WEEK 3: Activity Reflection: Human-Made VS Living Things

HUMAN MADE VS LIVING THINGS

What kinds of lines and angles did you see in most living things? How about in most human-made things? Are there typical lines and patterns that show up in living things vs. human-made things? Any exceptions to this?

Living things: trees, plants, snow.
These items all have complicated fractal-like patterns to them, requiring more attention and focus when trying to draw them. They seem to have more dimensions to them and more detail to include. Angles seem to be pointing upwards, towards the sun, 45 degrees or smaller in relation to the main trunk. I thought my pine trees in the back were an exception with the pointing down stricture, but as I look out at the trees again, I realise my drawing is false and they actually point up! This is not an observation I have ever made before as I have always sketched these branches going down.

Human-made things: road sign, power lines, building, window, parking lot, road.
These items were very linear, many straight lines and near-90 degree angles, they took a fraction of the time to draw, and were very simple structures to add to a page.

My drawing!

A photo of my view!

Why do you think these patterns exist (if you notice patterns, that is!)

I believe that the patterns in living things exist for optimal living conditions, plants and trees are built to sustain the weather, and be positioned in the right way to prioritise photosynthesis and optimize it. While humans are smart, we are nothing compared to nature, so keeping things linear and at simple angles makes construction and maintenance easier.

How might you use close observation and drawing or sketching to help your students learn about lines and angles?

This is a great way to start the conversation of the living world, and patterns and angles in real life, allowing students to draw the connections between math and the world.

Are there ways to experience lines and angles through whole-body movement or large body motions outdoors? In relationship to the living world?

I will continue to reflect on this. I did my drawing from inside as it has been -30 degrees Celsius this week, I was not able to sit outside while drawing. But I will be mindful of this when the polar vortex moves on and spending time outside is enjoyable again!

WEEK 3: Reading Reflection

SUSTAINABILITY EDUCATIONS GIFT: LEARNING PATTERNS AND RELATIONSHIPS

Traditional education contributes to the sustainability crisis by isolating academic disciplines from real-world contexts. In contrast, sustainability education teaches through patterns and relationships. The Learning Gardens model in Portland illustrates this shift by replacing mechanistic frameworks with systems thinking and holistic learning. This pedagogical approach is multicultural, interdisciplinary, and multisensory, integrating core subjects like mathematics and science with hands-on gardening. By embedding pedagogy in "place," students develop ecological literacy and recognize that the "web of life" is a network where the whole is greater than the sum of its parts. Such programs address critical social justice issues, including childhood obesity, food insecurity, and urban disconnection from nature. Through active participation, students cultivate a sense of ownership and belonging, discovering that the health of individuals, the land, and the community are intertwined. Ultimately, this model fosters an ethic of care, empowering students to perceive the hidden connections that define a sustainable world.

STOP #1: “The project is guided by several urgent issues nationwide: (1) The percentage of hungry children in the state of Oregon and nationally is increasing; (2) Obesity and diabetes among children are on the rise at an alarming rate; (3) The gap between the academic performance of white and ethnic minority students is growing; and (4) Students in urban schools are particularly vulnerable to a loss of connection with nature and to the source of food, which on an average gets shipped thousands of miles.” (p.43)

Although this quote speaks for itself. It did make me stop reading for a minute and think about how sad this is. Many of the children in these situations are in them due to external factors that they cannot control, but we as educators can make a smidge of a difference for these kids by exposing them to these types of sustainability projects.

STOP #2: This type of project “wove community service as an important component of this learning.” (p.45)

Community service used to be a requirement in school. We should be bringing it back. There are so many benefits to community service including social skills, which honestly many teenagers lack now. Community service also usually entails working in a group, and that requires that students “learn group dynamics” (p.45). An essential skill for the future as you will always have to work in some sort of group environment at some point, and being able to navigate those dynamics is crucial. If we can teach students these skills before throwing them into the workforce, that would set them up better for success.

STOP #3: “[...]because of the issues of obesity and diabetes increasingly affecting young children and youth, matters related to food are coming to the forefront.”

We are also seeing the flip side right now in teenagers, specifically girls, eating disorders and the obsession with “skinny” is currently a hot topic in our grade 8-10 girls. As a coach, I am continuously having conversations about the importance of food and healthy eating, and the impacts that your body may face if it is not fueled properly, or at all. These are all important things that students need to learn, but they aren’t exactly written into our curriculums, but by bringing in cross-curricular sustainability projects, we can embed them into the project while still hitting curricular points.

QUESTION: Can you think of another type of project that may contribute to sustainability while also hitting curriculum in multiple subject areas?

