Sustainability Education’s Gift: Learning Patterns and Relationships by

DILAFRUZ WILLIAMS

Summary

The article contends that traditional education, influenced by mechanistic and technocratic perspectives, contributes to the global sustainability crisis by fragmenting knowledge into isolated subjects and distancing learners from real-life experiences. Williams draws upon systems thinking and holistic education—ideas inspired by scholars such as Capra and Orr—to argue that sustainability education should prioritize understanding patterns, relationships, and interconnectedness over disjointed facts.

Using the Learning Gardens program in Portland, Oregon, as a case study, the author illustrates how garden- and food-based education allows students from kindergarten through eighth grade to engage in multisensory, interdisciplinary, multicultural, and intergenerational learning experiences. Students explore subjects like mathematics, science, social studies, and language arts through activities such as designing gardens, studying soil, cooking, and observing ecological systems. This embodied and place-based learning fosters connections among personal health, community well-being, and environmental sustainability.

 Stop 1: Tracing this disconnect to Cartesian modes of linear and clock-like thinking and being, in the past two decades we have seen scientists, philosophers and educators rally for a revamping of the  western models of education to a more ecologically literate one. Page 42

Explanation: I really relate to the thoughts of shifting education to a more practical mode because I often wonder what the true purpose of education is. I remember one of my students who did not enjoy the structured mathematics requirements, yet she excelled as a cook and makeup artist. I believe that instead of the world judging her by her grades, mathematics should align more with her passions and the unique contributions she can make in addressing today’s challenges. Is education merely about sitting in a well-structured classroom, memorizing formulas, and achieving high grades through rote learning? Or should it be a tool that helps learners adapt meaningfully to the world, connecting knowledge to real-life experiences and the environments around them?

In the context of mathematics, understanding should be relational and embodied—not just about memorizing terms and procedures for exams. Utilizing gestures, hands-on activities, and collaborative problem-solving can make abstract concepts tangible, allowing students to experience and relate to mathematics in ways that resonate with their lives. Much like how ecologically literate education emphasizes interconnection and holistic thinking, mathematics education can greatly benefit from approaches that highlight relationships, context, and meaning instead of reinforcing rigid, isolated, or linear thinking.

 Stop 2

Quote: Students learn ecology, chemistry and biology in working the gardens even as they learn mathematics in designing them. Through harvesting in groups they also learn group dynamics, along with content areas of social studies and agronomy. Page 45

Explanation: I am really amazed at how the planned activities on the farm have been able to teach so many disciplines. This exemplifies teaching through application to address today's problems, which is the essence of sustainability. I remember our last class with Susan when we took a walk to the garden we used for our lesson. The focus was on teaching us measurement, but I ended up learning more about my own body. The hands-on activities provided me with measurements of parts of my body that I never knew about, which could even be useful for a tailor. Additionally, I learned the importance of spacing my seeds when planting crops, which is fundamental to agriculture. Just one objective of measuring is connected to other valuable areas of life for us.

Question
How can embodied, artistic, and multimodal approaches to mathematics be meaningfully integrated into traditional classroom settings without losing curricular rigour while increasing student engagement and conceptual understanding?

 

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

Summary

The authors explore how blind students cultivate their mathematical understanding of symmetry and reflection, emphasizing the significance of multimodal and embodied interactions. They assert that mathematical cognition is fundamentally grounded in physical experiences, which goes beyond mere mental or visual processes. By incorporating insights from philosophy, neuroscience, and mathematics education, the study aligns with contemporary discourse on embodied cognition, such as Barsalou, Gallasee, Lakoff, Damasio, and Merleau-Ponty’s phenomenology.

Central to their argument is the connection between perception and conception, which relies on common neural mechanisms that influence behaviour and cognitive functions. The research is illustrated through two task-based case studies: Lucas, who has been blind since the age of two and primarily engages in tactile and bodily exploration to grasp spatial relationships without relying on visual analogies, and Edson, who lost his sight at fifteen and utilizes his visual memories to enhance his understanding of symmetry and congruence.

The findings reveal that blind students embark on unique developmental paths, distinct from those of their sighted peers, employing an array of multimodal resources, including tactile, kinesthetic, auditory, and memory-based inputs. Ultimately, the study concludes that the body is not an obstacle to mathematical learning but rather an essential asset for mathematical cognition, empowering blind learners to develop significant mathematical understanding.

Stop 1

Quote: “In our studies with students with disabilities, we seek parameters through which we ourselves might learn to see and hear mathematical practices even when they do not sound or look exactly as we have come to expect”

Explanation: I have often wondered how students with special needs learn, particularly because I have not had the privilege of teaching in that category during my years in Nigeria. This curiosity ultimately led me to enroll in the EPSE 511 course last year. My thoughts have always been a mixture of admiration and uncertainty, as I frequently asked myself how these students make sense of what is being taught to them.

A memorable experience that stayed with me occurred during a Christmas carol service at my church. A group of individuals with disabilities came to sing and perform various activities. Despite their challenges, they were remarkably connected and performed exceptionally well, even outshining those who were sighted. I found myself wondering if they possessed a special intuitive gift that allowed them to navigate life in ways I could not fully comprehend. Most recently, I saw a lighthearted video on Facebook of a bride who was blindfolded and tasked with identifying her husband. Despite several men being used for the test, she skillfully felt them with her hands and successfully recognized her own partner.

