Week 3 Activity - Sketching

 For this activity, I worked from the window and used my Kindle Scribe to attempt my sketches (I wanted to try something different and I have my kindle with me for reading and taking notes, so it might be nice to also use it as a sketch pad)  I drew the mountain scene in front of me while watching cross-country skiers move along the trail (the groomer also went by, though I didn’t attempt to draw that). At the same time, an elementary or preschool class was out exploring in the nearby bush, leaving winding tracks through the snow. 

What stood out to me right away was the contrast between human-made and living things. The skis, poles, Fernie sign, and a nearby light pole were all defined by very straight, clean lines, clear examples of the grid at work. In contrast, the trees and mountains were irregular, curved, and organic. Even the ski trail itself was noticeably straight, especially when compared to the meandering paths left by the children and by deer moving through the snow.

As I spent more time watching and drawing, I began noticing other patterns. One type of pine tree had branches that angled upward, while another type had branches that were more horizontal or slightly down. At home,  I also sketched a spider plant in a woven basket. The basket had clear symmetry and repeated patterning in the macrame adornment, while the plant itself had a loose spiral shape, but it was imperfect. Some of the leaves damaged and one side is fuller where it leans toward the window. 

I finished by drawing the bark of a bull pine in my backyard. Up close, the bark is rough, uneven, and difficult to capture, but when I stepped back, an overall pattern began to emerge, it just isn't a tidy or predictable one. It made me think about entropy, and how living systems tend toward variation, irregularity, and change, especially as they respond to their environment. The differences I noticed, branches angling upward toward light, fuller growth on one side of the plant near the window, worn and weathered bark, all reflected how surroundings shape natural patterns over time rather than preserving perfect symmetry.

This activity made me think about how close observation and sketching could really support students in learning about patterns. Slowing down to draw forces you to actually notice whether a line is straight, curved, angled, or irregular, and to see how those features show up differently in living and human-made things. Students sketching branches, paths, or bark patterns and then talking about the kinds of angles they see, rather than only encountering angles through worksheets.  I think this could make lines and angles feel alive and connected to the world, not just something drawn perfectly on graph paper. 

Week 3 Reading - Dancing Teachers Into Being With a Garden

 In this article, Gerofsky and Ostertag explore how schooling is shaped by “the grid”, the rigid structures of time, space, curriculum, and control that organize so much of what happens in schools without us even realizing it. Instead of suggesting we abandon the grid altogether, they ask what it might look like to play with it, using metaphors like swing dancing and parkour to imagine teaching that moves within, around, and alongside these structures. Through stories from garden-based teacher education, they invite us to think about becoming teachers with the living world, not just teaching inside classrooms. 

First Stop:

What stood out to me right away was just how pervasive the grid really is. The authors move beyond the obvious physical grids of schooling, desks, classrooms, tile floors, to show how grids also shape schedules, grade books, report cards, and even how knowledge itself gets organized. They extend this further into the world beyond school, pointing to things like pixels on screens and colonial practices of mapping and staking land. As someone drawn to the sciences, I find comfort in this kind of order, classification and structure help make sense of complexity (like the periodic table), but I also notice how physical spaces matter. My main work space in Cranbrook is a windowless, 10 by 10 white box that used to be part of the boys’ change room, while a secondary shared space in Fernie overlooks a nature path and the mountains. In the white box, I notice myself feeling more stressed, tired, and anxious, its as if my thinking narrows along with the space. The office in Fernie, with light and views of the outdoors, invites a very different way of being, one that feels calmer, more open, and I feel like my ideas are more connected to the world beyond the walls. Unfortunately, this space is over an hour away, so I only get there once a week or so. 

Pictured below are my "white box office" and the view from my other space.

Second Stop:

There was a lot of imagery in the reading and the image that stayed with me was the idea of teachers trying to “tame students into their desks in a regular classroom.” I have definitely experienced this, and I recognize how easily the desk can turn into a tool for control rather than a support for learning. In my prior job, when I switched classes I moved from individual desks, where it was much easier to keep everyone separated, quiet, and “on task”, to lab tables, where students had to work with a partner(s). The room got louder, which did make me uneasy at first, but then I realized that more talk equaled more thinking and learning, and far more meaningful conversations than I ever saw when everyone was sitting silently in rows. The reading also reminded me of our first course with Tim and discussions on "who" created school and curriculum. Bringing in ideas from Tim’s class, the classroom grid described by the authors oreflects I–It relationships, where students are positioned, organized, and managed rather than encountered as I–Thou, as full, relational beings as discussed by Martin Burber. As well, thinking of another reading from that class,  Heidegger’s fourfold makes this even clearer: the classroom grid often separates students from earth (the sensory, material world), sky (light, weather, openness, time), mortals (our shared vulnerability and becoming), and divinities (meaning, wonder, and what calls us beyond efficiency). 

