What Is The Logo?

Can there be a more European task than the one titled Sphinx? It derives from the puzzle area of mathematics. These types of puzzles were prominent in the late nineteenth century when many people had sufficient spare time to use mathematics as a recreation. Its title refers to classic Western history, which is sometimes misrepresented as the history of the human race, thereby potentially demeaning other much older and longer surviving cultures.

Students are given four wooden pieces shaped like this:

As it stands the task is a spatial challenge of moderate difficulty. At the teaching day which initiated this project, two Year 5 Aboriginal and Torres Strait Islander students, Tyler and Michael from Norris Road school, accepted the challenge. They solved it quickly, but then, since all Mathematics Task Centre Project tasks represent the tip of an iceberg, they were challenged to investigate further.

The solution of the task card problem shows that the base, height and side lengths of the new Sphinx are twice as long as the corresponding lengths in a single Sphinx shape. The boys' teacher pointed this out and asked them to relate this '2 times' information to the fact that the new Sphinx was made of four original ones.

Suppose we made the base as long as three original Sphinx shapes. If you could make a new, larger Sphinx how many original Sphinx shapes do you think you would need? If the '3 times' Sphinx could be made, would all the side lengths be three times longer than the original?

The boys now had a new challenge, made all the more difficult by the fact that only four wooden shapes were available. Their teacher did not know the answer and, at this stage, did not even know if was possible to solve this extension of the problem.

The students found a large sheet of paper and set about tracing. This can be a frustrating approach because, once traced, the drawing can't be picked up and rotated or reflected like the wooden piece can. But they persevered. In fact they stuck at the task for about 45 minutes and were still trying when time ran out.

This teaching day was held at a central location and included students from several schools. Michael and Tyler had to return to their own school. They chose to take their incomplete work with them.

Weeks later their solution to this quite difficult task was delivered to the project organisers. Their solution can be found at this link, but to appreciate the boys' effort, the reader should first try the original puzzle and then this extension - for several days!

Significantly the boys had claimed their solution by superimposing a drawing of the Aboriginal flag on their nine piece solution as in the logo. This act of leadership stands as testimony to:

• positive personal qualities such as interest, perseverance and tenacity
• command of mathematical content - in this case pattern, spatial and measurement concepts and skills
• a high level of mathematical reasoning
• a sense of community

It also points the way for other students and teachers to explore further. For example:

• Is the boys' solution the only '3 times' solution?
• If there is a '2 times' solution and a '3 times' solution, could there be a '4 times' solution (easy) or a '5 times' solution?

Can there be a more appropriate logo for this project which aims to support Aboriginal and Torres Strait learners who are taking on the challenge of western mathematics?