Draft Proposal

 

Exploring Math Concepts through Bharatnatyam Dance Form

“Incorporating music, art, role-playing, and games into the curriculum” made the lessons engaging to learners.” (Iyengar,2015). As educators, consider how to best facilitate understanding (Gerofsky,2015) poses an intriguing question: “When learners are approaching a new mathematical topic, would it be helpful for them to hear a mathematical relationship, to touch it, or to know it through movement?” These perspectives made us incorporate innovative teaching methods through dance that cater to individual learning needs. 

 

Objective: 

Classical dance forms like Bharatanatyam,  Kuchuppudi, Kathak, Mohiniyattam represent culture and tradition of people through different stories. In this project we aim to integrate math and classical dance forms to generate embodied math learning which helps students to get more connected to math ideas, especially geometry. Concepts like angles, geometry, parallel lines symmetry, pattern, transformation and coordinate plane can be taught by these classical dance forms in an outdoor setting. 

 

Grade Level: Elementary and Primary Level                             

Project components

Introduction to classical dance forms especially we are taking basics of Bharatanatyam, a popular dance form of state Tamilnadu, India. 

Explanation of various geometrical shapes formed through hand movements in Bharatanatyam, including triangles, right angles, line segments, diagonals, half circles, circles, diamonds, obtuse, and acute angles, polygons, coordinate planes and points etc. 

Comparison with different dance forms like Ballet, Tutting, and Latin Dance. 

 Outdoor Geometry Activities:  

 Engage students in outdoor activities to visualize and understand geometric concepts. Create large-scale shapes on the ground using ropes or chalk to represent angles, parallel lines, and coordinates. Encourage students to create their own steps and dance positions. 

Coordinate Plane and Graphs:  

Introduce the coordinate plane using outdoor spaces. Relate dance movements to coordinates, allowing students to see the connection between their body positions and points on a graph. 

We have found different articles related to math and arts.  

Bibliography

        Mannone, M., & Turchet, L. (2019). Shall We (Math and) Dance? In MCM (pp. 84–97). Springer International Publishing. https://doi.org/10.1007/978-3-030-21392-3_7 

        This paper explores the intersection of mathematics, computation, and music, investigating the potential of mathematical principles in enhancing dance experiences. Maria Mannone and Luca Turchet delve into how mathematical concepts can be applied to music and dance to create innovative and engaging performances, posing the question, "Shall We (Math and) Dance?" 

 

      Alida Anderson (2015) Dance/Movement Therapy's Influence on Adolescents' Mathematics, Social-Emotional, and Dance Skills, The Educational Forum, 79:3, 230-247, https://doi.org/10.1080/00131725.2015.1037512 

       This paper explores the intersection of mathematics and music, focusing on the influence of dance/movement therapy on adolescents' mathematical, social-emotional, and dance skills. 

Taeao, S., & Averill, R. (2021). Tu'utu'u le upega i le loloto—cast the net into deeper waters: Exploring dance as a culturally sustaining mathematics pedagogy. The Australian Journal of Indigenous Education, 50(1), 127-135.

doi:https://doi.org/10.1017/jie.2019.17 

 This paper is about the innovative use of dance as a pedagogical tool in teaching mathematics, particularly in culturally diverse contexts. It examines how integrating dance into mathematics education can support cultural sustainability and enhance learning outcomes.

       Radford, L. (2009). Why Do Gestures Matter? Sensuous Cognition and the Palpability of Mathematical Meanings. Educational Studies in Mathematics, 70(2), 111–126. https://doi.org/10.1007/s10649-008-9127-3 

       Radford's paper explores the significance of gestures in mathematics education, arguing that they play a crucial role in facilitating the understanding and embodiment of mathematical concepts. Through the lens of sensuous cognition, it examines how bodily movements and tactile experiences contribute to the palpability and comprehension of mathematical meanings. 

