Annotated Bibliography_ Week 3

Thursday, Jan. 20, 2022

Chinn, S., McDonagh, D., Elswijk, R. v., Harmsen, H., Kay, J., McPhillips, T., Power, A., & Skidmore, L. (2001). Classroom studies into cognitive style in mathematics for pupils with dyslexia in special education in the netherlands, ireland and the UK. British Journal of Special Education, 28(2), 80-85. 

This study is the third year of a study of dyslexic students in Netherlands, England and Ireland in Mathematics. The previous studies found that dyslexic students in all three countries had difficulty reading and recalling multiplication facts; and students’ preferred areas of mathematics differed by country. This study looked at two cognitive styles: “grasshopper” (intuitive and flexible) and “inchworm” (logical reasoning and fixed). They found that there is a prevalence for “inchworm” style among dyslexic students but the ratio between these two styles differed by country indicating a dependence on teaching style. It’s suggested that connecting math to reality and encouraging flexibility when problem-solving. 

Monday, Jan. 17, 2022

Malmer, G. (2000). Mathematics and dyslexia-an overlooked connection. Dyslexia (Chichester, England), 6(4), 223-230. 

The author draws on his years of personal experience to identify a connection between dyslexia and mathematical ability. This paper is important in my inquiry because it examines various causes for students’ difficulty with mathematics, how these may manifest in the classroom, and practical strategies for support and encouragement. Although the author, a retired teacher in Sweden, wrote the paper 20 years ago, many of his strategies involve theories that are being advocated today: advocating process over product, encouraging critical thinking over an axiomatic approach that relies heavily on memorization. I’m interested in doing further research into the centers in Sweden that the author mentions that have been established to support and teach compensatory strategies to students with dyslexia.

Annotated Bibliography for Inquiry II

Thursday, Jan. 13, 2022

Gernsbacher, M. A., Soicher, R. N., & Becker-Blease, K. A. (2020). Four empirically based reasons not to administer time-limited tests. Translational Issues in Psychological Science, 6(2), 175-190. 

This article explored reasons for favoring non-timed tests over timed test: validity, reliability, inclusivity, and equity.  The article reinforced my previous empirical finding from conversations with teachers and students, that giving students with dyslexia more time is the most prescribed accommodation. This article is of interest to me because it challenged my previous conceptions about allowing more time as an accommodation; it suggested that because extra-time may benefit all students this accommodation for learning diverse students may be unequitable; and because of this the authors strongly advocate that tests be untimed for all students. The authors reiterated common historical misconception of corelating ability with speed and offered much research contradicting this belief in many subject areas and education levels. The authors also cite research indicating that although a commonly used and accepted accommodation, most students given this accommodation do not utilize it significantly; in essence the authors suggest that the advantage in untimed tests is the absence of the “pressure of time ticking off” and associated anxiety. 

Monday, Jan. 10, 2022

Note: I chose to include both article because the first used many references to the second, and I wanted to read the original source. The article in The Dyslexic Advantage views the Beals and Garelick (2015) article through the lens of students with dyslexia, rather than the original article's more general viewpoint.

Dyslexia Advantage Team. (2020). Don't let working memory prevent math learning. https://www.dyslexicadvantage.org/dont-let-working-memory-prevent-math-learning/

This article talks about how working memory can affect a student’s math performance but not their inherent mathematical ability, and accommodations should be considered to offset this disadvantage. The paper specifically addresses the practice of asking students to explain their thought processes in math problems, which they believe may be particularly challenging to students with poor working memory. They also suggest that there is a significant benefit in streamlining a question into its basic mathematical representation for students who have dyslexia, as this puts less emphasis on working memory and tests mathematical ability. This is interesting to me because it's not something that I've considered before in potential accommodations or adaptions for students with dyslexia. I am aware of the potential disadvantages of word problems in terms of the extra required reading but had not considered their requirement of working memory, nor had I thought about asking students to explain their thinking. Personally, explaining thinking always caused anxiety for me, as it seemed something beyond my current state of thinking and felt like it was asking something quite separate from the mathematical problem itself.

Beals, K. & Garelick, B. (2015). Explaining Your Math: Unnecessary at Best, Encumbering at Worst. The Atlantic. https://www.theatlantic.com/education/archive/2015/11/math-showing-work/414924/

This article by Katherine Beals and Barry Garelick (2015) is the cornerstone of the previous article in The Dyslexic Advantage. The authors question the equity in requiring students to explain their mathematical reasoning process, and whether their ability to provide a correct answer should not be proof enough of their understanding. The authors reason that there can many reasons, other than mathematical ability, that challenge, or prevent, a student from being able to eloquently explain their thought process. This article gave me a fresh insight into potential disadvantages our teaching and assessment methods may present to students with dyslexia and other learning differences or needs.

