Making Mathematics Messy

"Mathematics is popularly conceived of as a pure body of knowledge, independent of its environment, and value-free."

 I agree with Renert, that mathematics today is considered as abstract and separate from reality, with the exceptions of well-posed contrived problems that promote linear and binary thinking; there's very little mess in a mathematics classroom. Students are consumed with getting the right answer, and sadly, the current state of teaching, perpetuates the value of that desire. But rather than "reform" or even "transform" this present state by looking to a more socially responsive future, I believe we should look to our past. I believe the Ancients did not create and develop mathematics to serve as a pure abstraction intended to live in parallel with reality. Mathematics was created from life for life; it arose organically to measure, predict, and understand nature so that they could plant, grow and ultimately sustain their existence. The Ancients would never have to question whether mathematics should concern itself with ecological issues. Therefore, I think Renert's arguments  are compatible with the age old idea of what mathematics truly was.

"It turns mathematics from a collection of objects, or a series of competencies, into an open-ended state of observing the world."

Renert's argument that "our number sense is almost entirely divorced from any quantity sense,"  underlines this chasm between a two-dimensional linear view of mathematics (right and wrong) and a fuller more holistic viewpoint that values process and possibility. Yes, we know what numbers are, and how they relate to one another; but what do they mean to us? When I first learned to swim I remember hearing that now depth didn't matter, because I could presumably swim in it regardless. I think this is what we are imparting to our students through our mathematics education; they learn the rules, apply them to any problem they are given, and make sure you get the right answer. But does depth really not matter? Surely we should know how much water lies below us, what could be swimming next to us, temperature or water composition. And yet, we are taught to focus on the surface, as the answer to such questions shouldn't affect our swimming technique: but they do! When we pull ourselves out of our trained monochromic thinking, we open our minds to messy, and necessary, complications - we open ourselves up to life. Telling a student that they got "42" tells them nothing without them further questioning, "out of what?" or "how did everyone else do?" Numbers need context to be understood, just as mathematics needs to be placed back into life to have relevance and meaning.

"'radial creativity'...shifts the responsibility of knowledge production from the teacher to the entire classroom collective."

I love the idea of making our classrooms a learning community; allowing ideas to flow unlimited in non-linear ways.  I want to make every student feel valued and that their contributions matter as much as anyone else's. I don't believe one correct solution is necessarily better than a hundred incorrect attempts. Indeed, promoting discussion and sparking our thoughts is, to me, what teaching is at its best. I think the ecological issues that face us are bigger than any one of us, and to assume we know more than our students is naiave and unproductive. Telling them what to do will not empower them to experience the problem and it won't initiate their curiosity and concern. I think this problem, like our planet, belongs to all of us and needs to have everyone's buy-in.

Exit Slip: Sept 23rd

Knot between you and world around

During the sitting activity I found a tree way past the shed, which had nice long branches stretching out so much that it arcs down to the ground creating a very nice dome. It had a nice thick trunk on a angle that I could lean against which makes a perfect reading tree or even napping tree. There is something about finding places like these out there that you can feel personal connection to as your secrete spots. It can be a place of comfort when you need to run away for a bit. Trees in places such as the garden, it is possible that it will be there for a long time,  and it can be a place that is a constant in live. Not a place where you come out for little bit to feel refreshed, somewhere you can come back to whenever you need to. 

Making knots was a interesting experience. One thing that it provides the creator is sense of accomplishments. This is important because it is what give us courage to solve the next questions and problems and have confidence in the solution they come up with. It is possible to get wrong answer, then you just have to try again and not give up. This is especially important for physics and math because students are often unsure of their method and solution that they question their approach and happy to just seek out help before giving meaningful attempt. 

Working with material give us opportunity to learn about material as you are working on project. It is a experiment on its own where students can learn about nature of the material and what they are capable of. This goes back to basic nature of science where you are conducting experiments and through experiences we learn about the nature and figure out how things work in the world. 

 Today's lesson was very relaxing and fun. I was amazed at how much I was able to take in and focus, just by being outside and grounding myself in the natural surroundings. I enjoyed creating our own poetry in our "sit spaces" and hope I can instill a little of that experience into my own students. I always think about how to connect with students, and how to connect them with the material; but today I realized how important it is for them to learn to connect with their inner-selves. I think when we can quieten down all our environmental noise - man-made and mental - we can truly be open for learning.

The rope was fun, and the 7-strand weaving was challenging. I decided after listening to the podcast, to stray from the "official directions" and incorporate nature and how I just felt like moving the ribbons. My "poem" is below.

Nature's "Gift"

Tapestry of dancing light,

leaves crisscrossing, 

gently nudged by whispering breeze,

the hum of passing cars stirring the air.

Mighty planes and tiny chirrups,

equal under the leafy canopy.

Soft support feels timeless and steady beneath me.

Rough bark melts under my touch, revealing a timeless echo of lifetimes past.

Age smells sweet here; 

verdant youth softly caresses its grounded slumber.

Dewy freshness taunts earth's slow breath - 

a youthful sweetness mellowed with a whisper of what is

inevitable

.

A stich, or nine, saves time...