 

        Schaffer, K., Stern, E. & Kim, S. (2001). Math dance with Dr. Schaffer and Mr. Stern: Preliminary edition. Santa Cruz, CA: MoveSpeakSpin.  

        This paper discusses the Whole-body mathematics and movement activities for the K-12 classroom, the studio, and the stage. Enables students to experience symmetry, shape, pattern, combinatorics, aesthetics, and storytelling as unifying concepts in mathematics and dance.

 

       Gerofsky, S. (2013, July). Learning mathematics through dance. In Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture (pp. 337-344).http://archive.bridgesmathart.org/2013/bridges2013-337.html 

         This paper discusses how the expressive medium of dance can enhance understanding and engagement in mathematical concepts, offering insights into interdisciplinary pedagogical strategies 

Kalpana, I. M. (2015). Bharatanatyam and mathematics: Teaching geometry through dance. Journal of Fine and Studio Art, 5(2), 6-17. 

This mixed methods study informed by is designed to recommend a framework for exploring how Asian Indian students can learn basic geometric shapes through Bharatanatyam. The study investigates dance movements called adavus, cultural relevance, integration of elements from dance and geometry, and the implementation of alternate strategies such as dance instruction to teach and learn basic geometric shapes.  

Belcastro, S. M., & Schaffer, K. (2011). Dancing Mathematics and the Mathematics of Dance. Math Horizons, 18(3), 16-20. Taylor & Francis, Ltd. on behalf of the Mathematical Association of America.

https://doi.org/10.4169/194762111X12954578042939

 

This paper explores how mathematical principles underlie different dance forms, revealing the interconnected nature of these two disciplines. Through an exploration of movement, patterns, and geometry in dance, the authors present a distinctive perspective on the manifestation of mathematical concepts in the artistic realm of dance, promoting a cross-disciplinary understanding for both math enthusiasts and dance lovers.

 

Wilson, R., & Wolfson, J. (Year). Mathematics and Dance: Notes from an Emerging   Interaction. Notices of the American Mathematical Society, 68(11), 1926-1929. 

In this paper, the authors discuss the growing connection between math and dance. They share observations on how these two areas are starting to collaborate and highlight interesting connections. 

 

Leandro, C. R. (2018). Interdisciplinary working practices: Can creative dance improve math? Research in Dance Education, 19(1), 74-90. https://doi.org/10.1080/14647893.2017.1354838 

In this paper, the author explores the potential of creative dance to enhance math skills through interdisciplinary working practices. He investigates how integrating creative dance into education could positively impact mathematical learning, offering insights into the potential benefits of combining artistic and mathematical approaches in teaching. 

 

Stern, E. (2021). Pattern Play: The Case for Dance in College Mathematics and Beyond. Journal of Dance Education, 21(3), 158-167. https://doi.org/10.1080/15290824.2021.1939357 

This paper explains the integration of dance into college mathematics education. Exploring the link between pattern recognition in dance and mathematical concepts, the paper makes a case for incorporating movement-based approaches to enhance mathematical understanding in college settings and beyond. 

  

Week 7: Activity Reflection

 

This week, I opted for Sarah Chase's "Dancing Combinatorics: Phases and Tides" activity, and I decided to try it out with my daughters Zainab and Yumna using 3x4 dance sequences. 

after creating the movements, I noticed that along with symmetry and pattern, angles can be taught best by using whole-body movements.

Extended Activity: 

Another method involved Zainab clapping every 4 beats while Yumna clapping every 3 beats. Consequently, they repeated the claps simultaneously after 12 beats, illustrating the concept of multiples, factors, least common multiple, and number patterns. Algebraic variables can also be introduced such as 4m and 3n, leading to form an equation of synchronized point.

Graphical illustration of Beat Activity: A star shows 3 beats and a circle shows 4 beats and can be seen that both beats can overlap after 12 sequences.

Curriculum Sketch:

Issues/ Guiding Questions: 

How can we effectively engage students in mathematical concepts through embodied learning activities like dance, rhythmic beats, and hand movements?