Week 2 - Reading Reflection

 TACTILE CONSTRUCTION OF MATHEMATICAL MEANING: BENEFITS FOR VISUALLY IMPAIRED AND SIGHTED PUPILS

This research explores how tactile learning activities can enhance mathematics education for both visually impaired and sighted students in primary classrooms. By moving toward a universal design approach, the authors argue that exploring shapes through touch helps all learners uncover hidden geometric details that vision alone might overlook. The study highlights how these inclusive practices challenge ableism by valuing diverse sensory perspectives rather than treating disability as a deficit. Findings suggest that when students engage with multimodal tasks, they develop a more versatile and comprehensive way of thinking mathematically. Ultimately, the paper demonstrates that such integrations of different perspectives benefits the entire class while fostering a more equitable and supportive learning environment. The study focuses on a grade 5 lesson where students used Wikki Stix (flexible wax and yarn tools) to explore shapes through touch while their eyes were closed.

Wikki Stix

BIGGEST STOP! I really appreciated how this study not only focused on tools and tactics that can help deepen mathematical understanding, but it also challenged societal injustice and hit a huge social justice issue - ableism. If we can shift towards such ways of inclusive education, we are not only teaching on a deeper level and creating more knowledgeable beings, but we are also de-stigmatizing and creating better members of society!

STOP #2: I really loved the flow from week one into this article. The focus on different perspectives was really enlightening and I feel will be and already is a huge part of this course. The emphasis in this article was on how different perspectives through senses allows for deeper understanding.

The researchers conclude that universally designed tactile tasks benefit the entire class by allowing every pupil to develop a broader range of ways to think mathematically. By inviting all students to experience mathematics through the same sensory tools, educators can create a more inclusive environment that values diverse forms of meaning-making.

QUESTION: Can you think back to a time in your educational path (before this week) where you learned math with your hands? 

Stylianidou, A., & Nardi, E. (2019). Tactile construction of mathematical meaning: Benefits for visually impaired and sighted pupils. In M. Graven, H. Venkat, A. Essien, & P. Vale (Eds.), Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 343–350)

Week 2 - Activity Reflection - PLAYING WITH MATH (& FOOD)

FLEXAHEXAGONS!!

While watching Vi Hart's videos on flexahexagons, I decided that I had to make one. I attempted this before even making it to the "how to" video and was actually quite successful... I could have had sharper edges and perhaps my triangles were not perfect equilateral triangles, but my flexahexagon did the job. While going through the series I was starting to add shapes of different colors, and added the arrows of direction. I was surprised to notice that when you flip it and starting turning it from the opposite side, you end up with the shapes in different orientation. Although I didn't (and still don't) fully understand what I was playing with or the full mechanics on how it worked, I was having fun. While watching Vi Hart, I noted down a few quotes that stuck with me:

“Mathematics is about making things up and seeing what happens.”

“Sometimes its more fun to let my hands solve the problem”

“You can think about it first or you can just try it.” “Sciencing your math is a good way to check your thought process and inspire your thinking”

Check our my flexahexagon here!: Taylor's Flexahexagon

BAGEL MATH ART!!

Bagel art was really fun. It took 2 bagels to get it right. The first I biffed but it allowed me to understand the cuts and why those cuts led to this result:



Watching the video was kind of boring, but working with my hands alongside the video was satisfying. I was creating something while learning, and when I finally got it on the second bagel, I was very proud! After this activity I believe that creating and learning with my hands (and food) allowed for a greater level of satisfaction to the end result and the learning. Although the flexahexagon was fun, and felt like the creation of a fidget, I didn't get the same level of pride because I didn't fully understand it as quickly or as well as I did the chain-linked-bagel.
Sometimes just watching the video does not allow us to fully understand the created piece. We cant move it to look at it from different angles/ perspectives. We can feel where the twists are or how the texture or thickness may be different, and we definitely cannot learn from trial and error like I did with bagel #1. Hand on allows for more play, more mistakes, more learning... although this would have been much easier if my bagel wasn't already pre sliced, I factor I did not consider when doing my groceries.
I think that this type of learning explores and enhances students senses, but not only working on cognition skills but by pushing all students to use diverse senses to work towards a common goal. I think that this aligns well with Stylianidou and Nardi's concept of working towards universal design rather than adapting to certain "disabilities" (2019).


QUESTION: How do the quotes mentioned above by Vi Hart resonate with you? Will this affect your way of thinking about math? How does the idea of playing with your food to learn math make you feel (my mom would not have been impressed!)?


Stylianidou, A., & Nardi, E. (2019). Tactile construction of mathematical meaning: Benefits for visually impaired and sighted pupils. In M. Graven, H. Venkat, A. Essien, & P. Vale (Eds.), Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 343–350

Week 1 - Activity Reflection - BODY MEASURING

 Oh how I love measuring...

