Week 2: Multisensory mathematics

As I delve into this insightful exploration of embodied mathematical cognition, several stops along the way have caught my attention. Here are two key moments that resonated with me.

1. Antagonistic Nature of Education: The introductory passage about living in an antagonistic society and the parallel drawn to education sets a powerful stage for the paper. The contrast of the real and the imaginary, the concrete and the abstract, creates a lens through which we view the challenges in education. The authors highlight the tension between what teachers are trained to perceive as "normal" and the diversity within their classrooms. This makes me wonder: how can educators learn to recognize and appreciate the diverse ways in which students perceive and engage with mathematical concepts? Indeed, this stop raises awareness about the need for a shift in perspective within the educational system, urging teachers to adapt our methods to embrace diverse learning styles.

2. Multimodal Resources and Embodied Learning: The paper's core argument revolves around the embodied perspective on mathematical cognition. The experiences of two blind students navigating symmetrical figures and geometrical transformations become a lens through which we understand the interplay between the body and cognition. One of the pivotal moment is when the discussion transitions from symmetrical figures to reflection. Edson, with visual memories, leverages his past experiences with mirrors to conceptualize and articulate mathematical properties. In contrast, Lucas, without visual memories, relies on tactile exploration and hand movements. This makes me wonder: how do the embodied experiences of individuals shape their approaches to mathematical understanding?  Certainly, this stop encourages a deeper exploration of how personal histories and sensory modalities influence cognitive processes.

Questions for Discussion:

1. How can educators cultivate an inclusive learning environment that recognizes and accommodates diverse embodied experiences in the teaching of mathematics?
2. In what ways might the reliance on sighted learners' trajectories hinder the development of effective learning scenarios for blind students, and how can educators overcome this challenge?

Lulu Healy & Solange Fernandes (2013), Multimodality and mathematical meaning-making: Blind students' interactions with symmetry. 

Week 2 activities

Engaging in hands-on mathematical activities, inspired by the videos and readings, has been a transformative experience for me. The combination of visual, tactile, and sensory elements brought the mathematical concepts to life in a way that simply reading or watching videos could not achieve.

Firstly, experimenting with data analysis using candies allowed me to apply abstract concepts in a concrete and delicious way. Creating a Bar Graph and Pie Chart with Rockets and Smarties not only reinforced my understanding of data representation but also made the learning process enjoyable. It was a reminder that mathematical activities can be both educational and fun, especially when they involve something as universally appealing as candy.

Bar Graphs:

Pie Chart

The exploration of hexaflexagons, following Vi Hart's instructions, provided a hands-on experience with geometry that went beyond traditional methods. The tactile sensation of folding and flipping the hexaflexagon enhanced my spatial awareness and geometric intuition. Decorating the surfaces added a creative dimension to the activity, making it a personalized learning experience.

Cutting a bagel into a mathematically correct breakfast, inspired by George Hart's video, shifted my perspective on geometry. The tangible experience of creating interlocking rings with a real-life object like a bagel added a practical dimension to the abstract concept. This hands-on activity demonstrated the relevance of geometry in everyday life, making the learning experience more relatable and memorable.

Considering the reflection questions, the hands-on experimentation with these mathematical activities made a significant difference in my understanding. It not only solidified abstract concepts but also made the learning process enjoyable and memorable. For students, learning from real 3D objects with various sensory elements could enhance their understanding and retention of mathematical concepts. The engagement of multiple senses, such as touch, smell, and taste, can make the learning experience more immersive and appealing. For students with sensory impairments, hands-on activities become even more crucial. Utilizing real-life objects with distinct shapes, textures, and sensory qualities can provide a richer learning experience. For example, exploring geometric concepts with objects that can be touched, smelled, or even tasted can compensate for the lack of visual or auditory stimuli. This approach not only promotes inclusivity but also recognizes the diversity of learning styles and preferences among students.

Embracing Embodied Mathematics to Connect the Dots between Body, Mind, and Classroom Beauty.

In our exploration of mathematics, it is crucial to question the perceived separation between mathematical concepts and the physical world, challenging assumptions about how and where math learning occurs. Traditional classroom settings, confined within four walls, often promote passive learning and portray mathematics as isolated mental calculations. However, our recent experiences with embodied mathematics have opened up new avenues for understanding, bringing beauty to the classroom.

This week's reading, inspired by Nathan's insights from "Foundations of Embodied Learning," demonstrates that the challenge in mathematics lies not in understanding ideas but in grasping the meaning of formal notation, which resonates deeply (Nathan, 2021, p. 147). Our bodies, with their unique measurements, offer an untapped resource for learning and teaching mathematics.

I engaged in a body measurement activity this week. The exercise is on calibrating my body, recording the results, and comparing them with a tall adult man(www.vendian.org).

The variability in body size, as evident in my measurements, challenges preconceived notions about standardized learning tools. When introducing the activity to my grade 8 students, their initial enthusiasm vanished when they realized it was not a graded task. They questioned the utility of measuring body parts without traditional tools like tapes and rulers. However, my grade 12 service student embraced the activity passionately, showcasing the potential for embodied learning.

Here is my grade 12 service student measuring:

His approach, guided by the conceptual metaphor of "NUMBERS AS PLACES ALONG A PATH," as discussed by Nathan, involved using body parts, including the index and hand span, to measure dimensions.

After calibrating his body measurements, he made measurements of an Elmer's Corrugated Tri-Fold Display Board-White (big rectangle) and French vocabulary sheet (small rectangle) using his body parts:

 

Then, he made calculations to find out how many small rectangles could fit into the big rectangles.

 

This embodied exploration showcased the potential of multisensory learning and integrated artistic expression into mathematical concepts. Therefore, the resulting Elmer's Corrugated Tri-Fold Display Board became a mathematical creation, exploring dimensions and measurements and a practical and aesthetic addition to the classroom.

 

His work is a fantastic opportunity to teach and learn concepts of dimensions and measurements. On one side, the product of his work serves as a board to display students' activities and, on the back side, the French vocabulary they need to learn. Moreover, it is a decoration for my classroom. For instance, my stand desk is a storage for my classroom games, dividers, and dictionaries that are not visible anymore when students sit on their desks.

Roger Antonsen's TED talk further emphasized the hidden beauty of mathematics in understanding the world. He argues that exploring mathematical concepts from various perspectives offers a transformative approach to learning (Antonsen, 2015). By engaging all our senses, incorporating movement, and observing the living world, we aim to unlock new pathways for understanding mathematical patterns and ideas.

The goal is clear – experimenting with alternative teaching methods beyond conventional approaches. This reflection does not advocate discarding traditional mathematical tools but aims to explore ways to augment them with embodied, arts-based learning experiences. In doing so, we challenge the perception that precision and accuracy in mathematics are divorced from the physicality of our bodies and the artistic expressions of the world.

Reflection Questions:

1. How can integrating embodied, multisensory learning experiences in mathematics address the challenges of understanding different math concepts?
2. In what ways do you envision the fusion of artistic forms of expression and exploration beyond the traditional classroom contributing to more comprehensive and enjoyable learning and teaching of mathematics?

Top of Form

 

 Hello

My name is Tony Domina. I live and teach in North Vancouver. This is the territory of the Coast Salish people. I express our gratitude to the Squamish Nation (Skwxwú7mesh) and Tsleil Waututh Nation (Səl̓ílwətaʔ/Selilwitulh), and I value the opportunity to learn, live, and share educational experiences on this traditional territory.

This blog investigates concepts and ideas for teaching and learning mathematics.