Some of our big questions for this working group!

Here are some of the big questions we want to address in our working group. We'll refer back to these

throughout our three days together:

1. How to integrate outdoor, embodied, sensory experiences with more typical mathematical work (writing, diagramming, symbolizing, calculating, etc.)?
   
   Some starting ideas: Connecting representations in ways that promote inquiry through both embodied and symbolic ways. Moving between representations in an
   
   
   
   
   
   oscillation or transdisciplinary way (weaving to poetry to mathematical diagram to group theory and back to weaving…)
   
   
2. How to help people re-story mathematics – tell themselves new and more inviting, more generative, more helpful stories about what mathematics is and how they might engage with it, through the natural living world, through the arts, through sciences?
   
   Some starting ideas: Mathematics outdoors in the living world as a way to move beyond fear/
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   rejection of school mathematics that many people experience. Can we get away from the stereotype of math as super-nerdishly precise, obsessive with precise measurement and calculation? (These are a small part of math but not necessarily what we love about math.) Math as patterns and their behaviours based on experiences of the world. 
   
   
3. How does observation in and with the living world inform mathematical ways of knowing?
   
   Some starting ideas: How can we observe and interact with the living world in ways that connect to mathematical observation? Mathematics as about careful observation in a way that leads to questions. (Aspects of observation in a mathematical way? → angle, line, shapes, distance, connectivity, chirality, concavity/ qualitative aspects of geometry, number, repeating or non-repeating patterns, transformations of figures or patterns; planes, surfaces, gradients, like exploring the ground in certain ways; curves, slopes, contours/ contour diagrams as in geography and 3D math; mappings of places and other things; space-filling curves, shortest or other optimal paths, optimization, relationships of operations on elements, how slight initial changes have large repercussions (chaos theory,...)
   
   Blueberry picking analogy, or koalas and kangaroos anecdote: you can see things once you are alerted or aware of them – a mathematical ‘lens’ or hearing. How are you introduced to things, so that you can build awareness and start to see, hear, smell, notice things in a new way? “Math is everywhere” iff you know how to notice it! You have to know a bit about it to be able to notice it!
   
   With these outdoor, embodied and less conventional math activities, you are learning how to see and notice and be aware of mathematical things and relationships. It takes some orientation (from a more experienced mentor, sometimes) and then patience and thoughtfulness. This is where students can become experts too. There can be a sense of mutual learning.
   
   
4. How to integrate mathematical learning with Indigenous ways of learning, knowing, caring for and living in good relationship, knowing that we are part of the greater-than-human world?
   
   Some starting ideas: What potential harm does mathematics bring to the living ecologies of our world through separation of “us” humans from everyone and everything else that we mutually depend upon for our lives? What is gained and what is lost from that kind of separation? Is it possible to appreciate and promote the wisdom that worldwide mathematical traditions bring, while also feeling and valuing respectful and reciprocal relationships with ‘our grandfathers, the rocks, and our grandmothers, the plants’, as well as all the other beings here? How can mathematics educators learn and connect with Indigenous colleagues and teachings to begin to find ways to move forward together?
   
   
   
   
5. How to generate mathematics/ mathematical understandings through mathematics outdoors?
   
   Some starting ideas: Justin Dimmel: The sun produces perfectly parallel rays – nature generates mathematical objects that we can work with in so many ways! The sun brings life and warmth and also brings geometry. What about trees – what do they offer and gift us? What kind of logic and math is embedded in it?We are not applying mathematics to something (like estimating number of trees in the forest for data, etc.); we are generating mathematics in different ways. We can listen to the pattern of the wind in the trees. This is transdisciplinary work. Math is also about naming and classifying: so if you have certain sounds, can you classify how you discern them? New Yorker article: training AI to listen to the language of sperm whales to learn what the whales are saying by making some sort of classification of sounds. (Example, Beaufort wind speed scale: flag is hanging down, or is flapping gently, or is making a lot of noise and flapping hard – each corresponds to a different wind speed) Is there something like a Beaufort scale that helps us recognize, name and work with other observations of the world in mathematical ways? Ex: qualitative observation of what happens to umbrellas or ocean wave → 40 km/h winds. Observing different hues of green in Lake Ontario in different seasons and winds – what can you start to recognize with experience? In Charleston, the Gulla people of the Carolinas make and sell sweetgrass baskets: how do you classify different turns and different angles in the basket making? There is specialized vocabulary and ways of noticing… how do we connect this with mathematical ways of thinking?
   
   
6. a) How to understand the intrinsic interweaving of movement (rather than only static images) with mathematical patterning and mathematical interpretations? 
   
   b) How to have experiences in the outdoors that let us read backwards from the sensory gestalt phenomena to know what we might be looking at, smelling, hearing, tasting, touching?
   
   Some starting ideas: From Gerofsky & Milner sprang paper: “In a sense, a weaving is a record of movement, of certain actions and interactions, just as certain graphs are records of movements or actions. In the braid theory sense, a completed sprang weaving is a record of crossings, of chiral permutations; it is the composition of each enacted crossing that defines a particular sprang weaving. However, it requires a certain familiarity, initiation, or skill with weaving to look at a finished product and have a strong idea of how it was made or how another could be made. As we weave sprang individually and collectively, we experience and enact in real time the composition of simple braids which together form the sprang weaving. We develop the capacity to look at a finished weaving and imagine the crossings which make it possible, reading backwards from the result.”
   
   Partly mathematical (abstract) ideas but also sensory, holistic embodied experiences. Developing intuition through experiences – Ex.: Dr. Tom Banchoff who worked with hypercubes and 4D objects so much that he developed intuitions about them.
   
   
7. What are the qualitative differences between learning mathematics in a classroom and in the forest, garden, riverbank or other outdoor living places?
   
   Some starting ideas: Affective aspects and emotional aspects: Nature experiences come with all sorts of feelings: discovery, awe, excitement, familiarity, peacefulness, calm, feeling that we ARE part of the living natural world, not separated from it.