One example was probability. We started this unit playing lots of games of chance - using dice, spinners, coins and so on. I wanted the students to really get into the topic before we started to delve into the maths. During these classes we talked about what makes a fair game, and we also talked about the concept of theoretical and experimental probability. In pairs, students then had to design a game that could be played by students throughout the primary school. They had to make sure that the game was fair, and also that they knew what the chances were of winning. We set up our "Chance Encounters" game fair in the foyer of the school and classes booked to come and play the game. The students recorded how many played the game and how many times the students won the game, and then back in class again they looked at their games and tried to work out why the experimental probability did or did not match with what the maths would have predicted. You can see some more examples of the games students designed here.
Another time, along with reading the story of Gulliver's Travels, we looked at scale. Students made artefacts to scale based on the various lands where Gulliver found himself, for example in Lilliput where the people were only 6 inches tall, and in Brobdingnag where the people were giants. What would a stamp look like in Brobdingnag, for example, or a fork in Lilliput? During this same unit we also made some scale models of the school and we went on to use geometry to look at designing buildings around the world (click here to see student examples). We called this unit Designing Spaces and it involved visualizing, planning and building. Students used geometry to analyse buildings from around the world, to design and build their own house models, and to create plans for their designs. Rather than studying mathematics, the students became mathematicians, engaging in a form of mathematical thinking that is applied in all societies to design living spaces to meet people's needs and to make sense of the physical environment.
In both the above examples the students were engaged in various tasks that would develop a mathematical mindset - they learned about the true nature of mathematics in a practical real-world way. And they were excited! Jo Boaler writes, "Interestingly I found that mathematics excitement looks exactly the same for struggling 11 year olds, as it does for high flying students in top universities - it combines curiosity, connection making, challenge, and creativity and usually involves collaboration. These for me are the 5Cs of mathematics engagement."
It has been fun today for me to look back at these student projects from 1998 (almost 20 years ago - wow!) and to reflect on how all those years ago, before we'd even heard of Jo Boaler, my students were engaged in inquiry in maths and were certainly excited to use the 5Cs of mathematical thinking in their learning.