Keeping the doors open for everyone

I like to think of the question as being: how can we, as teachers of math and science, provide a learning environment that is welcoming and inclusive to everyone no matter who they are.  I appreciate that equality fails to address the inherent disadvantages some societal groups face, but I think, as teachers, we should want to nurture, engage, connect with, and appreciate what every one of our students may bring. As a woman who took math and physics in the 80s and 90s, I am unfortunately familiar on just how destructive sexism can be to a career and self-confidence. It is probably one of the main factors that caused me to leave academia. However, as a mother of three sons, I would be very upset to hear that, in an attempt to right past wrongs, a teacher would encourage them less than another student based on their gender. I remember seeing a flyer advertising an opportunity to learn about being a firefighter. My young son, who had his share of struggles with self-esteem and difficulties at school, was extremely excited. I called the number and was told that he could not register because of his sex. While this action may have been trying to brute force a solution to a real systemic problem, it used the same weapons that perpetrated the initial wrong doing.

 I have tussled with my thoughts on this question a lot, but I think my belief is that we should acknowledge that there are certain students who may have an instinctual reticence for the subject based on societal factors, and actively do our best to neutralize those preconceptions and increase their comfort and self-esteem with the subject. However, I do not want to push some students at the expense of others; I hope to get to know all of my students and seek to find ways to help them all realize success. I looked up my physics department from my undergraduate degree and there is now 10% of the faculty who are women compared to a single female when I studied there. I do not think that is much of an improvement, but I am not comfortable forcing a a biased solution.

In my classroom I want to provide examples of mathematicians of all genders, races and cultures. I also want to be aware of any subliminal message on race or gender any of the materials and resources I use may carry. I hope to constantly question myself about any inherent biases I may have and make sure I do what's in the best interests for each of my students. I also don't want to ever make assumptions on whether a student may or may not be interested in learning more or pursuing further in the field, but instead try to offer encouragement to all of them. I'm all too aware of how one single thoughtless comment on a teacher's bad day may change the course of a student's life.

Inquiry Project: Addressing Dyslexia in Math Education

 

I am interested in this topic because two of my sons have dyslexia and their high school experiences in mathematics have generally not been positive because of this. When one of my sons was in elementary I homeschooled him for a couple of years because I found that the school system could not accommodate for his learning differences. During that time I did some research on some tools to help students with dyslexia, but the main recommendation I found was to make sure his own self-confidence and esteem did not suffer. I learned that dyslexia has nothing to do with intelligence, and in many cases students with dyslexia will be able to find their own coping strategies to help them get through, or succeed at school. The most damaging effect of this learning difference was the toll it took on the student's confidence and self-image. Many of these students who are not diagnosed or given support believe they are not as intelligent as their peers. These students also encounter invisible hurdles that our education systems unnecessarily puts into place. Just giving a student larger squared paper can make a huge difference.

One of my sons consistently 'failed' mathematics in his grade 11 and 12 years, and was even asked to drop out of his grade 12 pre-calculus class. he remained in the class and won a math prize in his second year studying math at university. When I asked him what the difference was between high school and university math he told me that "high school math was difficult for me because the teachers made learning it difficult, but math at university is difficult in a fun way because it's the subject that's difficult." One of my main motivators for becoming a math teacher is because of my sons experiences and the realization of the difference a teacher's attitude can make in a child's future.

Presentation Link: Here

Performance Prisons

My "student bird" gets both motivated and extremely stressed about assessments and grades. I completely relate to the student comments in the Sarte and Hughes paper as grades and peer competition being a powerful motivator. I remember always wanting to know what everyone else got on an exam seconds after I received my mark. However, I've become increasingly aware of the stress the grading process puts me under and how that stress is related to the methods of assessment. A continual assessment approach, and especially assessments that are done in your own time, e.g., essays, give me much less stress compared with formally constructed assessments given under a time constraint. It's significant that my knowledge of coursework, or even interest and enjoyment of the work, has little effect on my stress level as compared with mode of assessment. However, I also find that when I'm told nothing will be assessed, my intrinsic motivation is crucial on what effort I put in, not external duty to complete the course.

As a teacher I do recognize the importance of using assessment as a measure of my effectiveness, and a gauge about my pacing and content. I am acutely aware, however, how a grade may not be a reliable representation of a student's knowledge or ability. I agree with the authors in that we should think carefully about why and what we are assessing and its effects on students. Though I find assessment necessary I do think we can do a lot to reduce its negative effects by seeking student input in how they want to be assessed and giving them qualitative feedback over quantitative. I do think that the article has an inherent bias towards high performance and highly motivated students because it was conducted on grade 11 physics students. This selection bias may minimize the motivator concerns, as all of these students were interested in pursuing post-secondary education. In another group of students, removing assessment altogether may remove significant motivation to participate in the course.

The more I learn about assessment, its lack of equality and negative effects on social and emotional health, the more I am inclined to rely more on learning maps and track my students' individual learning journeys. I do not agree with ranking students, even though some students may use this as a strong motivator. I think ranking students based on some particular aspect of their abilities, or their ability to display that ability, is not humane and does not fit in with the type of world I want to work towards building. While I anticipate resistance, I do hope to minimise marks and letters grades in my teaching and focus on effort and understanding.

