8 Way Maths
There is a shift we need to make in the teaching of maths in Indigenous contexts. It is quite simply this:
Rather than trying to bring out the culture in maths, we need to bring out the maths in culture.
We also need to shift our understanding of what culture is for the purposes of education. Material culture (i.e. didgeridoos, dot painting, dance, bush tucker) is very important, but arguably is the least productive aspect of our culture to include in curricula.
The more productive side of culture is the intangible, the unseen, the previously unexamined. We're talking about the genuine lived reality of our students here. You might find this side by examining the following questions in the community, questions which actually pertain to the students' authentic home cultures as they impact on the learning of maths:
- What is their attitude towards money?
- What do they believe about luck and chance?
- What kinds of patterns do they habitually respond to in the world around them?
- What substitutions and abstract symbols or ideas do they use? (e.g. this stands for that).
- How do they customarily make predictions and estimations?
- How do they compare things and assign value?
- How do they classify and categorise objects, people, and places?
- What are their strategies for memorising? Solving problems and dilemmas?
- Do they ever have to concentrate on two things at once? What is their technique for doing this?
- How do they divide and distribute resources amongst family members?
- What kinds of instructions are they used to following? Oral or print? Single- or multi-step?
While we are questioning the accepted orthodoxies on cultural inclusion, we may as well also be questioning the orthodoxies of maths teaching. For example, it is widely accepted that the process of learning maths is vertical, meaning you have to learn "a" before you can understand "b" and so on. Is this really true, or is it possible for maths to be approached as a non-sequential, integrated, connected, learner-directed body of knowledge explored through authentic projects and tasks?
We know teachers who have improved Indigenous maths outcomes teaching this way. Do you?
Working with Fibonacci sequences and spirals is a good example of how to teach basic maths using Land Links, Symbols and Images, etc.
There is a lot of potential here for hands-on learning (non-verbal) - students making spirals, measuring and drawing etc. Land Links are also strong here, as students can work with plants and natural phenomena, biology and even measuring the dimensions of their own bodies. Working this way is approaching maths indirectly (non-linear) through other knowledge domains like science, music and art. The links to art (golden ratio) in this topic, as well as the visual aspects of drawing diagrams and the Fibonacci spiral, offer easy links to visual learning approaches (Symbols/Images). Working from the spiral mapped on the Fibonacci squares, students have an holisitic image to refer back to when working with number sequences and simple equations - they can see and anticipate where the sequences are going (Deconstruct/Reconstruct). A unit on Fibonacci can cover sequences, equations, geometry, decimals, multiplication, division, measurement, etc. As such, it could be the organising focus for a whole term of work, or even just a recurring theme that a teacher can refer to throughout the year. This theme can inform community-based projects like gardens, murals, etc.
But why stop at basic maths? Why not raise the bar and do some "ideal gas equations"? Aboriginal knowledge can be explored at the highest levels of education - it is not limited to primary school students. Culture is good for more than just colouring in some boomerangs on a counting drill worksheet. Why not apply advanced maths to the study of aerodynamics in the flight of boomerangs?
If that's a bit too scary for now, then try these everyday perspectives to introduce through your pedagogy:
Have a yarn-up about times when you've used maths to solve real problems in your life. Highlight the importance of yarning as a way of creating and passing on knowledge in Aboriginal culture.
Use pictorial graphs to make learning maps showing student progress and desired outcomes. Explain that visualising plans and pathways is an important part of Aboriginal culture.
Do hands-on problem-solving activities and allow time for reflection. Explore unspoken values and ethical issues in content. Explain that learning without words by using your hands, thinking deeply and finding unspoken meanings are all central to Aboriginal culture.
Use visuals and create symbols to help students understand and remember content. Promote this as an Aboriginal form of communication.
If you have to measure something, why not measure natural objects from the local landscape? Highlight Aboriginal connection to Country.
Apply mathematical knowledge to unrelated/unexpected domains and contexts. Set problems with multiple creative solutions. Celebrate this kind of creative and adaptive thinking as the reason for Aboriginal culture being the longest surviving culture on the planet.
Model every activity for students, promoting an Aboriginal protocol of "Watch first, then do".
Relate problems and maths applications back to community life wherever possible. Where a community equivalent does not exist for content you are teaching, discuss ways in which the new knowledge could be applied for community benefit. Create outlets and projects for students to teach/apply important mathematical knowledge to the community.