Movement-based Mathematics: Enjoyment and Engagement without Compromising Learning through the EASY Minds Program by Nicholas Riley et al

Summary

The article addresses the concerning decline in mathematics performance among students in Australia. In response, researchers conducted a study involving an intervention for grades 5-6 to understand students' and teachers' perceptions using the Easy Mind program. This study included focus groups with 66 students and 4 teachers, utilizing the NSW Quality Teaching Model as a framework to assess the teaching strategies implemented. The key findings are as follows:

- Nearly all participating students expressed an increased interest in mathematics, finding the program highly engaging. They particularly valued the opportunity to learn outside the traditional classroom, allowing hands-on experiences in a more open environment.

  - The program effectively captivated both high-achieving and struggling students, indicating that it provided benefits across the board, regardless of individual student capabilities.

  - Students reported a deeper understanding of mathematical concepts, as the integration of physical movement enhanced their learning experience without sacrificing academic rigour.

  - Teachers expressed high satisfaction with this teaching approach, noting that it was intuitive and resulted in relatively low discipline among students.

In conclusion, the authors affirm that integrating movement into the primary mathematics curriculum is both feasible and highly effective. Such an approach can significantly boost student engagement and foster exploration through physical activity, all while maintaining academic quality. This underscores the potential of innovative pedagogical methods to transform traditional learning environments that students often find unengaging.

Stop 1

Quote: “Quite a few students commented on “multi-tasking” (doing mathematical and physical activities), noting that being presented with an additional challenge aided in their learning.  Students used different ways to explain these benefits; "the exercise makes the brain work clearer"; "because your mind has been doing exercise, it kind of gets it ready for mathematics”. Page 1665

Explanation: This emphasizes how students see a link between physical activity and better math thinking. It has been proven that physical exercises help improve brain function. When they mention that exercise helps clear their minds and gets them ready for math, it challenges the idea that math should only be learned while sitting still in a classroom. This finding is particularly exciting because it offers a solution to the ongoing issues with declining math performance. By incorporating outdoor activities and sports into math lessons, students can connect what they enjoy with what they need to learn, making math feel less intimidating and more engaging. This inspires a more holistic approach to teaching, highlighting the need to involve both the body and mind.

Stop 2

Quote:” Before EASY minds, most students reported mainly doing paper- and worksheet-based activities as part of their Maths lessons.  Not being able to move around, being inside and simply being exposed to didactic teaching methods were perceived as dull, boring, repetitive, and uninteresting.

Explanation: This quotation strongly resonates with some classroom experiences I witnessed in Nigeria, where I often observed students placing their heads on their desks during classes with teacher-centred instruction. Watching students disengage made me question whether traditional approaches truly support meaningful learning, especially for children who are naturally energetic and curious.

What excites me about this quote is the deliberate effort being made to move away from dull and repetitive teaching practices toward more engaging and embodied ways of learning mathematics. I recall my own experience as an adult learner when Susan took us outside to explore quadratic equations and parabolas through movement. That lesson transformed my understanding of the concept, as the physical movements helped me visualize and feel the shape of the parabola rather than merely memorize it. I became deeply interested in how our bodies could generate mathematical meaning.

This reflection leads me to imagine how much more powerful such an approach would be for younger students, whose energy and need for movement are even greater. Providing children with opportunities to move, explore, and physically experience mathematics could change their relationship with the subject from one of boredom to one of curiosity and excitement.

Question: If the Ministry sets the curriculum and time for each topic, are these truly the barriers to embodied mathematics learning, or is it our fixed image of what a mathematics lesson should look like? What might change, for better or worse, if teachers began to teach differently?

 

 

Bridges: A World Community for Mathematical Art by KRISTO ́F FENYVESI

Summary

The Bridges community brings together mathematicians, artists, and educators to explore the intersection of mathematics and art. Originating from the vision of Iranian mathematician Reza Sarhangi, the first Bridges conference in 2005 in the Canadian Rockies transformed the typical academic format into a vibrant festival of creativity, where participants engaged in building, performing, and collaborating.

Over the years, Bridges has expanded globally, fostering new partnerships and innovative ways of thinking across countries like Spain, Korea, and Hungary. It emphasizes the idea that mathematics is deeply human and can be expressed through various artistic media. The movement promotes an inclusive atmosphere, blurring the lines between experts and novices and between different disciplines.

Fenyvesi describes Bridges as a “worldview” that celebrates creativity and collaboration, serving as a precursor to the STEAM concept and exemplifying the joyful relationship between mathematics and the arts.

Stop 1

Quote:” As is often the case with active and successful communities and networks, Bridges was begun by a many-sided individual with contacts in both science and culture” pg. 37

“Mathematics, arts, and crafts coexisted side-by-side during the medieval period of Persian history”. Pg 37.

Explanation: I am deeply intrigued by Reza Sarhangi’s vision and the role he played in shaping the Bridges community. The article’s description of him as a “many-sided individual with contacts in both science and culture” resonates with me, especially given how seamlessly he wove mathematics, art, history, and performance into a single intellectual practice. Learning that “mathematics, arts, and crafts coexisted side-by-side during the medieval period of Persian history” immediately reminded me of a workshop I attended at the Secret Lantern, where Malihe presented Persian geometric art. Seeing how mathematical shapes were carefully arranged into patterns on carpets, buildings, and everyday objects—and how Farsi numerals themselves carried aesthetic intention—helped me understand the cultural energy Sarhangi brought into the mathematics community. His work affirms my belief that bridging mathematics and the arts can transform the subject from something feared for its functional calculations into a creative, inviting practice grounded in beauty, pattern, and elegance.

Stop 2

Quote:” Bridges’ transdisciplinary program has elaborated new transdisciplinary standards and has productively solved a high number of unforeseeable and unprecedented challenges. These are risks run by any truly transdisciplinary venture; they may never emerge in relatively homogeneous scientific or artistic communities with established traditions and history. Pg.42

Explanation: In all honesty, I have heard Susan talk about bridges, but I never knew the depth and sacrifices made until I read this article. Bridges’ claim that its transdisciplinary program has had to elaborate new standards reflects the reality that once mathematics is brought into conversation with art, culture, music, dance, and community participation, the traditional rules of either discipline are no longer sufficient.

In homogeneous communities—such as a conventional mathematics department or a traditional art school—everyone shares the same expectations about what counts as good work, how to evaluate it, and what the goals of the field are. But Bridges operates in a space where a geometric proof might appear as a sculpture, where a dance performance can express symmetry, and where cultural artifacts carry mathematical meaning.

This is exactly the kind of challenge Bridges faces: when mathematics becomes a creative, culturally grounded, and aesthetically rich practice, it opens doors for people who fear traditional calculation. However, it also requires new standards for teaching, evaluating, and understanding mathematical knowledge. These are the “unforeseeable and unprecedented challenges” that only a truly transdisciplinary venture encounters, and how it has been able to soar despite the heavy challenges from the various disciplines beats my imagination.

Question: What are the greatest challenges that arise when mathematics intersects with art, performance, or community practice? Additionally, which assumptions or beliefs from your own field might you need to reevaluate or let go of to engage fully in a Bridges-style community?

 

 

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?

Welcome