The Story:

The story of exploring mathematical concepts like multiplication and patterns through Sarah Chase’s dance movements and sequences in Math Classroom.

Integrating Embodied Learning & Other Learning:

Embodied learning techniques are seamlessly integrated into the curriculum, allowing students to physically engage with mathematical concepts. Through dance clapping and hand movements, students embody abstract mathematical ideas, fostering a deeper understanding through kinesthetic experiences.

Possible Extensions:

Students collaborate to create dance and rhythmic sequences, experimenting with different beats and patterns to learn multiplication. Students can use dance to explore concepts like symmetry, transformations, and graphs. Students can use rhythmic beats to make algebraic expressions and equations.

Implementing the Curriculum:

Introduction: Introduce the concept of multiples, symmetry, and transformation through Sarah Chase’s dance form.

Embodied Learning Activities: Engage students in dance and hand movement sequences, guiding them to discover patterns and synchronization points.

Reflection & Discussion: Facilitate reflective discussions to consolidate learning, encouraging students to articulate their understanding of mathematical concepts.

Extension Activities: Provide opportunities for students to extend their learning in Algebra and graphs through creative projects, cultural explorations, and interdisciplinary connections.

Assessment: Assess student understanding through performance tasks, collaborative projects, and, allowing for multiple forms of expression and evaluation.

Week 7: Reading "Riley et al: Movement-based mathematics without compromising learning"

  

02-25-2024

Weekly Reflection 

Summary: 

The paper explores the implementation and impact of the EASY Minds program, which integrates physical activity into mathematics education in primary schools. Both student and teacher perceptions were examined to understand the program's potential, challenges, and outcomes.

The study was conducted in grade 5/6 classes across eight public schools in New South Wales, Australia. Students were randomly assigned to either the intervention (n=6) or control (n=4) groups. Teachers in the intervention group received one day of professional learning, a resource pack containing physical activity-promoting equipment, and sample lesson ideas aligned with the NSW mathematics syllabus. They were instructed to incorporate movement-based learning into their mathematics lessons at least thrice weekly over six weeks. The control group continued with their regular mathematics program. Focus group methodology was used for student samples due to time constraints and the potential for group interaction to elicit valuable insights. A total of 66 Grade 5/6 students participated in 11 focus groups. Semi-structured discussion frameworks were developed by the research team for both student focus groups and teacher interviews. 

Some key findings include,

• Students and teachers reported increased enjoyment and enthusiasm for mathematics. Movement-based lessons enhanced students' social, emotional, physical, and cognitive development.
•  The program addressed issues of engagement and disinterest in traditional mathematics instruction. Teachers required additional preparation and creativity but were confident in continuing with the program. 
• Professional development and resource support were crucial for successful implementation. 

A key theme that emerged from both teacher and student groups was that of increased enjoyment and engagement in mathematics lessons. Previous studies emphasize the significant impact of teacher behavior on intervention outcomes, suggesting that teachers' interest in physical activity can influence their effectiveness in delivering movement-based lessons. Incorporating movement-based learning throughout the school day, as exemplified by the EASY Minds program, could profoundly enhance children's attitudes and engagement in mathematics, while also fostering quality teaching and enriching the overall learning experience.

Stops: 

Most students perceived their teacher as having enjoyed the program either due to having liked to "try something a bit different", teaching in new ways, or (more commonly mentioned) not having had to attend to so many discipline problems (e.g., students talking and being off-task, general behavior problems) both during outside and classroom time. 

"I think Mrs. G has enjoyed it too because … she's not so stressed because we're doing something we enjoy, not something that we're going to run off and talk if she's not looking at us. So, I reckon she's pretty happy with that. We're not making so much noise and stuff inside the classroom." 

The comment from a student about the teacher, Mrs. G, enjoying the program because it reduced discipline problems is particularly insightful. It underscores the importance of creating a positive and engaging learning environment where students are motivated to stay focused and on task. It also emphasizes the role of the teacher in facilitating such an environment. 

