacher please add #sateachers to your tweet. Our hashtag for this unworkshop is #ict4champions.

Saturday, October 15, 2011

Weekly maths bookmarks (weekly)

Posted from Diigo. The rest of my favorite links are here.

Tuesday, October 11, 2011

Great maths book review by Charles Smith

Book review by I have just bought a book at Exclusive Books which I would highly recommend for all Maths teachers. It's called Maths 1001 by Richard Elves. I covers "Absolutely everything you need to know about Mathematics in 1001 bite-sized explanations." It cost R221 but it is worth every cent. It's going to take a long time to get through it all but the presentation and the content make it something I'm going to want to jump into on a regular basis. The explanations cover topics from "Factors & Multiples" to "Game Theory" to "Combinatorics" and "Cryptography." Most explanations are completed in less than 20 lines.

A great source for interesting lesson starters or challenges for inquiring minds. If your school has a "reading" period then this is the ideal book.

Get it - if you love's worth it.

Here's a link to view the table of contents.

Monday, October 10, 2011

11 ideas for what and how to share for mathematics teachers

I came upon a request for teachers in our closed South Africam FET mathematics group to share local maths classroom resources. I have been on a personal mission to get teachers (especially maths and mathslit teachers) to share for donkie years so this request did create a flutter of excitement! I have found that despite our country being credited with the spirit of UBUNTU, it does not really happen down on the ground. There are the few sharing individuals that will always share and then there are the USERS. They want stuff, and they want it now, and please don't ask them to give anything in return. Most of the time they don't even bother saying thank you.

So this post is dedicated to the sharer bees...those who unselfishly share the fruit of their classrooms, their tests,exams, their lesson plans, and most of all- their wisdom, allowing us to look over their shoulders and learn from them- not only from their successes but also from their failures!! Bravo to your braveness!!

Which bring me to the whole thing of sharing. Quite a "complicated" concept. Firstly I want to  look at what we can  share.

When talking to teachers, their idea of the "what"is mostly restricted to actual sharing of set papers and tests. We are working under severe time pressure and have to get students to "pass" and "excel" as dictated by current assessment standards, which may or may not be of the highest standard. This make the sharing  of assessment items a priority in order to set tests, exams as well fast drill- and- practice kind of exercises. We do not even get to the sharing of useful inspiring articles and ideas that could support and underpin creating 21st a century problem solving, critical thinking breed of citizens. We do not look at sharing of materials to include sharing of wisdom, what- worked- and- did- not- in- my- classroom- stories. We do not share stuff that could help us develop  in our own lifelong learning pathways. We simply do  not have time. Then we wonder why we feel disenchanted, uninspired and isolated.

So if we look at the WHAT to share:
  • Lesson plans, work schedules, tests, exam papers, curriculum documents and briefs as not all teachers in districts always get it it. (the basics)
  • Teaching ideas (e.g. I am thinking of doing a twitter project with my students to harvest real time statistical data- any ideas?)
  • What works and what does not work in my classroom.
  • How I teach.
  • Internet articles of value (this is a great way to filter relevant knowledge for your colleagues and learning network)
  • Online simulations and interactive material that can be used on whiteboards.
  • New technology (ICT) tools (e.g. facebook, twitter, edmodo, animoto, google+, diigo...) and how you use them in your classroom.
  • Tutorials- learn something new that you can use in your classroom and for your won professional development.
  • News of professional development opportunities, events, conferences and seminars. (locally and globally, online and face to face)

How can we share.  (My bandwagon- hop on please)
  • If you want to share any of the above QUICKLY, twitter is your answer. Just add the URL (web address) to your tweet with a short what it is about (you have 140 characters to do so) and add a hashtag so that interested people can find it quickly. (e.g. #mathematics, #mathchat, #mathslit #sateachers). If we then search for #mathchat we can find "fresh" cutting edge resources. Example: See the #mathchat twitter stream!/search/%23mathchat
  • We need a database to store all these wonderful resources that we were talking about and here I want to scream DIIGO. This great tool allows you to, not only bookmark relevant resources, but have discussion about a resource, annotate resources, share it to twitter, create automated blog posts, embed automated feeds in your school's Learner Management System or website, create reading lists, and share with other interested colleagues or students in groups. It is also cross platform and you can access and share your bookmarks from any computer, operating system browser, cellphone, ipad or tablet. My mathematics sharing group is here:
  • File sharing tools. There are many to choose from, see my database here: My favourite file sharing tool is Dropbox as it gives you 2GB free to start off with (you can get extra GB's by getting your friends to join), fully integrates with your computer filing system and not only syncs all you files across all your devices but also syncs automatically with your colleagues' devices the moment you save a file in a shared folder on your device/PC . I have written a howto tutorial on how to get started with Dropbox that you can download from here:
So let's get going and start sharing!! If you are a maths teacher and want to start sharing with me and other maths sharer bees, please go and join my maths group here:

My local South African mathematics websites and resources can be found under the tag's Mathematics+sateachers here:

Photo credits:

Saturday, September 24, 2011

Tuesday, September 20, 2011

"I hate maths" seminar at Wits

The SA Numeracy Chair project at Wits School of Education, in collaboration with the Wits B Ed Concepts and Literacies in Mathematics course, is proud to host its inaugural: I Hate Maths seminar, presented by Professor Mike Askew, Claude-Leon Distinguished Scholar, Monash University, Melbourne.
Professor Askew will introduce some of the issues relating to primary teacher mathematics content knowledge and pedagogy in the international landscape. The central part of the session is focused on the presentation, working through and discussion of some mathematics problems with the audience – problems based on primary mathematics concepts which require some thinking, representing and explaining – all critical features of the 'connected' repertoire of understanding and skills needed for good primary mathematics teaching.

The aim of the seminar is, in particular, to attract an audience of primary teachers and parents, as well as primary teacher educators and other academics – many of whom freely express the 'I hate mathematics' sentiment, to engage in some fun and communal problem solving and discussion! And hopefully to leave the seminar entertaining the possibility that you do not maybe need to hate maths as much as you might have thought! Bring pencil, paper and willingness to engage!
Date: Wednesday 2nd November
Time: 15:00 for 15:30-17:30
Venue: Staff Lounge
RSVP for catering purposes: Nomonde Mda: (011) 717 3412

Saturday, September 17, 2011

Weekly maths bookmarks (weekly)

Posted from Diigo. The rest of my favorite links are here.

Saturday, September 10, 2011

Saturday, August 27, 2011

Weekly maths bookmarks (weekly)

Posted from Diigo. The rest of my favorite links are here.

Saturday, August 20, 2011

Weekly maths bookmarks (weekly)

Posted from Diigo. The rest of my favorite links are here.

Saturday, July 30, 2011

Weekly maths bookmarks (weekly)

Posted from Diigo. The rest of my favorite links are here.

