September 24 Exit Slip

 We modern-day humans are not great at embodiment. Many of the tasks and activities of our everyday lives - both leisure and work-related - are in some way assisted by machines or entirely given over to technology. The result is a sense of distance from the natural world and a kind of disconnect from the physical realities around us. The time we have spent in the Orchard Garden has brought these things to my attention, but especially on this past Tuesday. Both in the consideration of measurement and the movement of the sun through the sky, I felt connected in my body to concepts I had previously only thought of in more scientific/mathematical/abstract terms.

The measurement activity was fun and informative: I never knew what the "cubit" or "fathom" were, for example, or that pouce in French means "thumb" and "inch" for a reason! There were several such examples for me, reminding me that many concepts I simply accept as "normal" today have a history if only I take a moment to look them up. But beyond the fun of understanding where some measurement terms came from, there was something gratifying about using my own body as a tool to take measurements. Other than my height, I'd never measured any other dimension of my body, or of my step and pace. Somehow I think of my body as the means by which I use other tools, but not as a tool itself. But knowing the distance of my step, for example, makes me think more about the distance between everyday places I walk. I am better able to think of my body moving through physical space when I think in terms of measurements. And all of this connected me to people of other times and places for whom the use of the body for such tasks was (and is) quite natural.

But if the first activity gave me a better grasp of my body in the physical space in which I move day by day, the second activity gave me a better grasp of "space" on a much larger scale. It's a funny thing: before class, I could have offered a roughly accurate version of a scientific, textbook-like explanation for the movement of the sun in the sky, how that changes between the solstices, and why. But how well did I understand it? The simple act of roughly measuring angles with our outstretched arms and fists to locate the height of the sun in the sky at the equinox and at the solstices made this understanding more real, somehow. And I now understand how to calculate the angle of the sun at the equinox and solstices without needing to look it up. Embodying the movement of the sun will help me remember that information for a long time to come.

These simple activities in the garden have reminded me that I can use my body to understand the world around me, both near and far. The physical actions connected with the new information I learned will help me to remember for much longer. Both of these are important insights as I think about teaching secondary students in the years to come.

September 24 Entrance Slip

 One question I have in my mind as I begin my journey towards teaching is whether I think of myself as a math teacher or a teacher who specializes in math. The difference is in a way somewhat subtle, but for me, the distinction matters greatly. If I am a teacher who happens to teach math as my main subject, that helps me to think through the fact that I am of course always teaching a great deal more than mathematical content to my students.

This opening reflection brings me my main "stop" in reading Gerofsky's article, "What we have learned from campus teaching and learning gardens: The UBC Orchard Garden and Cultivating Learning Network." This stop wasn't first in terms of where it occurred in the article, but rather it is first in significance for me as I reflect on my reading: on page 110, Gerofsky writes, "In acknowledging the garden as co-teacher, we are concerned with developing empathetic relationships with living ecosystems." The reason this is my primary stop is actually two-fold. 

First, this was the moment when it became clear to me that while there are some ways the garden can be used to teach math (or any other subject), the garden itself has something to teach all of us, quite independent of whatever subject we happen to be focused on. That is to say, simply the act of having my students spend time thinking, working, dialoguing, and conversing in a beautiful natural space such as the garden teaches them something about what it means to be a human person in the world. Gerofsky continues: "The quality of empathetic relationships with the living world is of deep importance in the development of sustainable ways of thinking and living...the methods developed in Enlightenment/Modernist sciences and technology involved a distancing and separation of human researchers from the rest of the living world, with an increasing emphasis on logic and rationality and a repression of emotion, spirituality and even respect for other, non-human forms of life" (p. 110). 

If that is all true - and I deeply believe it is - I have a responsibility as a teacher to work towards something better for my students. This was the second reason for this "stop" in my reading. I was led to reflect on the fact that math is a subject that for many connects directly and most naturally to our modern, industrial, technological society. That is, math is implicated in what Gerofsky describes regarding "Enlightenment/Modernist sciences and technology." It must then be part of my goal as a teacher to give my students a different perspective. Doing math in a garden (or some such place) would no doubt strike many students (and parents? and administrators?) as jarring, perhaps "odd," maybe ill-advised. But the act of teaching and learning in a garden-space is all the more important for just that reason: we need to counter "the human-centric approaches of modernity," as Gerofsky puts it. And would it not be more natural to reflect on and be inspired by the beauty of mathematics when one is surrounded by the beauty of the natural world of which we as mathematical thinkers are also a part? To put it simply, kids (and all of us) need to spend time in nature - so why not spend it there while doing mathematics? Goodness knows that many of them get precious little such time outside of school, what with our busy modern lives and the always-accessible phones and screens that fill our existence.

