Final Project Draft

 Here is the link to my Draft Project EDCP 553 Project Gill

Week 9 (Mathematics & traditional and contemporary practices of making and doing )

Reading Reflection:

Excerpts from Sharon Kallis, Common Threads: Weaving Community Through Collaborative Eco-Art 

The Chapter titled “Building for the Change from Ground Up” is from the Book Common Threads : Weaving Community through Collaborative Eco-art “ by Sharon Kallis. This reading is about promoting local production of goods and services that we so heavily rely on external resources, industry - all dictated by purchasing power.

STOP 

The act of learning to make for personally use what we have previously purchased is perhaps the most fundamentally important gift we can give to ourselves.

This statement really resonated with me. In today’s fast paced lives, we depend so much on the consumer industry. Most recent example being when we decorated our new home with market bought expensive wall hangings. Recently my mom had gone back to India, and she brought 3-4 of the art work pieces that she had made herself. We framed those and have replaced our “expensive wall hangings” with mom’s art work. The beauty of it, and the fact that we are able to relate more with it, and mom can talk about her work gives so much peace, satisfaction and just brings a new life to the walls of our home.

STOP

It is really important to be able to step outside of the consumer lifestyle….if you think about how a lot of kids have grown up the last few decades, not having any agency outside shopping…wanting something, getting it, being disappointed and then looking for ht next thing…..whereas when you make something…you share the skills for making something with others and people value that –its an incredible thing, there is a real worthiness to that.

Again, this really struck the chord with me as these days as a parent I am feeling frustrated with how quickly the kids lose interest in a toy and want another new one. Reflecting back to my childhood, we dint have many toys- and found value and interest in the select few ones we had. The point shared here above that when you share the skills for making something with other - there is a real worthiness to it. My husband & I recently had a debate about that he wants to get a outdoor swing and play set  to be placed in the backyard (worth $1500)....I am against this type of setting. He says the kids should have something to play with outdoors. But now I am thinking what can we create with them outdoors - involve them in the process. Starting at very basic, I think we will start by getting kids to grow their own mini vegetable garden in the backyard….something they will take care of, and take proud in watching the crops grow. 

Activity

For this week’s activity I tried doing the 5-strand braid with my daughter’s hair, it just turned out to be a big mess and my daughter dint have patience to sit through another of my tries. So we stuck to our standard three strand braid. As we do the three strand braid on a regular basis, I dont have to think about the process that goes behind it. My husband on the other hand has never tried doing braids. So for this activity I guided him through the process of doing a three strand braid. Finally after many tries, he did get the hang of it…here is a pic of his attempt of braiding my hair. He described the whole experience as a very unique way in which our hands and brain are working together to make a beautiful pattern.

Week 8 (Mathematics & fibre arts, fashion arts and culinary arts )

 Reading Reflection:

 Gwen Fisher (Bridges 2015) Highly unlikely triangles bead weaving

In this paper Gwen Fisher has described their work on using impossible triangles and its variations to create a series of sculptures with beads using a bead weaving technique. The beaded art objects generated surfaces that twist like Mobius bands around the objects. 

STOP - What are impossible triangles

This is an unfamiliar subject to me, So I took some time to understand the concept of impossible triangles. As per Fisher(2015), impossible triangles are two dimensional drawings that represent three straight beams with square cross sections and the beams appear to meet at right angle. An impossible triangle is only impossible to be constructed in 3d (assuming edges are straight and connections are right angles. While in two dimensional drawing, they are not actually impossible, they just seem to twist in an impossible way. Below is an image for impossible triangles:

STOP - Beading the highly unlikely triangle

Fisher states that a beaded version of an impossible triangle is very much possible because of flexibility of beadwork. In the beadwork, the twist allows the impossible triangle to be constructed in 3d. 

This was very interesting to me as it doesnot appear very intuitive. The figure below shoes the highly unlikely triangles in three sizes:

Fisher showed in detail about how to convert an impossible triangle into a beaded version. As depicted in the image below, they talked about imagining the beams as little cubes. And then place beads on each line segment of the cube so that the hole of the bead is aligned with the line segment. 

