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.