Reflecting on my past experiences as a teacher in a traditional school, I recall the challenges of maintaining student focus and enthusiasm, especially during math lessons. The monotony of the same curriculum and repetitive worksheets often left me feeling uninspired. Reading about programs like EASY Minds and how they improve student learning and engagement is encouraging. It makes me want to explore different teaching techniques and include more activities that involve movement in my lessons. 

However, during the weekend, when conversing with some of my colleagues from Saudi Arabia, it became apparent that fully incorporating movement-based learning into the classroom seemed impractical for them. They cited challenges such as the need to meet curriculum requirements and lack of teacher training in this regard. 

Question

My question is how do you think movement-based learning could be adapted to suit different classroom settings, considering factors like curriculum requirements? 

Week 6: Activity Reflection

From the 2014 Bridges conference, I chose the artwork by John Arden Hiigl (1943-2017),  a painter, teacher, and humanist. As an artist and thinker, he was largely inspired by the oeuvre of Richard Buckminster Fuller. John's artwork has contributed to Fuller's exploration of the geometry of space uniquely and brought synergetic arts onto a new level.

Chrome 203 shows twelve groups of three '3/4 squares'. Each group of three '3/4 squares' is enclosed, or contained within a white square, which itself is enclosed within a black square. These three '3/4 squares' groups are translated vertically and horizontally. Of course, any of these fractal-like series of '3/4 squares' can continue indefinitely or to the limit of one's drawing instruments. 

The following is my replica of Chrome 203,

 

I arranged sixteen sets of '3/4 squares' on an inch of paper. I used two different versions in alternating rows and these sets of squares are enclosed in a white square which is further enclosed in a blue square. These sets of three '3/4 squares' are translated vertically and rotated by 90 degrees. The piece has visible vertical lines of symmetry. these fractal-like series of '3/4 squares' can continue indefinitely or to the limit of the space of one's drawing tool.

Reference 

https://experienceworkshop.org/farewell-to-john-hiigli-our-mentor-and-friend/

Reading Week 6: Dylan Thomas & Doris Schattschneider (2011) Dylan Thomas: Coast Salish artist, Journal of Mathematics and the Arts, 5:4, 199-211, DOI: 10.1080/17513472.2011.625346

  02-19-2024

Weekly Reflection 

Summary:

The article delves into the rich cultural heritage of the Coast Salish people, focusing on their traditional arts and the revival of their artistic traditions in the modern context. It also highlights the historical significance of Coast Salish art forms such as spindle whorls, carvings, and woven crafts, integral to their culture and identity. The narrative also discusses the impact of colonization and urbanization on traditional Salish communities, leading to the decline of their artistic practices. The paper provides a comprehensive overview of Coast Salish artist Dylan Thomas's artistic journey, emphasizing his mastery of mathematical concepts within the context of Coast Salish art and his ability to bridge cultural divides through his creative expressions. 

Thomas's artistic endeavors, particularly his tessellation works such as "Salmon Spirits" and "Infinity," showcase his fusion of Salish design motifs with mathematical precision. Drawing inspiration from the tessellation techniques of M.C. Escher, Thomas adeptly incorporates rotational symmetry and intricate patterns to create visually striking compositions. The discussion provides insights into the meticulous process of designing tessellations and the mathematical principles underpinning them.

 

Thomas's exploration extends beyond tessellations to encompass other traditional Salish art forms, such as houseposts. His conceptual designs, exemplified by "Ravens Housepost" and "Eagles Housepost," demonstrate his reverence for Salish cultural heritage while offering innovative interpretations of traditional motifs. 

Moreover, Thomas's artistic evolution includes a cross-cultural exploration of mandalas, inspired by Eastern philosophies and sacred art traditions. His piece "Mandala" reflects a harmonious blend of geometric precision and Salish symbolism, highlighting his work's interconnectedness of diverse cultural influences.