STORY TIME: I am a body measurer through and through. I use my hands, arms and feet to measure things all the time. As someone with a partner who is extremely OCD when it comes to things being centered and straight, I can proudly say that I am very good at my body measuring. I hung Christmas lights all through the hallway of our house, draping from one side to the other, perfectly distanced hooks were confidently installed, using my head as a "center" from both my hands (yes we checked it after, it was quite accurate). This was not meant to be a abstract way of measuring, this was simply a "I don't feel like finding a measuring tape, nor do i feel like actually spending time measuring, I got this" moment. Reading this short except on different body types used to measure, I then realized that I do this a lot... 

My beautifully spaced ceiling hooks for Christmas lights!

ACTIVITY: As I sit here in my kitchen, my love-for-projects brain thinks about what my next update in my kitchen may be. As I look around, I realize that I used my feet when I measured to see if my new table would fit before I bought it. Not to brag but I have a almost-perfect-foot foot, so measuring with my feet is quite easy. I decided to consider a back splash, as we don't have one right now. Using my arms and hands for convenience, I found that my backspace is roughly 14.5 cubit's squared. Rough translation to m^2, that about 7.25m^2. This was with a little extra, since when purchasing material you always account for a few little errors! This MAYBE took me 35 seconds to measure, far quicker than finding a measuring tape, measuring, and doing the math... just saying! 

EXTENSION: This strategy can be used for almost anything, I used it for spacing in my garden last spring, I use it to decorate for holidays, for figuring out how much supplies I need, for hanging things on the wall, you name it. I love the idea of teaching students how to use such a practical and useful way of measuring. I did a massive garden project last year and would love to incorporate this into it as a modification and upgrade to the unit this year. This could also be a fun way to show the uniqueness of using our own bodies, everyone measures the same thing with their own self, and then we compare how many hands/feet/cubits/etc. everyone got and then see if when converted to standard measuring units, how accurate was everyone?!

Week 1 - Reading Reflection!

 Gesturing Gives Children New Ideas About Math - Summary and Reflection

Article Summary: This study investigates how hand gestures facilitate mathematical learning in children. Researchers found that children required to produce correct gestures during a math lesson learned more than those producing partially correct or no gestures. The hand gestures that were pointing and making a “V” with two fingers to symbolize grouping. This effect was mediated by children extracting information from their own hand movements (that were modelled) and adding the word “grouping” to their spoken repertoire. Notably, the grouping strategy conveyed through these gestures was never verbalized by the teacher, implying that children developed new ideas specifically through their physical movements. The authors suggest that body movements can play a large part in creating new knowledge rather than just processing old ideas, like many other studies suggest. Ultimately, the research indicates that educators may lay foundations for learning by simply instructing students on how to move their hands, and with time and practice these gestures will lead to greater success. 

Stop #1: “[...] people use hand gestures when no one is watching [...]”

This partial sentence made me stop reading and reflect on my own gestures. People often comment on how much I “talk with my hands” and I often hit things (ex: knock things off my desk) when teaching or talking to others. I then reflect on when no other eyes are around; I drive with my knee or one hand when I am on the phone and I put my phone on speaker phone at home so that I can gesture. Clearly gesturing is a big part of speaking for me. 

https://advancingwomenconference.ca/2021/09/12/talk-with-your-hands/

Stop #2: The notion that the word “grouping” was never used, but students incorporated it into their post lesson speech. 

This made me happy. I find it fascinating when the human brain can process and create things subconsciously, but it is even more fascinating when multiple brains do the same thing without human-human interaction. “[...] gesturing can facilitate learning by helping children extract information from their own hand movements”. The importance seems to lay on what gestures are modelled. In this case the use of a “V” later indicated to students minds how this was a grouping method and then they later understood that and were able to verbalize. I use a similar notation when teaching order of operations, where I group each step using a “V” on paper. I am curious to see how students would translate this to speech, perhaps something I will try! 

Notes from Ms. Taylor's SST Math Class.

Question: What hand gestures do you use when teaching? Have you ever paid attention to them? Is this something you would explore more to enhance student success? 

Citation: Goldin-Meadow, S., Cook, S. W., & Mitchell, Z. A. (2009). Gesturing gives children new ideas about math. Psychological Science, 20(3), 267–272. https://doi.org/10.1111/j.1467-9280.2009.02297.x

Hello World!

 Hello everyone, I am Taylor! I teach senior math in small town Quebec. These are my babies, who love ice cream very much! 

This is Nelli! 

This is Archie!