Notes on I-It vs I-Thou from last year

Question to continue the conversation:
I really appreciate how the authors don’t suggest getting rid of the grid, but instead learning how to move within and around it. I admit that I struggle with how to do that in my position (mainly working with teachers), but maybe I could encourage them to add in movement and music and outdoor etc... into their lessons and also find some lessons to model for them.

 In your own teaching context, what might dancing or parkouring through the gird look like for you?

 ** I unfortunately only have my notes from Tim's class and not the links to the articles we read on Burber and Heidegger. I did, however, read through these two articles to complement my notes

https://that-which.com/heidegger-the-fourfold/

https://www.awakin.org/v2/read/view.php?tid=2217&sso_checked=1

Week 2 - Activity Reflection

 This week’s Vi Hart videos brought back some memories for me. I used to watch and use her videos regularly when I taught Grade 7 math, and we did several art-based math activities inspired by her work in class. I am not sure why I never carried this approach as intentionally into my older classes. Watching her now, especially before reading Kepler, reminded me how powerful playful making and exploration can be in helping mathematical ideas come alive.

In the videos, Vi Hart takes something as unexpected as rocket candy and turns it into geometric shapes, explores hexaflexagons, and plays with symmetry in a way that feels accessible and makes me want to try as well. Before reading Kepler, I also cut open fruit to look for symmetry (side note - dragon fruit does not appear to show any symmetry internally) and I also built a couple of shapes including a  dodecahedron and an icosahedron. I have to admit that geometry, especially when it involves three-dimensional objects, has always been a stretch area for me in mathematics. Building the models helped me far more than reading a description ever could, and it made Kepler’s observations about shape, structure, and beauty much more tangible. I found myself wishing I had been able to find an actual piece of honeycomb for that section of the reading as well as that would have been helpful for me.

One of the reasons I think that 3-d shapes are an area I struggle with become clearer a few years ago. I read a tweet by John Green (see below) where he described discovering that he has aphantasia, a condition where a person cannot form mental images. He expressed surprise that other people can actually see images in their minds. Reading that was a moment of recognition for me. I also do not see clear pictures in my mind’s eye. When shapes, structures, or even directions are described verbally or in writing, I am not visualizing them internally. I need to rely on external representations, either models or maps/diagrams. This made the hands-on work this week especially meaningful for me. Building models, manipulating materials, and physically exploring symmetry helped me understand Kepler’s ideas in ways that text alone could not. (See the picture for the different levels that people can visualize in their minds eye - I fall around a 4.)

One thing I often tell my students is that I like how in England they use the word “maths” to describe math. There are many kinds of mathematics, and it is okay to like some parts more than others. In my Grade 8 class, I see this clearly when we work with isometric dot paper and three-dimensional drawings. I struggle to even demonstrate how to use the paper, yet some students shine, often those who struggle in more symbolic areas like algebra. For them, the visual and artistic aspects of mathematics become a strength rather than a barrier.

Connecting all of this back to this week’s guiding question, I am reminded that multisensory mathematics is not only about supporting students with identified sensory impairments. It is about recognizing the wide diversity in how people perceive, process, and make sense of mathematical ideas. Designing learning experiences that include building, touching, seeing, hearing, and moving does not simplify the mathematics. Instead, it opens multiple pathways into understanding, allowing more learners to access ideas that might otherwise remain abstract or out of reach.

Reading Post #2 - Kepler

 In On the Six-Cornered Snowflake, Kepler reflects on the repeated appearance of hexagonal forms in nature, including snowflakes, honeycombs, and pomegranates. He wonders why these shapes appear so consistently and considers whether they arise from an inherent form, from the dictates of the material itself, or from an external cause, possibly divine. Throughout the text, Kepler connects mathematical structure with beauty, design, and order in the natural world.

My first stop in reading this text, also prompted by one of Vi Hart’s videos, was the realization that snowflakes always have six corners. I am not sure I knew this at some point in life, but I definitely did not remember it. Kepler’s questioning about whether nature follows an archetype of beauty or divine purpose immediately sent me to my chemistry background and to molecules with fixed symmetries, such as benzene, as well as to the special properties of water that make life possible here on Earth. Water molecules are polar and have a bent shape, which means they form hydrogen bonds at specific angles when they freeze. As these molecules lock together, they arrange themselves into a hexagonal crystal lattice, creating a structure with six directions of growth. I looked up what we now know about snowflake structure, and we now understand that the six arms of a snowflake come from this underlying molecular arrangement. The fine details and branching come from environmental conditions like temperature and humidity as the crystal grows. In this case, the six-ness of the snowflake seems clearly dictated by the material itself.

My second stop was the honeycomb. When I think about how well everything comes together in this structure, it is hard not to feel a sense of awe. The hexagonal cells allow bees to face outward for movement and safety, share walls so less material is needed, and maximize the volume available for storing honey. Without performing calculations, bees construct a design that appears incredibly efficient and elegant. I find myself wondering whether, even with our advances in mathematics, technology, and computational modeling, we would be able to design something that works better? I can see why Kepler pauses to consider the possibility of divine influence here. I also wonder whether all bee species around the world build similar honeycombs, or whether there are variations where this hexagonal form does not appear.