I share Kallis's thoughts and sentiments about looking to the past in order to build a sustainable (and fulfilling) future. I've always enjoyed crafting as I find it helps engage a different part of my brain, and relaxes that part that's always fretting or trying to work something out. I hear from many people about the "waste of time" it is to spend days making a simple hat or pair of gloves, when we could have purchased those things almost instantly. Again I agree wholeheartedly with Martin Borden (quoted in the article), that, "when you make something..., there is an incredible sense of worthiness to that." I often think that  because "we have happily divested the responsibility of taking care of ourselves", to corporations with large factories overseas, we are not only putting strain on our planet, but missing out on a great source of joy and accomplishment. I always tell my kids that I can buy them what they want for their birthdays, but if they're really lucky, then I'll make them a pair of socks. Many many think they can buy a dozen mechanically made pairs for a fraction of the price to knit a single pair; but in that pair single pair I've spent literally hours twisting, weaving, making mistakes, correcting mistakes, and all the while thinking about the person I'm making them for. I look at a blanket I knitted squares for over several summer vacations, and I think of the kids surfing waves while I watched and worked away. Time is possibly the most precious thing we can ever have, and I think finding ways, as our ancestors before us, to treasure that and invest in each moment are very important. And, as Kallis notes, this wonderful opportunity to slow our lives down, has the added benefit of nurturing our planet.

I enjoyed trying the rope and weaving techniques, but the lacing was a bit complicated for the time of night. I hope to revisit the lace though as it looked exquisite, and the technique looked a fun challenge. When I was making the rope, I remembered a Coast Salish Weaving group I attended (pre-COVID), as I had a similar feeling of what Kallis describes as "un-venting ancestral knowledge," - just an indescribable connection to the people that created and repeated this technique countless times and many years before me. I enjoy knitting for many reasons: the colours and patterns, the challenge, the way it makes me relax and slow down, and the idea of creating something from virtually 'nothing.' But I think a large part of why it's so important to me is because, while I'm doing it, I feel part of me is in Scotland with my grandmother knitting beside me.

Lessons from Nature: Exit Slip for Sep. 16

 Today's class had us sketching both natural and man-made objects to appreciate the concept of angles. I found the experience calming and thought provoking. I felt that the more I looked at the natural objects I was studying - leaves, fennel "blossoms", fir branches - the more intricacies I discovered; in contrast the main-made objects were much simpler to "understand" and process. I loved seeing the man-made structures being adapted by nature: crooked sticks, warped planks, sun-bleached metal, shadow-play across surfaces. This gradual adaption of something so ordered and precise, made me think of how we could adapt our mathematics teachings and also how our students can make the concepts we teach their own. 

Another thing that struck me was that I didn't really need to actually understand all the natural complexities I was seeing to enjoy them. I learned math through proofs and practice - there was no artistic creativity incorporated in the lessons. Consequently I tend to focus on understanding something before I can appreciate it, but today's experience gave me a different perspective that I hope to take into my own teaching practice.

I'm sharing a pic I took on my way home as it really resonated with my experience today.

Reflections on Reflections: Entrance Slip for Grant & Zeichner article

I found the paper, "On Becoming a Reflective Teacher," by Carl. A. Grant and Kenneth M. Zeicher, helpful and relevant despite its being written forty decades ago. The education system has come a long way in terms of integrating students with learning differences, encouraging girls in STEM subjects, but it still has inherent biases that give credence to the authors' arguments. I had a slight issue with the rather heavy-handed delivery for a paper promoting independent thought, but their key principles on reflectiveness resonated strongly with me.

The principles of reflectiveness - open-mindedness, responsibility and wholeheartedness are, for me, ideals to strive for throughout our lives. I have anxiety which can lead to a rigidity in how I respond in certain situations. I find I can be openminded in "safe" situations, but when I'm feeling overwhelmed, I tend to react with a certain rigidity, and I am less able to be receptive to the situation. Having teenagers has helped me become more aware of this challenge (and many others), and so I resonated with what the authors said about being open; especially reflecting afterwards is just as valuable, if not possible during the situation. The "hidden curriculum" made me conscious about how careful we need to be in what we may bring into our classrooms with our conversation or teaching choices. I also appreciated the note they made about not just forming our own philosophies and beliefs, but using our time in the program to be open to, and learn from, our peers' beliefs. My main takeaway from the article is that that we need to always be willing to question our thoughts, actions and beliefs so we can stay connected to the ever-changing needs of our students.

Fun with Resistance: Exit Slip for Frank McCourt Interview

Instinctively I imagined "teacher inquiry" to be delving deeper and staying up-to-date with the latest developments in the subject area. However, I think Frank McCourt's inquiry was of himself and his relationship with his students. He "wanted [his] students to think for themselves," and his own humility allowed this to happen. He did not assume he knew everything, nor did he dictate a single pathway for his students. Instead he was open and willing to learn about the best ways to connect with his students. He states, "you'll always have resistance," and that there's "no use fighting it. In such a beautifully warm and relaxed way, this statement, like his lessons, is transformed from a warning to a promise of constant inquiry and all the joys and excitement that brings.

[Thoughts on a  Frank McCourt Interview]

First Ever Blog Post!

This is how I'm feeling about my very first blogpost.