Saturday, July 23, 2011

Monday, July 18, 2011

Prof Michael's July 2011 Math e-Newsletter

Dear Colleagues & friends
Happy Madiba day, 18 July! Hope you all spent a little time in service to others in recognition of the great man. This newsletter is my own modest contribution.
My homepage at has been updated with the following new items:
1)      "Equi-angled cyclic and equilateral circumscribed polygons", PDF (2011)
2)      2010 "Reflections on Van Hiele" paper now available in Portuguese & Croatian
3)      mathematical/mathematics education quote
4)      mathematics/science cartoon.
My dynamic geometry sketches Link at has been updated with the following (new & revised) sketches:
             1) Fermat-Torricelli point generalizations (updated)
             2) Semi-regular angle-gons and side-gons (new)
             3) Some parallelo-hexagon areas (updated)
             4) Some unproved conjectures (updated)
and the Student Explorations section  with:
             1) Collinear conjecture (new)
             2) Gielis Super-shape formula (new)
             3) Napoleon variation problem (new)
             4) Paul Yiu's problem and a generalization (new)
             5) Varsity Readiness Test (new)
Please REFRESH pages if they don't load properly the first time.
Tinkerplots 2, the innovative data handling software for younger learners (and quite adequate for Math Literacy in the South African Curriculum) not only has some great new features, but is now available as a download. Hence, it is available at a lower cost than before, e.g. currently at about R150 for a student license and about R370 for a Single User (and even lower for bulk orders). For more information and to download a free demo go to Please contact for more information and to order.
The books below might be valuable additions to add to your university, school or personal libraries.
a) Exploring Number and Operations in Grades 3–5 with Sketchpad 5
b) Exploring Geometry and Measurement in Grades 3–5 with Sketchpad 5
c) Exploring Ratio, Proportion, and Probability in Grades 6–8 with Sketchpad 5
(For more info about the above 3 books or to order please contact )
d) The Preparation of Teachers of Mathematics: Considerations and Challenges, download FREE PDF from
e) Statistics for People Who (Think they) Hate Statistics, 2nd Edition Excel 2007 Edition by Neil J Salkind from University of Kansas, SAGE publishers. 2010.
f) Sweet Reason: A field guide to modern logic. 1995, By Thomas Tymoczko, James M. Henle. (For more info or to order please )
g) AMESA (Assoc. Math. Ed. of South Africa) Congress 2011 Proceedings are now available online at )
a) Useful free book for Math Competition & Olympiad Enthusiasts on "Elementary Number Theory" at 
b) View a video clip or read the transcript of Conrad Wolfram's 2010 talk "Stop teaching calculating; start teaching math" at
c) Free Interactive Math Crossword Puzzles Online at 
d) PROJECT MATHEMATICS by Tom Apostel at has several wonderful short video clips on topics for classroom use such as Similarity, Pythagoras, Pi, Sine and Cosine, History of Math, Polynomials, etc.
e) SAGE- Viable free open source alternative to Magma, Maple, Mathematica, and Matlab Sage is free open source math software that supports research and teaching in algebra, geometry, calculus, elementary to very advanced number theory, cryptography, numerical computation, commutative algebra, group theory, combinatorics, graph theory, and exact linear algebra. Download for Win, Linux and Mac at 
f) The Community for Undergraduate Learning in the Mathematical Sciences Newsletter is available online 
g) International lists of Mathematics Educations journals are available at and 
h) Download a number  of great articles for free from NCTM's three journals, "Teaching Children Mathematics", "Mathematics Teaching in the Middle School" and "Mathematics Teacher" at
i) Curriki is an online environment created to support the development and free distribution of world-class educational materials to anyone who  needs them. It is a great place to find and post classroom activities and course curriculum. Go to
j) A list of articles and their abstracts from the Far East Journal of Mathematical Education, May 2011, is available at
a) BRIDGES 2011 Conference: Connections between Mathematics, Music, Art, Architecture, Culture, Univ of Coimbra, Portugal, July 27-31, 2011. URL:
b) 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
c) 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.
d) 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.
e) 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.
f) 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:
g) 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:
h) 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
i) 1st Computer-Based Math Education Summit. Organised by in association with Wolfram Research at The Royal Institution, London, 10-11 November 2011. Visit:
j) 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
k) 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
l) 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
m) The didactics of mathematics: approaches and issues. International colloquium in honour of Michele Artigue (Professor UniversitŽ Paris Diderot, ex-president of ICMI), Paris 31 May Р2 June 2012. First Announcement with a description of Scientific Activities of Plenary Lectures, Panels, Workshops, Poster Session is available in French, English and Spanish at
n) 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.
"Moreover, there is a growing consensus that human minds are fundamentally not very good at mathematics, and must be trained ... Given this fact, the computer can be seen as a perfect complement to humans - we can intuit but not reliably calculate or manipulate; computers are not yet very good at intuition, but are great at calculations and manipulations."        – Dave Baily in e-mail discussion with experimental mathematician Jonathan Borwein (during 2010)
"The art is not in the 'truth' but in the explanation, the argument. It is the argument itself which gives the truth its context, and determines what is really being said and meant. Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity— to pose their own problems, make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs — you deny them mathematics itself. "    - Paul Lockhart in A Mathematician's Lament
"Often the key to answering a mathematical riddle is not to focus on fine details, but to look at broad details. Less can mean more. When it works, this trick is spectacular ..." - Ian Stewart in Taming the Infinite, Quercus Publishing, 2008, p. 236.
Martin's Law of Committees: "A committee is a group of people who, individually, can do nothing, but collectively can meet and decide that nothing can be done."
"Photons have mass? I didn't even know they were Catholic." - Woody Allen
A wife asks her husband, "Could you please go shopping for me and buy one carton of milk, and if they have eggs, get 6." A short time later the husband comes back with 6 cartons of milk. The wife asks him, "Why the hell did you buy 6 cartons of milk?" He replied, "They had eggs."
Solve the problem at: 
(Use a free, Java enabled web browser like Firefox or Safari or download & install Java for Internet Explorer).
I'm always grateful for any feedback I receive. Humberto Bortolossi from Brazil kindly wrote to point out that
the video clip mentioned in the previous e-newsletter "Fibonacci Numbers - The Fingerprint of God" at has some popular misconceptions.
The following article by George Markowsky. "Misconceptions About The Golden Ratio". College Mathematics Journal, vol. 23, n. 1, pp. 2-19, 1992 at discusses this and other misconceptions.
Humberto has also implemented a Java Applet (in Portuguese) where it's possible to experiment and to see that the shape of the nautilus shell is actually not well described by a golden spiral as often popularly claimed:
Geometrically yours
"With the aid of dynamic geometry, my ability to discover new conjectures exceeds the available time to prove them and sometimes even my mathematical background and ability."

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

Saturday, July 16, 2011

Weekly maths bookmarks (weekly)

Posted from Diigo. The rest of my favorite links are here.