Final Reflections

This course pushed me out of my comfort zone and made me think more deeply and broadly about things I hadn’t really considered before; and for that I am very grateful. Looking back over my past blog posts, I find it difficult to summarize succinctly what seems like years of experiences crammed into a few short months. A few favorite moments that come to mind are my times in the garden, especially my “sit-spot”, and listening to Jo Boaler and Frank McCourt. I loved the calmness I discovered in the garden, and the creativity it allowed. Some of the experiences outside, like drawing and writing creatively, brought me much joy and helped me realize the importance of giving myself balance in the things I do. It’s now something I hope to expose my own students to one day.

A lot of what I’ve gotten from this class is the experience of joy that open-mindedness can bring, and how learning experiences can be anywhere – not just in textbooks. Frank McCourt told us that in teaching “you’ll always have resistance,” but this course has helped me see this as an opportunity rather than an obstacle. I’ve learned the importance of practicing what I hope to preach, by being open to new learning experiences, taking on challenges and embracing mistakes. The latter has always been difficult for me, and I think this course has helped me get a little more comfortable with my own limitations. Honestly, it’s still a struggle but I am beginning to accept that I don’t have to do or know everything; I just have to try. I really appreciated learning about math anxiety from the Jo Boaler talk; that it can affect our ability to think through mathematical problems, and that speed has no bearing on ability. I loved the idea that that "every time a student makes a mistake, they grow a synapse;” that making mistakes is actually good for our learning process. The idea of fixed and growth mindsets also helped me learn a lot about myself and why I react the way I do in certain situations. It also made me realize how important it is to allow my students to make their own personal connections to the subject and have their own reasons for being successful and what success may look like for each of them.

I think the course helped me appreciate what inquiry is and the value of it in my future teaching. I enjoyed all the classes and felt I took away something valuable from each of them. The only suggestion I have for possible “improvement” would be to use Canvas at least in addition to the blogging. I found it a little frustrating to have to scroll through blog posts to find what I had to blog about for an entrance or exit slip as sometimes some of the posts did not appear on the class blog or were not in order. I would often have to go into the back end of the blogger site and look through each post to find what I had to do which, given the number of courses we had to do this term each with their own sizeable amount of readings and assignments, was frustratingly time-consuming. At times, I had set aside time to do a blog post but could not access the reading which was frustrating. Also, having each of the students have author access to each other’s blogs was quite cumbersome and resulted in us having to scroll through over 60 blog sites every time we had to find our own and make a new post. I even posted some of my blogs on my peers’ sites by mistakes at times or found they had done the same. Conversely, our other courses on Canvas made finding assignment details, lesson topics, and submitting assignments very quick and straight forward. While I did enjoy the writing and reflection of the blogs, I think this could be done on Canvas without losing any of the benefit.

Reflection on Inquiry Project

 

I have really enjoyed this inquiry process so  far, and I feel that I've learned a lot. There are a few things that really struck me during the research process.  I loved the quote from Erin Kline, a teacher at Fraser Academy, whose presentation I attended: "Kids with dyslexia, see the forest and the trees." These words really affected me because it's how I see my sons. They see the world in such a beautifully different way that really is a gift; the struggles they face with the simplest of tasks creates amazing creativity and invention. However, it also perfectly describes the difficulty in seeing a clear message when being overwhelmed by so much extraneous information in the way of inefficient cognitive processing.

A huge takeaway for me was that every teacher and specialist I spoke to or heard from, reiterated the message that adaptions for dyslexia were "just good teaching" and would benefit all students. This is frustrating, because it's not always being done, but also very hopeful because it needn't be reliant on funding, time or vast amounts of training for teachers already in the field.

When my son was first diagnosed with dyslexia (about 16 years ago), I did a lot of research on what dyslexia was, its manifestations, causes, and how it could be "overcome."  Honestly, this process was not very thorough as I had four young children to care for, and I was quite distracted with worry and concern about my son's future. When I was preparing this project I realized how little (if any) research I have done about dyslexia since those initial panicked days or weeks; and how all of my time and effort has been in advocating for my son in his schooling. This surprised me, and then made me realize how much of a disconnect there is between researching and understanding dyslexia and helping students with dyslexia succeed in school.

My interview with the VSB literacy enhancement specialist was extremely valuable for me. She gave me several  names of educators who have done active work to help students with dyslexia and was able to pass on insights from several different schools. I was only able to look into these resources superficially, and so I'm excited to have more time to learn about them further. What was really interesting to find out was that although there is a strong advocacy and support system in place for literacy support, there is no equivalent in mathematics. I believe there is an great need for such a program and hope to delve deeper into what such a program could look like and how it could be implemented and executed. The specialist told me that she thought a math support program may have been attempted in one of the school districts (not VSB) but she was unclear on the details. This is definitely something I want to find out more about.