Then beads are woven together with the beaded cubic right angle weave (I didn't fully understand this technique just by looking at the images)

Overall, the work as described in the article at first glance was very confusing and beyond comprehension for me. Upon reading multiple times and deeper analysis, I got some basic idea of the complex beading technique that was involved in creating beaded versions of impossible triangles.

In my teaching practice, I have only used beading in making bracelets to show repeated patterns in terms of repeated rows and columns and have also used beading for helping to learn area and perimeter. 

I have not used beading for anything more complex or anything remotely similar to constructing impossible triangles.

Question - In what context have you used beading in mathematics classrooms? 

Activity

 

For the activity this week, I tried shoe lacing activity. I chose this activity as  lately I have observed that I am not very good at tying my daughter’s skating shoe laces. My toddlers have been wearing the Velcro shoes, and my older one recently started her skating lessons, and I have been helping her tie the shoelaces  but I have noticed that in the just rush of getting her ready of skating lessons, I have been ending up with either uneven length of laces ends or too short of ends. This morning I tried to tie her laces with a different method, but in the end I had to come back to criss cross tying as that's the only technique I have ever used myself and seems very intuitive. Any other method seems very confusing. I would definitely be going back to the video as this is something I would like to improve on especially to make the lace tying more clean and neat looking.

Week 7 (Mathematics and Poetry)

 Reading Reflection

Radakovic, Jagger & Zhao: Writing and reading multiplicity in the uni-verse

This paper starts with  the analysis of two poems ( A Love Letter by Nanao Sakaki ) and the poetic response by one of the authors of this paper ( My Universe by Nenad Radakovic). The second author Susan Jagger then brings poetry to her elementary mathematics teaching methods course and invites students to write poems about their place and connect it to explorations of place. The focus of the paper is on analysis of the various poems written by students.

STOP

The poem A Love Letter by Nanao Sakaki is a beautifully written example of how mathematical themes of scale, measurements, distance, geometry, concentric shapes and imagery have been interweaved and threaded along with the personal emotions that are vividly expressed throughout the verses. The authors of this paper have described this poem as a disciplinary interplay between mathematics and poetry. This poem is a great example that  I can foresee using in my own classrooms that will help students make real life connections between mathematical measurements and their lived experiences.

STOP

The meaning of a poem is not a fixed characteristic in the process of it reading but rather it is created by the reader using a repertoire of interpretive strategies including cuesand schemata provided by external resources to construct their own textual understandings (pg.4)

Embracing Multiplicity - One of the key takeaways from this paper was that any given poem can be interpreted by readers differently. It is very important to acknowledge that the meaning of the poem not only lies in the structure of the poem but is also influenced by the reader. There can be multiple meanings and interpretations of the same poem by different readers. 

Video

Luisa A. Igloria - Infinity is not a number  - This poem depicts that even though infinity for most part is useless and holds no value, it reflects the vastness of the universe which goes beyond the countable numbers.

Lawrence Mark Lesser - E(X) - Creative representation of the expected value, E(X), is the mean of all possible outcomes of a statistical experiment where each outcome is weighted by its probability. The poem explores expected values in the context of social media.

Dan May - Eight Minutes - Poem written as a cadae. It is structured by the mathematical constant π in two distinct ways: it possesses five stanzas of 3, 1, 4, 1 and 5 lines (in that order), and the poem’s 14 lines consist of 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, and 7 syllables (in that order). 

Pedro Poitevin  - The author first started writing poetry as mathematical palindromes. Eventually he moved to writing free verse.  “I write poetry because doing so helps me exercise a form of attention, one that benefits from varying degrees of freedom and constraint.” (Pedro Poitevin)

Kate Jones - Climate Extinction  - A strong piece of statement on climate change:

It would be a pity, don’t you think, For humans to vanish in a blink 

Activity

For the activity this week, I wrote PH4 poems . My first poem draws inspiration from the significance of the month of February for me - Valentine Day, Family Date, Anti-bullying - Spread kindness - My heart is so full of love.

The Second poem reflects my learning experience in throughout this MEd program

Week 6 ( Mathematics and dance)

 Reading Reflection :

This week I chose the following reading:

Jim Henle (2021). Mathematics that dances.

