Many senior mathematics teachers will remember workshops throughout Australia in the 70s and 80s led by well-known Scottish educator Geoff Giles. Younger teachers may not realise it, but the best quality teaching practice you have seen in others, or applied yourself, owes a major debt to Geoff's work. His influence also extended from Scotland to England, Canada, USA and elsewhere.
Geoff Giles died in Scotland on August 4th. The Task Centre Project is conscious of losing a valued friend and extends a blessing of peace to his wife, Bet Sampson, and his family.
Geoff's work was introduced to the MAV through a conference around 1974 on Recent Trends in British Mathematics Education. A few years later he was invited to be Keynote Speaker at the 1978 AAMT conference in Melbourne. The paper he prepared for that address is recorded in Learning & Applying Mathematics, papers of the 7th Biennial Conference of the Australian Association of Mathematics Teachers. But these are words and, as such, a poor image of the spirit of a man who loved kids, loved mathematics, loved connecting kids and mathematics ... and demonstrated a significant degree of flexibility dancing a Scottish jig on the table at the conference dinner.
Geoff was passionate about all students having access to, and ownership of, mathematics. His creative, sometimes fiendish, mind developed scores of materials within the Fife Mathematics Project and, later, DIME Projects to support concrete, self-directed learning. His 1978 paper contains several examples, including an exploration of the transformation of shapes in a concrete hands-on situation which leads to the idea of, and need for, that most esoteric of secondary school mathematics concepts, Imaginary Numbers.
In partnership with Bet, Geoff took the Task Centre project under his wing in 1993 and became the British base for its work. He contributed many of his ideas and materials to the Project and his endowment will live on every time your students use Algebra Through Geometry, Octaflex, Tricubes, Angle Estimation, Rectangle Nightmare, and a range of other Project tasks. As recently as last year, although in his 80s, Geoff wrote a paper for us exploring the depth of Rectangle Nightmare.
Sharing his expertise was all that Geoff ever wanted to do. In the closing paragraph of his 1978 paper, he invited us all, and now invites us anew, to continue this process:
If this miscellaneous collection of bits and pieces has convinced you that mathematics in school can be made more interesting, accessible and understandable I will be happy. Should it also motivate you to work with others on the improvement of mathematics education in the classroom then I will be delighted. But please don't keep your insights to yourself. Share them and let them multiply.
Have you noticed our new Big Picture link on the left. The Task Centre Home Base has grown to a little on the down side of huge. We often have reports from people who find our site valuable, and we hope this additional link will make it easier to see our site, services and products in summary.
Within the link there is also a PDF file (8 pages) which you are welcome to print and distribute to encourage interest in students learning to work like a mathematician in happy, healthy, cheerful, productive, inspiring classrooms.
There is great deal on this site to support teachers whose systems are moving towards an Essential Learning approach. In Victoria for example curriculum shift is towards the Victorian Essential Learning Standards (VELS) and many schools are noticing how consistent the Task Centre Project and its companion projects are with this direction.
In News for last month we mentioned the services of our Distribution Manager, Ina Koetsier, had been enlisted by Albion North Primary School to refresh their task centre. Well here she is providing the same service, and happy it doing it, for Mornington Secondary College.
Also in News for last month you learnt about the Saturday Workshop for Southern Cross Primary School, Canberra. Here Sue Whitney, who organised the day, and who will be managing the use of the task centre in the school, shows off their compact, portable, efficient storage system.
But Sue didn't have to do all that labelling work. In around twenty minutes of the workshop day the staff worked as a team to...
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Peter Barbarossa is the creative Head of Department of Mitchelton State High School, Queensland. He recently purchased a Working Mathematically Curriculum Pack to resource his staff. The choice was stimulated by the learning needs of their students and a desire to address the Queensland curriculum which emphasises Working Mathematically within an Essential Learning framework.