I loved the research studies that I read, and felt I only touched the surface in this area. There's so much information to be learned from the scientific research and also the practical "on the ground" strategies that have been tried and tested for decades. Although, I want to dive into the research and learn more about current teaching and scaffolding strategies, I think the area that may be most exciting is the sweet spot in between these two and, again, how to implement a program like the "Reading Recovery" program for literacy but for math into schools.

Here is a link to my Inquiry Project presentation.

Inquiry Project: Annotated Bibliography

Andreassen, R., Jensen, M. S., & Bråten, I. (2017). Investigating self-regulated study strategies among postsecondary students with and without dyslexia: A diary method study. Reading & Writing, 30(9), 1891-1916. https://doi.org/10.1007/s11145-017-9758-9
This paper compares study strategies (as listed in a diary) between post-secondary students with and without dyslexia. I am interested to learn which strategies were useful, the differences they made, and whether they can be applied to high school students.

Black, J. (2010, May 8). In Their Right Mind. New Zealand Listener, 18-21.
This is a popular magazine article on well-known people who have dyslexia. I think this will help provide background information, context, and a positive perspective that could later we shared with students.

Cawley, J. F., Hayes, A., & Foley, T. E. (2008). Teaching math to students with learning disabilities: Implications and solutions. Rowman & Littlefield Education.
This book approaches the teaching of mathematics from the perspective of adapting the entire pedagogy of mathematics so that it is meaningful and accessible to students with learning differences, rather than find access points and adaptations with a current curriculum. It aims to go beyond helping these students, but to use mathematics to help them develop cognitive and linguistic skills. I am particularly interested in their detailed treatment of word problems.

Chinn, S. (2020). The Trouble with Maths: A Practical Guide to Helping Learners with Numeracy Difficulties (4th ed.). Routledge. https://doi.org/10.4324/9781003017714
This textbook presents various learning differences that affect mathematical learning and offers techniques to help students with dyslexia and other learning differences be successful in mathematics. This is a key book for providing context and a comprehensive treatment of the field of alternate learning and teaching strategies for students with learning differences.

Davis Dyslexia Association International. List of Dyslexic Achievers. https://www.dyslexia.com/about-dyslexia/dyslexic-achievers/all-achievers/
This is a list of famous people who have had(have) dyslexia, and it’s a great resource to give an audience insight into the potential a student with dyslexia has; and it’s an encouraging message for students who have dyslexia.

Hannell, Glynis. (2013). Dyscalculia: Action plans for successful learning in mathematics. Routledge.
I am interested in learning about dyscalculia, how it differs from dyslexia, and if any of the techniques used to help students with dyscalculia can be used for those with dyslexia.

Henderson, A. (1998). Maths for the dyslexic: A practical guide. David Fulton.
This book gives a detailed and comprehensive account of teaching strategies that can be used to help students with dyslexia in several specific areas of mathematics: number, algebra, shape, space, measurement, data.

Jane Roitsch, Silvana Watson, An Overview of Dyslexia: Definition, Characteristics, Assessment, Identification, and Intervention, Science Journal of Education. Vol. 7, No. 4, 2019, pp. 81-86. doi: 10.11648/j.sjedu.20190704.11
This is a frequently cited paper on dyslexia from a technical psychological perspective. I have chosen this article because it gives an extensive overview of dyslexia, its characteristics, assessment and identification, and in particular it addresses intervention techniques.

Leong, C. K., & Jerred, W. D. (2001). Effects of consistency and adequacy of language information on understanding elementary mathematics word problems. Annals of Dyslexia, 51(1), 277-298. https://doi.org/10.1007/s11881-001-0014-1
This is an interesting paper on how the way word problems are constructed, and the language used in them, can affect all students and those with dyslexia. They also investigate how students cognitively process these word problems which can provide much insight into how to support students with learning differences.

Sandman-Hurley, K. (2013, July). What is Dyslexia? [Video]. TED Conferences. https://www.ted.com/talks/kelli_sandman_hurley_what_is_dyslexia
A short informational video to help the viewer appreciate dyslexia. This gives good background information and may help me relate this topic to an audience.

Soiffer, N., & Larson, J. L. (2020). Rainbow math: A case study of using colors in math for students with moderate to severe dyslexia. (pp. 401-409). Springer International Publishing. https://doi.org/10.1007/978-3-030-58796-3_47
The authors investigate whether differences in font, colour and spacing influence the performance of students with dyslexia. This is interesting because it covers a few strategies that could potentially aid students with dyslexia in the classroom.

Turner Ellis, S. A., Miles, T. R., & Wheeler, T. J. (1996). Speed of multiplication in dyslexics and non-dyslexics. Dyslexia (Chichester, England), 2(2), 121-139. https://doi.org/10.1002/(SICI)1099-0909(199606)2:2<121::AID-DYS31>3.0.CO;2-V
This paper compares several aspects of how students with dyslexia perform multiplication compared with students who do not have dyslexia. This interests me because it provides insight in how dyslexia may affect mathematical ability and performance.

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.

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.