A Multidimensional Approach to Mathematics

 I really enjoyed today's class and got a lot out of both talks, particularly Jo Boahler's. Ironically, a classmate and I had just shared with our group that we find we need more time to learn things, and 'lessons' where we are expected to pick up a concept quickly in class and then start performing places a lot of pressure and anxiety on us. I found just hearing someone describe having a similar learning process to mine eased a lot of anxiety for me about this. Joe Boahler's talk then reiterated this concept that maths shouldn't be  concerned with the speed that students perform. I got so much value and comfort in learning that anxiety actually affects our brain in a way that we cannot access our mathematical knowledge. I've experienced this so much in my life, and it's been quite damaging to my confidence at times.  I loved hearing how valuable mistakes were and that "every time a student makes a mistake they grow a synapse." How wonderful and amazing that is to hear, and find that scientific research enforces it. It's not just ok to make mistakes - it's actually good for us! I feel so strongly about this, and it's one of the most important things I want to teach my students.

The differences between growth and fixed mindsets really resonated with me too. I am definitely the poster-child for the fixed mindset, and just hearing about how that came to be and how it affects my thoughts on myself is quite freeing. I was praised for each high mark I got, and eventually life somehow became only about attaining the next highest mark. There was tremendous pressure and little joy in living like that as I was only ever as 'good' as my latest mark. It's really given me a lot to process and think about in terms of how I view myself, and how I want to influence my own kids and students.

I agree wholeheartedly with Alfie Kohn. I too think assigning numbers and grades to students gives a skewed impression of what learning is about. Without having them discover their own  reasons for doing things and natural interests we turn learning into a mechanical process of memorization and regurgitation. I think systems like this are exactly why I got to a point in my life and realised I had completely lost touch with what I actually liked doing.

"Dancing Teachers into Being"

I loved the metaphorical use of parkour and swing as being vehicles to weave a delicate  and necessary balance between teaching the two-dimensional representations of our subject that have been preserved in tradition and practice, and trying to instill a playful vibrancy in the delivery and humanistic relevance of those subjects. I relate to the idea of taking comfort in our grid-like learning and teaching structures: I find comfort in scheduling and making lists and plans. I agree that a certain amount of this structure is necessary, just as roads and playground structures need to exist before creative ways of using them can be discovered. I always find joy in leaving the grid's confines, and find the ideas I get from this re-energize how I interact with the grid. I place a lot of value on the human experience, and the importance of letting our students make the learning personal to them: "to bring multi-sensory awareness and ways of learning to consciousness, and to help learners notice sounds, smells, tastes, textures, balance, temperature, movement and other sensory impressions." To offer such a full-bodied learning experience one has to keep sight of the foundational grid, but have  the flexibility to see around and beyond it. 

"Parkour remakes the city a playground, turning intended barriers into handholds," I think was my favorite image. I really love the idea of being playful, and thinking outside of the box in terms of how we ask our students to experience mathematics. I especially love reframing how we think of barriers, as not preventing learning but being places where we take our time and allow ourselves to be slowly guided by what we discover about ourselves.

I had not heard of the concept of Alter-Global principles and am happy to have been introduced them as they resonate strongly with what I think as important ways to live and approach learning. Much of these practices seem akin to embracing Indigenous learning perspectives which help me visualize strategies on how to incorporate these practices in my classroom.

The repeated metaphor of "Dancing teachers into being" is such a lovely image that expresses so much more than words can suffice. We can't simply read, write or practice to become teachers, but in fact becoming a teacher who can sway with the tides of our changing world, one has to experience a full-bodied experiential transformation to both lighten and ground our spirit to tradition and inspiration.

From: https://www.heatherbeardsley.com/dissolving-grids.html

Reflections on Nature's Designs

 Sit-Spot Reflections

Today I noticed the Sun seemed brighter and more piercing, the air felt icy, and the high-pitched squeal of the tractor seemed to constantly intrude on my thoughts. I then started to focus on some spider webs that I noticed in the branches, and how sometimes they were obvious and then at other times they were invisible. I also noticed how I couldn't capture them with my camera and how this was representative of an experience that cannot fit on pen-and-paper or neatly in a box, but needs to be experienced with our own organic senses.

Musings on a Sprider Web

Machine, metal, leaves, wood - no place that fits...

Intricate - understood, a pale comparison to man's technology,  yet unreproducible...

Invisible - divine presence teasing the limits of modern eyes...

Intimate - born from life, for life, yet not living...

A lacey tendril suspended between two worlds - thought and feeling -

life's breath...

Reflections on leaf Geometry

It felt quite foreign and challenging to begin the task of turning nature into geometric pattern s, but it was ultimately very enjoable and relaxing. The more we looked at our leaves, the more patterns we saw, and the easier it became to think in this free and open way.

This is an acivity that I would definetly like to do with my classes. Just taking the time to get outside, sit with nature, and be open to whatever thoughts come is very valuable. I may follow up the activity by having students think about connections and relationships between objects we see, e.g., a tree has a certain amount of branches that then have leaves, etc. It may be a way of taking some of the fear and intimidation of mathematics away, and building up our own organic ways of forming logical structures and discovering relationships, connections and patterns. Being outside it also a great way to introduce spatial relationships and the need to be able to describe and know where we are.

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.