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.
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 3 ... Doug's Tablecloth
The problem appears simple. Fold the given piece of cloth to fit exactly into the depth of the given 'drawer' pictured on the card. However, partly because of most people's pre-disposition to fold things in half, the problem is more challenging than it first appears. Measurements and other information are provided to encourage thinking the problem through at a deeper level.
Materials
A piece of cloth 36cm (exactly) x 72cm (approximately) to fit the drawer pictured on the card.
Content
Spatial perception, counting, number facts, division, length measurement, whole and parts, fractions
A Special HistoryThis problem began with a real cloth that would not fit back into the real drawer it had come from after first being used for a dinner party. Sally Farr, who had come from Queensland to investigate the use of tasks with Indigenous students was present as Doug tried - unsuccessfully - to refold the cloth to fit. She suggested there could be a task in this problem ... and she was right.
Later, towards the end of the 1990s, Per Berggren, a well-known and respected teacher in Sweden purchased Doug's Tablecloth to add to his school's collection of tasks (mattegömmor). He was so puzzled by it that he eventually flew to Australia to try it with the actual drawer and actual cloth which had first generated the problem at Doug's house.
As you can see, it was no less puzzling 'in the flesh', but perseverance won out in the end.
Iceberg
A task the tip of a learning iceberg. There is always more to a task than what is recorded on the card.
The strategy of working backwards plays a big part in this task:
- You can solve the problem by trial and improve and then look back and ask What could I have learnt from the numbers in the problem?.
- You can work backwards from the given numbers to solve the problem in the first place.
- As in the second part of the task, you can work backwards from the solution to decide the exact measurement of the other side of the cloth which would allow it to fit into both the depth and width of the drawer.
- How will you fold a piece of paper so that the rows represent halves and the columns represent thirds?
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.
To convert this task to a whole class investigation each pair (or student) will need a cloth the correct size. Perhaps a parent, or the craft faculty, could cut sufficient pieces. This only has to be done once if the pieces are stored after each use. Some schools use filing boxes made from recycled cardboard to store class sets of task materials. This is an efficient use of preparation time - one preparation, multiple uses. In the future, when teachers reach the part of the curriculum document that requires a whole class investigation of a task, they simply select the appropriate box from the shelf and everything is there.
Some teachers have thought of using paper instead of cloth for Doug's Tablecloth, but there is a lot of experimental folding done before the problem is solved, and paper holds its creases. Consequently, paper becomes confusing. In the long run material also retains creases, but it can easily be ironed flat again after a few uses.
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.
Doug's Tablecloth is an integral part of:
- MWA Number & Computation Years 5 & 6
- MWA Number & Computation Years 7 & 8
If so you missed information about:
- Our new Big Picture link.
- Notes about the success of our Refresh Your Task Centre service.
- A thought about using Raeco Hangbags for storage.
- An idea about sharing professional development and raising faculty funds.
- Notes from an Inspector's Notebook.
- Notification of a task-related article by Neville de Mestre in the Australian Mathematics Teacher.