This Week’s Question

I find myself admiring Kepler’s ability to look closely at the natural world, notice mathematical structure, and hold onto a sense of curiosity and beauty long enough to investigate it. It feels like children do this naturally, noticing patterns and shapes in the world around them, but many of us seem to lose this way of seeing over time. I know I have.

My question is: Do you think maintaining, or reclaiming, this sense of wonder is an important part of our work in education, especially in how we invite students to experience mathematics? Do you feel that you still have this sense of wonder yourself and if not, how can we as adults get it back?

Blog Post 2 - Week 1: Measuring With My Body (and Buying a Couch)

 

For this activity, we were asked to explore ancient, body-based ways of measuring by first calibrating our own bodies and then using those measurements to plan something practical. I started by calibrating my own “body units,” and while I was fairly close on most of the traditional measures, I quickly noticed a pattern. I was short on almost everything - not surprising given that these systems were often based on the bodies of adult men. One thing that really stood out to me was my hands. I’ve always known my hands were small for my height, and this activity confirmed it. Anything involving finger length or hand spans was noticeably off, while hand width was surprisingly accurate.

For my measuring project, I decided to focus on our family room. Our couches are very much on their last legs, and we’ve started talking seriously about replacing them. Right now, we have a couch, a loveseat, and a chair (see pictures), but we’ve been considering switching to a sectional recliner with the same chair. Using my body-based measurements, I sketched out the walls of the room and the current layout, then started experimenting with what might realistically fit in the space (see drawings).

As a family, we talked about how we actually use the room, what we want in a new couch, and what would realistically work in the space. From there, we did some research, looking at two local furniture stores in our small town and then Costco (since they deliver). We narrowed it down to three possible options and found their dimensions to see if they would work (see sketches).

One small moment from the activity stuck with me. Measuring a yard using my arm, from fingers to nose, brought back a clear memory of my mom measuring fabric the same way, pulling it out to the tips of her fingers, folding it back, and continuing on. I didn't realize that she was actually estimating yardage at the time.  Watching Roger Antonsen’s talk reminded me of the fact that math shows up in all aspects of life, it is a human activity. He talks about math not just as numbers and formulas, but as a deeply imaginative, creative way of seeing patterns in the world, almost like an art form that helps us make sense of what’s around us.

Reading Post 1 - Seeing the graph vs being the graph

This article  (Gerofsky (2011). Seeing the graph and being the graph, pp. 245-256.) looks at how gesture and movement play a role in how students understand graphs. Drawing on classroom research, the author shows that students who use more whole-body gestures tend to notice more important features of graphs. The big idea is that being the graph, not just looking at it, can support deeper understanding and engagement. 

My first stop came before I even got into the assigned article, in the discussion of Plato and Descartes and their influence on how we think about mathematics. What made me pause was how we are still fighting against their thinking. The idea that “real” math lives in the abstract, separate from the body. I have been working hard this year on the idea of building understanding around the Concrete-Pictorial-Symbolic method in my role as a numeracy support teacher. I am finding that teachers are reluctant to use manipulatives past the primary grades. Realizing how far back this mind–body split goes was frustrating, but also kind of reassuring. It helped me see that the resistance I run into is deeply rooted in beliefs around what counts as mathematical thinking.

My second stop came from the reading on gesturing in math class. I was surprised to realize that I don’t consciously use gestures when teaching graphs. When I tried to picture myself explaining one, I honestly couldn’t remember doing much beyond pointing at graphs already on the board. That said, when I thought about where my “origin” would be if I did gesture a graph, I immediately placed it around my chest. With my arms stretched out like the x-axis and my body forming the y-axis. This is different than were the author places the origin more at her naval. I asked my daughter the same thing and she had the same answer as me. I definitely never invited students to be the graph rather than just look at it. If gesture is such a natural way to make sense of shape and change, why is it not something that I have not used?

My final stop came from the strong link between gesture and understanding. Like the author, I find myself wondering about the role of early, intentional intervention. The more confident students in the study seemed to use large, embodied gestures naturally, without being prompted. That made me pause and ask myself: is gesture something that appears once understanding is already there, or could intentionally teaching and modelling gesture help students get there? As with the author, I am curious about what might happen if gesture was treated as a legitimate learning strategy, something we explicitly teach early to students to help improve their understanding (this is her second hypothesis for further research).

Question for the group: Do you notice yourself using gestures when you teach math, especially graphing? Where would you imagine your “origin” if you were gesturing a graph? And could you see yourself explicitly teaching gesturing as part of your math class?

I was reminded of this T-shirt as I was reading the article

Hello There

 This blog is where I will keep track of my math inquiries as I work through the EDCP 553 course. I am excited to learn all about teaching math through movement, the arts, and being outdoors. I am excited to use this space to play with ideas, try things out, and reflect on what it looks like when math is creative, hands-on, and connected to real places and real people.