(There were other stops for me in this article, but I feel most strongly about the one I just described, so I'll not mention the others here.)

But what does this all mean practically? First of all, it means that at the school where I teach I need to identify and/or begin a project to create a suitable outdoor space where class can sometimes meet. Perhaps this will be straightforward, or perhaps not. Perhaps other teachers would be on-board and willing to help and participate in garden-based learning. Secondly, it would require some physical elements and a way to get them there - such as bucket seats or something similar, a rolling blackboard (or whiteboard, I suppose), maybe benches. (There would also have to be some convenient way to store those items in a shed or in the school building, perhaps.) Thirdly, it would require dealing with the elements...especially in BC in the winter! Perhaps, depending on location, it would have to be a fall and spring season garden primarily. And fourthly, it would require establishing a culture of teaching in this way. I would need to be dedicated to it and work at experimenting with what works and what doesn't. I do not yet know all the ways I could teach math with the garden - I think those would need to develop over time. But growing as a teacher working in a garden or natural setting would create a culture of learning that is unique and hopefully transformative for me as well as my students, in ways that go far beyond the mathematical content itself.

September 17 Exit Slip

 My family (me, my wife, and three children) have a practice of connecting with my and my wife's parents each weekend, usually through a FaceTime or Zoom "call" (they all live far away in the U.S.). In describing for them this past weekend my experience of being in the Orchard Garden for my math cohort-based education courses, I have been amused by their reactions. Some questions are: "How can you focus outside?", "Why be in a garden to learn about math education? - math is about numbers, not plants", and even "You're spending all this money to go sit in a garden" (as if nothing else could be happening there but sitting).

So it is most instructive for me to reflect on our September 17 class in the Orchard Garden in light of these questions. What are we doing there? What lessons is the garden teaching us that will be useful as math educators?

The first part of our class involved being in a "sit spot." In this exercise, we were asked to find a place that "calls to us" in some way and to sit quietly there for a length of time as we noticed the world around us. We were asked to sketch two things that were alive and growing and two which were human-made, with attention to the lines and angles of what we were observing. There were a number of ways in which this activity informed my own thinking about teaching - and teaching math in particular.

First, what a pleasure it was simply to "settle in" somewhere quietly in a natural setting. Math people are perhaps known for being analytical sorts. The development of the ability to observe and the chance to get into an observational state was helpful. In math education, we want our students to cultivate the ability to make observations of what they notice as their mathematical knowledge increases; the "sit spot" activity is perhaps way to help develop that skill.

Second, there was for me a fascination in thinking about how both the natural and man-made objects I observed reflected mathematical concepts. As I was sketching my objects, I couldn't help but wonder: what mathematical concept might be illustrated in these objects? Obviously the man-made objects brought to mind the mathematical use of angles and tools and precision equipment and fractions and so on. But I began to see math in the natural world as well. For example, the arc of the grape vines I was observing formed what was essentially a beautiful paraboloid (I enjoyed looking directly up to the high point of the paraboloid from underneath it). There was also a lovely symmetry in the shape of a grape leaf. Math is found everywhere.

Third, I thought about how moving myself to a new place in the garden meant I was able to see things from a different perspective. This is another skill I hope to cultivate in my math students. 

Fourth, a comment was made that has stuck with me: we ourselves are part of the natural world. When we observe man-made objects (and math often seems to be taught with reference to such "real-life" applications), with all their precision and right angles and structure, how much more interesting and satisfying these objects are when situated in a natural setting. There is a sense in which the "natural" and "man-made" worlds are meant to complement one another. I'm not sure I had ever thought of things in that way before and I was grateful for the insight. How is the beauty of the math we study and teach enhanced by simultaneously considering the natural world around us.

After the "sit spot" we had a time of discussion about being a reflective teacher (one who is wholehearted and openminded and responsible). The discussion itself contained a number of helpful insights for me, but what has stuck with me is how it felt to have that discussion in the setting of the Orchard Garden. In the indoor classroom, I tend to feel "constrained" and "uptight" a lot. I find having genuine conversation and penetrating discussion to be challenging. Something about being in the garden impacted me differently: in the open outdoor space with my senses engaged by the natural surroundings, I felt myself also open up in my mind and heart. I seemed better able to listen and more willing to contribute. Perhaps "garden-based learning" sometimes just means that we simply learn better because we are there in the garden. It made me want to get my own blackboard and take my future high school math classes outside! (My daughter told me that means we should move somewhere like southern California, where the weather would allow for such instruction on a regular basis!)