Finally, Thomas's print "Infinity" is a culmination of his artistic exploration, drawing parallels to Escher's geometric tessellations while incorporating Salish design elements. Through his innovative approach to artmaking, Thomas not only pays homage to his cultural heritage but also transcends boundaries, showcasing the universal language of art and mathematics.

STOPS:

1. "Art itself is one of the only practices that can be found in all cultures. Art is one of the things that makes us human, and bridging different cultural art forms helps me to feel the unity of humankind."  (pg. 208)

When my daughters began attending their new school here three weeks ago, their teacher welcomed them with a simple yet profound directive: to express themselves through drawing or painting. Recognizing that they were transitioning from different cultural backgrounds, the teacher cleverly utilized ART as a means to facilitate their integration. By encouraging creative expression from the outset, she aimed to bridge cultural differences and create a sense of belonging for them. This seemingly small gesture had a significant impact, highlighting the power of art to transcend boundaries and foster inclusivity. It underscored how ART can serve as a universal language, bringing people together and making them feel understood and valued, regardless of their cultural origins.

In today's interconnected world, the sentiment that "art is one of the only practices found in all cultures" holds true more than ever. From traditional paintings and sculptures to digital media and street art, artistic expression transcends geographical and cultural boundaries. Through platforms like social media and international art exhibitions, people from diverse backgrounds can share and appreciate artistic creations from around the globe. This exchange not only fosters cultural understanding and appreciation but also serves as a powerful tool for fostering unity among humanity.

2. "I simply called the image infinity. The idea is that theoretically this ever-diminishing pattern of salmon could go on forever, but due to the limitations of human ability, it cannot be fully realized. Where the image finally stops represents the limitations of human skill and the emptiness at the center represents the infinite possibilities of nature." (pg. 209)

I stopped while going through the piece "Infinity" and wondered how I could relate it to different perspectives of nature and disciplines whether it can be an exploration of the cosmos or mathematical concepts like infinity. Despite significant advancements in technology and space exploration, our understanding of the universe remains limited. The emptiness at the center of the image can be likened to the uncharted territories of space that lie beyond our current capabilities. Thus, the artwork serves as a metaphor for the boundless mysteries of the cosmos and infinity and the humbling realization of our limitations in unraveling its infinite complexities. 

Questions:

1. How can we as educators foster a collaborative learning environment where students can share their cultural backgrounds and perspectives through art in tessellation, symmetry, transformations, and geometrical patterns?

2.  Reflecting on the relationship between mathematics and art, what interdisciplinary approaches can be used in the multicultural classroom to deepen the understanding of both disciplines and promote cultural exchange?

3. What are some potential challenges or limitations as an educator one can feel while incorporating indigenous art into a mathematics classroom? 

Week 3 : Activity Reflection

 

Drawing living beings and human-made things

A couple of days ago, my children took an English assessment test at the Welcome Center, so I spent my time observing the living and non-living things and sketching on the school grounds.

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 in living things vs. human-made things? Any exceptions to this?

I observed curves, arcs, and flowing lines in living things like in the limbs of seagulls and crows, and in the branches of trees while human-made objects tend to feature straight lines, right angles, and geometric patterns, reflecting the structured and often utilitarian nature of the human design. Yes, exceptions exist in both the categories. For instance, some human-made designs like I observed the swings in the playground intentionally mimic natural forms, incorporating organic shapes and irregular lines. On the other hand, in the natural world, organisms like certain crystals or microorganisms may exhibit highly ordered geometric patterns that resemble human-made designs. 

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

The repetitive patterns in architectural designs of school buildings may optimize structural stability or facilitate construction processes, also patterns in human-made objects can be influenced by cultural norms, traditions, and historical contexts. The branching patterns of trees optimize the capture of sunlight for photosynthesis.