Reflecting on these moments, I now realize that what I once interpreted as “extra intuition” was actually an indication that their ways of perceiving, expressing, and coordinating were simply different from my own. A phrase I encountered recently encapsulated this thought: the true challenge lies not in the students' understanding or capabilities, but in our limited expectations of what learning should encompass.

This perspective has taught me that when students express themselves differently, whether through gestures, rhythm, movement, or alternative forms of communication—it is all too easy for teachers to misinterpret their abilities. This insight compels me to acknowledge that students with disabilities are not lacking; instead, we must cultivate new “parameters” and develop fresh ways of seeing and hearing. By doing so, we can recognize their mathematical thinking and comprehension, even when it does not align with traditional forms. Just like the children who sang beautifully at church, their abilities were always present; it was my perception that needed to expand.

Stop 2

Quote: “On the one hand are the teachers, who might ask themselves how they can learn to use their eyes and their ears, trained as they are to recognize the so called “normal”, to see and to hear the diversity that composes their classes. On the other hand we have the students, who, wishing to achieve that which is expected by their teachers, their families and by society at large might enquire of themselves “how can we learn to see and to hear that which we are supposed to be perceiving?” page 37

Explanation: This quote resonates with what goes on in the teaching and learning settings, were cultural expectations and large class sizes shape classrooms. It emphasizes the need for teachers to recognize the diverse ways students learn, moving away from the traditional focus on quiet, compliant learners.

In Nigerian schools, success is often defined by standardized exams and visible discipline. As a teacher, I was trained to categorize students as “attentive,” “serious,” or “weak,” but this limited perspective overlooked many students' true potential. Some of my most insightful students were those who didn't fit the traditional mould, finding unique ways to express their ideas through gestures, local languages, or storytelling.

At the same time, students feel pressured to act in ways they believe teachers want, such as sitting quietly and following instructions. This leads many to hide their real thoughts for fear of judgment, causing them to abandon their creativity in favour of what they think is expected.

This misalignment creates a classroom dynamic where genuine learning is stifled. The quote calls for a shift in teaching, encouraging teachers to recognize diverse perspectives and for students to feel safe sharing their authentic voices.

My experience in Nigeria taught me that when teachers truly listen, they can discover brilliance in unexpected places. When students feel seen and valued, they move beyond mere performance and engage in meaningful learning.

 Question

“What specific instructional strategies can we implement to integrate multimodal approaches in our mathematics teaching, enabling all students to express their understanding in diverse ways?

 

Gesturing Gives Children New Ideas About Math by Susan Goldin-Meadow et al

Summary

The authors investigated how gesturing supports children’s learning of mathematical equivalence, moving beyond the question of whether it helps. They worked with 128 third- and fourth-grade students who initially showed no understanding of equivalence problems and assigned them to three conditions: no gesture, correct gesture, and partially correct gesture. All children learned the same verbal strategy, but only the gesture groups produced hand movements—either accurately highlighting the correct numbers to group or pointing to an incorrect pair.

After a gesture‑training phase, all students received the same gesture-free lesson and completed a post-test. Children who produced correct gestures learned the most, those who produced partially correct gestures showed moderate gains, and those who did not gesture improved the least. Crucially, a mediation analysis showed that gesturing helped children by prompting them to add the grouping strategy to their speech, even though grouping was never taught verbally. This demonstrates that children extracted new ideas from their own movements.

The study concludes that gestures are not just attention cues or memory aids—they are cognitive tools that help children construct new mathematical insights, illustrating the generative role of the body in learning.

Stop 1

Quote: “These studies suggest that gesturing can play a role in memory and learning, but they do not specify a mechanism” page 267.

Explanation: As I reflected on the quote, a powerful memory emerged from my experience writing the EDUC 500 proposal. In that proposal, I argued that gestures, as dynamic semiotic resources, play a crucial role in fostering mathematical flexibility, particularly when they are integrated with speech, artifacts, and technology. However, my instructor posed a thought-provoking question that has lingered with me: Was my proposal focused solely on gestures, or did I consider how gestures interact with other semiotic tools? This inquiry prompted me to delve deeper into the ways gestures contribute to meaning-making in mathematics.

Revisiting this topic after reading the article sparked a renewed reflection. The article emphasizes that while children may learn effectively by mimicking their teacher’s gestures, they can also gain insights by creating their own gestures. This revelation led me to reconsider my earlier question: What is the true role of gestures in helping students grasp and adapt to mathematical concepts? The findings indicate that gestures do not function in isolation; they derive meaning from their context, particularly when accompanied by speech or other representations. This understanding clarified why my instructor challenged my proposal, reinforcing the idea that gestures are integral to a broader semiotic system. It deepened my appreciation for the interplay between gestures, speech, and other tools in facilitating mathematical thinking.

 

Stop 2

Quote: “Children who produce gestures modeled by the teacher are more likely to profit from the lesson than children who do not produce the gestures. “Page 267

Explanation: Research indicates that when students learn exclusively through verbal communication, as in a typical lecture format, their retention rates are generally low. In contrast, incorporating visual elements—such as the teacher's gestures—alongside practical exercises enhances their learning experience. This approach allows students to mentally integrate information more effectively by combining auditory and kinesthetic learning styles. Gestures provide a tangible, visual link to concepts, which helps reinforce memory retention.

 

Question

How can we effectively balance the intentional planning of gestures as semiotic resources in our teaching with allowing them to flow naturally during lessons, and how might this balance impact our effectiveness in the classroom?

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