September 17 Entrance Slip

What kind of teacher do I want to be? What does that mean for my time as a teacher candidate now? Before reading Grant and Zeichner's article, "On Becoming a Reflective Teacher," I think I would have responded to the first question in some way like this: "I want to be a teacher who is always growing and seeking the growth of my students." And for the second question, I might have said, "I want to take in all I am learning and ask the question: 'How might this impact my teaching practice?'"

So yes, as a new teacher candidate in Vancouver in 2026, Grant and Zeichner's article "speaks to me," but not as introducing an entirely new way of thinking about being (or becoming) a teacher. In some sense, I think I already wanted to be a reflective teacher. I would even say I don't think I've met a single teacher candidate in the last couple of weeks who is unreflective! But perhaps there is something more to that observation: the world in which we live in 2026 is quite different than that of the 1980s (when I was a young child, but before most of my fellow teacher candidates were born). Approaching the teaching profession in this technologically saturated, AI-infused era, it seems to me there is a drastic urgency for education that creates critical thinkers, equips students to engage the world wholistically, and instills in them an appreciation for what it means to be a human being in the universe. How could teaching that has such goals be anything other than reflective? It certainly won't be the kind of teaching that is guided by "impulse, tradition, and authority" (p. 104).

Grant and Zeichner are not, therefore, saying anything that seems "surprising" to me. But what they write still "speaks to me" in that it gives me a framework and way of thinking more thoroughly about what becoming a (reflective) teacher means in practice. The three attitudes the authors identify (following Dewey) as prerequisite for reflective action are all helpful as a way of approaching my time as a teacher candidate, to varying degrees.

Regarding openmindedness, the authors suggest that we should adopt an openminded attitude to alternative ways of looking at existing teaching practices in the schools in which we spend time as a teacher. While I hope I would have such an attitude, their examples seem somewhat dated (and U.S.-centric, since Thanksgiving and Columbus Day are not the same or do not exist in Canadian schools). Allowing for different points of view and beliefs seems now to be expected, rather than something that would go against the mainstream. But I certainly do hope to "keep an open mind about the content, methods, and procedures used in [the] classroom" (p. 106) where I will be on practicum, as well as about the many ideas, philosophies, and examples I am already beginning to encounter in my teacher education program. 

I found the article most helpful in drawing attention to the responsibility I have as a teacher to consider the consequences of the decisions I make, particularly in explaining that these consequences may extend far beyond the classroom. As a teacher candidate and future teacher, I can imagine it will be tempting at times to prioritize the immediate utility of an action. So it helpful to have this clearly stated: "The costs associated with what works in the short run to help you get through a lesson smoothly at times may outweigh the benefits to be gained" (p. 112).

With regard to wholeheartedness, at this stage of teaching candidate experience, I think this requires of me to be actively seeking out the skills and knowledge I know I need to be an effective teacher. It would perhaps be easy in the midst of this busy program to take "shortcuts" in various ways in order to meet the requirements that seem pressing, perhaps at the expense of growing in the ways I need to. Being wholehearted would mean I do not think or act in this way.

Looking ahead, I return to the statement I made at the outset about the kind of teacher I want to be: "I want to be a teacher who is always growing and seeking the growth of my students." Such growth seems very natural at this stage, but what about when I am further along into the teaching profession? Here I think Grant and Zeichner are helpful, because a reflective teacher will be an inquiring teacher. As reflective teachers, we are never "set" in our ways, but actively considering how we can expand our knowledge in the subjects we teach and how we can learn from new and evolving teaching practices. A reflective teacher will have the skills and the desire to pursue professional inquiry throughout their career.

September 10 Exit Slip

 From the Frank McCourt video and class discussion, I was struck by what McCourt calls the "ideal" of being honest as a teacher. He compares teaching to good acting, which, he suggests, is best done when you do your lines but be yourself. He suggests we need to "drop the mask." I have been reflecting some on the comparison of teaching with acting. For most people, "acting" means to put on a different persona, to adopt a different personality. And yet, if McCourt is right, the best actors are those who are in some significant way working out of who they are as people. I find this to be a very helpful parallel to thinking about teaching. Surely we have to "act" at times as teachers: we will not always be in the right mood or mindset to teach. We will need to be able to put on our "teacher self." And yet, teaching would seem to require a deep level of honesty and appropriate vulnerability. Student transformation and growth (and all genuine learning) means more than the transfer of information -- students are impacted not only by the content of what they learn but by the experience of learning it from a person. I am pondering that line between "acting" and showing up genuinely day by day and look forward to growing in my understanding of this space inhabited by the teacher.

Hello world!

 My blog for Inquiry I.