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:
- How
can educators cultivate an inclusive learning environment that recognizes
and accommodates diverse embodied experiences in the teaching of
mathematics?
- 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?
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.
I’m incredibly impressed that you had success with the mathematically correct breakfast, Tony! I could not for the life of me achieve the same result; all that I ended up with was a pile of mangled bagel bits.
ReplyDeleteA couple of the papers that I examined for our educational research course looked at the impact of personalizing mathematical contexts to individual students. The researchers collected data from children through interviews and other activities, then put word problems and activities into contexts that were more interesting and relevant to them. While they acknowledged that it might be time consuming for homeroom teachers, they found this explicit collection of knowledge to improve both student engagement and outcomes on word problems and other math engagements. This year, I’ve attempted to personalize the contexts of our problems a little more with similar methods when possible.
As all of the articles this week seem to have centred, all students benefit from varied learning approaches in math class. I think the aim should be to not include visually impaired students, but to construct a learning trajectory and series of engagements that allow all students to explore many avenues via different senses. While VI students may be completely unable to access one type of engagement, there are likely many more who could theoretically engage but would prefer a different angle!
Tony, your blog post really got me thinking about education. The comparison between the challenges in society and education is eye-opening. Your questions on how teachers can better understand diverse ways students learn math are spot on and show the need for changes in teaching methods.
ReplyDeleteThe part about blind students navigating math using touch and movement is fascinating. Your question about how personal experiences shape math understanding is intriguing. It's impressive how you connected these thoughts to a hands-on activity, making abstract concepts more enjoyable and memorable.
Your commitment to inclusivity, especially for students with sensory impairments, shines through in your suggestion of using real 3D objects with different senses. It's clear you're making a positive impact. I'm eager to hear more about your experiences and how these inclusive methods continue to benefit students.