This was a fun reading and I got some great ideas about some activities that can be used in a classroom as a warmup exercise or icebreaker activities. The authors started the article with a disclaimer that this article is for mathematical structure that gives us pleasure. Usefulness, significance or truth are not the point of this column. (I appreciated this honest disclaimer - many times I have wondered -that if I am the only one who is not able to see or understand the mathematical curricular connections of a particular fun activity that is presented in conferences, or pro-d days etc. Some activities are meant for pure pleasure and as an educator that gives me a lot to think about  - often times we are so involved in trying to find the relevance or usefulness of what we are teaching  that the fun element tends to be overlooked). Definitely a food for thought - how can I make my classroom a more pleasurable experience for the children.

I enjoyed the various examples of mathematical dance structure activities shared in this article - Change ringing exercise, Challenge square dancing, juggling, Boxtrot. I would recommend book marking this column if you are looking for some creative fun activities to do with your class. The one activity that really stood out to me - I am sharing here and will be definitely using in my classroom as a fun icebreaker. 

Triangle Game : The participants of the game spread out randomly. Each player mentally (silently) selects two of the other players as “partners.’’ Then, when the organiser tells them to start, everyone moves, attempting to form an equilateral triangle with their partners. Of course, those partners are in turn seeking their own equilateral relationships.

Question :  Is there a particular fun activity/icebreaker game that you use in your classrooms or gatherings for a group activity.

Activity  

 I chose to do the clapping hands activity - did it with my family at home as this was our second consecutive week being sick at home. 

Clapping hands is a great exercise in terms of lessons and sequences and I can totally see this being used in a math classroom for younger children. My 3 year old really enjoyed this activity, it did take her some time to get a hang of what we were doing., but gradually she seems to be grasping the ideas of patterns. We combined the clapping hand activity with counting, so it was easier for kids to follow. It was 5 of us doing the activity. So our pattern looked like this:

 1 1 1 1 1       12  12  12  12  12  12       123  123   123   123   123  ………..

Overall, I thought this weeks’ readings and activities were fun and engaging and intriguing and can especially be used with younger children.

Draft Outline for Course Project

Project by : Kanwaljit Gill

Bringing Yoga into Math Classrooms

Grade Level : Intermediate (sd42)

Outline : 

• I am preparing a resource that educators of intermediate grade level can adapt in their own classrooms in terms of integrating the practice of yoga in their classrooms and exploring the various concepts of mathematics and science that tie along with different asanas.

• Cross-curricular - Physical Education, Mathematics and Science

• Mathematical Concepts - Lines, Triangles, Angles, Symmetry, Sequence and patterns, Fixed point theory

• Science concepts - Joints and movement of joints

• Physical Education - Whole body fitness and movement

• Pedagogy with focus on learning through movement and whole body collaboration 

• Outdoor Education ( Building connection with mother nature) - practising yoga outdoors

• I am still figuring out the exact details, but my broader vision is that students will be introduced to a sequence of yoga asanas e.g Sun Salutation sequence - and they will learn to mathematically analyze the various different poses in the sequences in terms of angles formed by different body joints. As a certified 200 hr yoga instructor, I am very excited about being able to tie my love and knowledge of yoga into the math classroom. 

Annotated Bibliography:

Bhambhani,A. (2022). Yoga asans with correct mathematical movement for optimal health benefits. Journal of Emerging Technologies and Innovative Research, 9(2), 814-841.

In this article by Dr. Ambika Bhambhani, the focus is on using mathematical concepts to improve and correct the yoga poses for optimal results for mind and body regulation. Different yoga asanas (poses) have been described in detail to highlight the concepts of math, particularly geometry (angles, lines and shapes) involved in body movements and poses.

Chezhiyan, P., & P, D. (2019). Joint-angle-based yoga posture recognition for prevention of falls among older people. Data Technologies and Applications, 53(4), 528-545. https://doi.org/10.1108/DTA-03-2019-0041

The focus of this paper is on identifying angle limits of sitting and standing postures with a focus on identifying parameters so as not to overstress the hips and joints. The authors have designed a posture identification framework comprising the sitting and standing postures that are fundamental to all yoga asanas, using joint angle measurements.