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

According to Piaget (1948),

"children begin drawing shapes as scribbles. They then draw curves to make different shapes. From curves, children later abstract them into straight lines".

In my opinion, close observation, drawing, and body movements are great ways to teach students about angles and lines. Static angles are simply pictorial or figurative representations and students can have a difficult time identifying angles in different positions, such as 0, 180, and 360. Students can understand and identify a variety of angles from nature, and indoor or outdoor observations and gain a deeper understanding of angles.

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

Yoga is a good example of showing lines and angles through full-body movement. 

Reading Week 3: Doolittle, E. (2018). Off the grid. In Gerofsky, S. (Ed.), Geometries of liberation.

 02-05-2024

Weekly Reflection 3

Summary:

The grid, a common tool for organizing space and time, provides a sense of familiarity and control but sparks concerns about its potential for misleading sensations and dangers. Instances like Hamilton's precarious streets and the perplexing grid on the Six Nations reserve underscore its limitations. Uniformity sometimes needs to pay more attention to a place's unique qualities. Alternatives like hexagonal patterns or Riemannian geometry offer more adaptable approaches. Like correction lines in Saskatchewan's grid, failure points unveil the grid's challenges with nature's complexity. Recognizing these limitations is an antidote to uncritically promoting the grid, encouraging the exploration of alternative geometries suitable for diverse needs, including education. Indigenous perspectives introduce concepts like string figures, time grids, and territory definition, connecting them to alternative geometries. Explore Indigenous geometry's contemporary relevance, exemplified by the time grid in clocks and calendars. Unlike settler farming on fixed grids, Indigenous practices harmonize with nature, challenging grid-based rigidity. The concept of territory, exemplified in the Haldimand Deed, transcends mapped lines, embracing the entire drainage basin. Describing and navigating territory relies on the land, not imposed structures. Unfortunately, the history of the Grand River Mohawk territory reveals dispossession, emphasizing the need for a nuanced understanding of Indigenous geometries.

Stops:

1. "Once one accepts the abstraction, what one might call the linearization of the problem, we can go no further than Euler’s negative result. On the other hand, we can find a new insight by widening our perspective, moving off the grid, and looking at the underlying reality of the situation. We have been drawn off the grid by following ancient traditions of giving thanks, thinking of the river and the town as just parts of a whole, and opening our eyes and widening our perspective to see the world as it is, not as we might just imagine it to be." pg.119

The given quote shows the importance of expanding our view beyond conventional methods. Just as Euler's solution was limited by a linearized approach, we should prepare our students to reflect on instances where thinking beyond established boundaries led to new insights and creative problem-solving and encourages them to recognize the value of diverse perspectives and the innovation potential when stepping off the metaphorical grid in their own experiences. Within the framework of traditional teaching approaches, I experienced a teaching style that does not give students any liberation to think outside the box or can allow to use traditional/indigenous approaches, and standardized evaluation asses them in a conventional way. My question is In what ways could educational systems foster an environment that encourages innovative thinking? With the rigid course outline, how might teaching can foster diverse talents and abilities?

2. "We go from “straight” lines and “right” angles to well-defined “equal” plots, to “rules” governing our own behavior, and finally, to a sense of control and mastery. This progression is due in some degree to culture and to some other degree to innate human nature, and the weight of each cause is subject to debate." pg. 104

A few years ago, I had the opportunity to explore Mohenjo-Daro, an ancient city dating back to 2500–1700 BCE in the Indus Valley Civilization of Pakistan. It struck me as one of the earliest instances of urban planning on a grid system, reflecting the cultural advancements of that era. This visit deepened my understanding of the historical roots of grid-based city layouts. Simultaneously, it sparked my curiosity about indigenous communities, highlighting their unique perspectives on culture and living, which stand in contrast to the organized grid patterns found in cities. There is an equal need to show respect for the diverse perspectives and needs of different communities and their ways of living.

My question is how can we establish a society where the imposition of a grid system aligns with the natural flow or needs of a community and nature?