The WM Curriculum Pack is only sold with Professional Development. Peter took the opportunity to share the workshop with local schools and had 30 participants on the day. The surrounding schools were happy to pay for their teachers to attend. This financial contribution has left Peter with sufficient funding to provide post-workshop teacher release for his staff so they can 'strike while the iron is hot' to finalise the implementation of their resources.
Creative financing ... and everyone is happy.
Neville de Mestre, creator of the Task Centre concept writes a regular column in Australian Mathematics Teacher, a journal of the Australian Association of Mathematics Teachers. It is usually secondary schools which receive this journal, so look for it on your shelves. Neville's piece this month is titled Discovery: Hands-on Numbers. You will find it in Volume 61, #2, pp. 14-15.
You have met John Hibbs before (see April News below). He is a retired HMI (Her Majesty's Inspector) and lifelong learner and teacher through hands-on problem solving. This is his latest contribution to our site - a chance to make your own task(s).
I was reminded of the Glaeser's dominoes when Kath Cross (another retired inspector) introduced the problem below at a recent ATM workshop in Leicester.
CHESS BOARD PROBLEMSTake a chess board and a set of 32 dominoes, of matching size! It is relatively easy to see that the board can be completely covered by the dominoes. |
As a young teacher of mathematics I collected problems and kept them in what I called a commonplace book. I used this book as fill-ins: for kids who had finished, homework, starters, mains and the rest. It contained one of my all time favourite puzzles about dominoes but the book was lost. Many years later I found the puzzle on a poster at the then West London Institute of Higher Education. So the puzzle again found a place of honour in my inspector's notebook.
GLAESER'S DOMINOESGeorge Glaeser of Strasbourg put a set of dominoes, more or less randomly in a flat tray and took a photograph. The exposure was not correct, and although the numbers could be discerned, the positions of the dominoes could not.3 6 2 0 0 4 4 6 5 5 1 5 2 3 6 1 1 5 0 6 3 2 2 2 0 0 1 0 2 1 1 4 3 5 5 4 3 6 4 4 2 2 4 5 0 5 3 3 4 1 6 3 0 1 6 6 |
John Hibbs
19 July 2005
Stop wondering! Learning to work like a mathematician, rather than merely learning the skills of a mathematician does make a difference to student success and teacher satisfaction. Rachel Boyce, Crossways Lutheran School, Ceduna, South Australia adds another piece of evidence to support that fact in her recent contribution. You can find this short but important story in both the Do Tasks Work? link and the Indigenous Students link on the left.
Task 2 ... Cars In A Garage
Cars and garages are familiar to students of all ages. In this task the challenge is to find all the ways to park the cars in the garages.
- How many parking solutions are there?
- How do we know when we have found them all?
4 toy cars
Content
Counting, 1:1 correspondence, mathematical language of position and order, visual patterns, including patterns of colour, multiplication, multiplicative thinking, multiplication principle of counting, permutations & combinations, logical reasoning, problem posing and solving, recording mathematics
Iceberg
A task the tip of a learning iceberg. There is always more to a task than what is recorded on the card.
Possible iceberg investigations for this task are:
- What happens if we change the number of cars?
- What happens if we change the number of spaces?
- If I tell you any number of cars are parked in the same number of spaces can you tell me how many parking solutions there are?
- What happens if there are more spaces than cars?
- What happens if we make conditions on where particular cars can park?
As delivered tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.
The whole class lesson for this task is detailed in Maths300 Lesson 128, Cars in a Garage. This lesson also extends the investigation with software.
Is it in Maths With Attitude?
Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.
Cars In A Garage is an integral part of:
- MWA Pattern & Algebra Years 3 & 4
- MWA Space & Logic Years 9 &10
If so you missed information about:
- Notification of our face lift.
- A report on refreshing a Task Centre at Albion North Primary School.
- A reminder about July MOTM in Adelaide.
- A report on a Saturday workshop for Southern Cross Primary School.
- Price changes for a range of Support Resources.
