Significant episodes

Planning authentic and meaningful learning acknowledges that learning isn’t always predictable and by using a clear framework it allows for connections between Maths and the real world of Aboriginal and Torres Strait Islander learners. 

Below is an excerpt from the significant episode 'Moment in maths' by Iain Hand, Alberton Primary School in authentic and meaningful learning on teaching fractions. Iain has applied the process of contexutalisation and mathematisation as outlined in the framework - see diagram immediately below -  the Cluster developed.

Diagram: The Alberton Cluster model of mathematisation and contextualisation (Thornton, Statton & Mountzouris, 2012).

...I have always taught fractions using oranges or pizzas (you know what I mean). This year it was through the perfect face. Artists use rules to draw faces. Once you know these rules you can draw any kind of face and it will look like a face, not like 'some sort of alien' (Karl – Maths Student). It involves fractions, half way down the head you place the eyes, halfway between the eyes and the chin you place the nose, a quarter of the way between the nose and the chin you place the mouth.

This information was given to the class verbally and visually. There were lines drawn to show position and the symbols to indicate half and quarter. The students were engaged; they loved the fact that their portraits actually looked like faces. They were proud of their pictures.

The next part of the project was for the students to draw a self portrait. They were given pictures of themselves and the idea was for them to apply the rules they had learnt about drawing faces to their self portraits. It was at this point that the questions began and learning took off.

After drawing an oval for his face and dividing the face in half both horizontally and vertically, he asked me what the symbol for half meant on the board. I went about explaining the concept using pictures, he understood but then asked what would happen if you had more than two pieces. Another two students, Janelle and James, joined in the discussion about halves and quarters, talking about cutting things into four bits and taking one bit and what would you have. They both showed him one quarter which he understood but then corrected them by adding that I had one quarter and he had three bits left. I asked him what that would this look like and he showed me. The other two students exclaimed, 'Oh Yeah!", almost like they had also just got the concept. It was an ah ha moment...