Cox, D. G. (2018). Yoga's flexibility in math. Strategies (Reston, Va.), 31(4), 45-49. https://doi.org/10.1080/08924562.2018.1467184

This paper by Dannon Cox (2018) highlights the importance of integrating physical education in Math classes to help support the development of holistic programming in our education system. In this article, various examples have been provided in the form of a series of illustrations that demonstrate basic maths skills in two dimensional drawings of yoga poses.

Kelton, M. L., & Ma, J. Y. (2018). Reconfiguring mathematical settings and activity through multi-party, whole-body collaboration. Educational Studies in Mathematics, 98(2), 177-196. https://doi.org/10.1007/s10649-018-9805-8

This  article  by Kelton & Ma describes the two case studies which involve using movement and whole body collaborations to engage learners in mathematics. The findings from the study highlight how the whole body collaboration can transform mathematical learning both outside and inside the classroom. 

Omkar, S. N., Mour, M., & Das, D. (2011). A mathematical model of effects on specific joints during practice of the sun salutation – A sequence of yoga postures. Journal of Bodywork and Movement Therapies, 15(2), 201-208. https://doi.org/10.1016/j.jbmt.2009.07.008

In this article, one of the most common yoga sequences - the 10 poses of sun salutations has been analysed for its clinical benefits. A mathematical model has been developed in terms of angles formed by movements of joints during the sun salutation sequence based on rigid body mechanics.

Subedi, K., Panthi, D., Jha, K., & Bhatta, C. R. (2021). role and importance of sthira bindu (fixed point) in yoga philosophy. International Journal of Research - Granthaalayah, 9(6), 311-329. https://doi.org/10.29121/granthaalayah.v9.i6.2021.4022

This article analyses the art of yoga from a philosophical perspective keeping the practice of meditation at the forefront. The role of fixed (sthira bindu) in yoga meditation has been investigated in this paper from a mathematical perspective (through the lens of The fixed point theory - one of the learning theorems of mathematical perspective).

 

Week 5 (Developing mathematics pedagogies that integrate embodied, multisensory, outdoors and arts-based modalities)

 Reading Reflection:

Kelton & Ma: Reconfiguring math settings with whole-body, multi-party collaborations

 This article was a challenging read for me and took me longer than expected to read and comprehend.  This article was a study that examined how the whole body collaboration can transform how learners experience learning environments and make sense of important mathematical ideas. 

STOP  In the first case study presented, students chose homespots in a fixed physical space (school gym) and a long blue tape line that went across the gym. The students took part in various activities that involved problems around co-ordination and developed strategies for movement along the blue taped line. Students were treated as physical objects that occupied a space on the number line. Co-ordinating the movements of all students was the major focus of the mathematical practices that went along with this activity. 

STOP - The fact that students were moving and doing math physically rather than on pen and paper. Understanding the relationship between physical space and their body movements from the angles of  integer, fractions was a very cool concept and gave me practical ideas about something that I can try in my own classroom. I am actively seeking ways in which I can incorporate movement in maths classroom as I have been noticing that  in my classes the students are spending most of their time sitting in one spot which can be quite challenging for students as our periods are 90 minutes long. I do try to incorporate movement breaks (stretching, laps around the school etc). But I haven't tried a movement activity which directly relates to doing and learning math.

Activity - 

I enjoyed Sarah Chase’s videos on dancing combinatorics. Personally, I really am a slow learner when it comes to coordinating and balancing. So I got to thinking about a simple beginner level activity that will be easy to comprehend and teach for me as a teacher and easier to comprehend for my students.

As it so happens that I was home sick all this week, I ended up trying this activity with my kids at home. I kept the focus on simple counting for my three and half year old.

We came up with a movement sequence:

1 step forward, 2 step back, 3 step to left, 4 step right, 5 step forward, 6 step back, 7 to left, 8 to right.

And repeat. I am including a rough sketch of my initial vision for this movement sequence:

This was a really fun one to try with young kids at home and as an extension of this activity for older kids, we could integrate the concept of distance vs displacement in terms of vectors. The sequences of steps can also be in various different patterns as multiples of 2, 3 or 4 or skip counting. 

I think, depending on the grade level and math concept being covered in class, this activity can be modified accordingly and is a simple yet powerful and engaging example of incorporating movement in a mathematics classroom.