Assignment 1 Reflection

 

• one paragraph on what the experience of this project was like for you -- where it was challenging, satisfying, frustrating, intriguing, etc.

I truly enjoyed this project. It showed me new perspectives on how ideas and concepts can come together and, most interestingly, be open to a diverse range of interpretations based on the perspective of the viewer. The area I struggled with most was thinking of how to extend the concept into something more. I knew I wanted to work on something related to time, but it took many attempts with different shapes and sequences to find one that would work to demonstrate a full life span down to every individual second. However, once it all came together, it was worth it and showed us how many applications this practice of using shapes and symmetry to represent ideas can have.

• one paragraph on your thoughts about what you take away from this project as a teacher. What could you (and couldn't you) use with your own classes? Any ideas for parallel projects bringing together math with other subject areas like the arts, history, science, etc. that you might consider developing and trying out in your own class?

 I believe that the idea of using shapes, rotation, symmetry, etc. to dhow how ideas can be interconnected is one that can be used in most classrooms. A very effective way of learning a new subject is to see how the different areas of study are connected. This exposure to the subject can help ignite ideas in the student's mind and presents them with a holistic view of the concepts. While I will definitely use this in Math, I feel like one area where this idea would be very effective would be in History. It can show how different eras and dynasties may share similarities, how they differed, how one led to the development of the next, and can also be broken down to smaller units of time to see how the events of a certain type within a single year are all interconnected.

Overall, I truly enjoyed this project and learned a great deal from it.

Assignment 1: Artistic Representations of Numbers and Ideas

 David A. Reimann is an artist and a professor who combines his expertise in mathematics and computer science with art to create visually engaging pieces that embody mathematical principles. His work centers around using geometric shapes, patterns, and numbers to build often complex visual representations that reveal more details as viewers change their perspective. Reimann’s work emphasizes themes like symmetry and repetition, and it shows how simple shapes can transform into intricate designs that reflect the interconnectedness and balance inherent in mathematics. This combinations invites viewers to engage with his art on many levels, experiencing different aspects of the work depending on their distance and perspective, making each viewing a unique exploration of the mathematical concepts depicted.

In our extension, we created a fractal that represents a person's full (average length) life. Each level zooms in to show the next measurement unit of time. It goes from years to month to days to hours to minutes to seconds. The idea behind this fractal is to demonstrate the interconnectedness of everything in our lives and how there are endless ways to make connections between everyday tasks and life experiences.The full sequence of zooming in can be seen in the slides.

Slides: https://docs.google.com/presentation/d/1EDY6Su6ugMxCtElC73x1hUmscdMLUFaG/edit?usp=sharing&ouid=112020147131374519557&rtpof=true&sd=true

Lockhart's Lament

I agree with Lockhart's discussion on the lack of engagement in Mathematics education. This is something I have felt for a long time and have always tried to work practices into my classrooms that can change this tradition. What emphasized this point in my mind even further was the comparison he made of the teaching a formula for the area of a triangle and them moving on to an art class instructing students to colour in numbered regions with predetermined colours. We see often how this plays out in a Math classroom, but most rarely ever consider this a problem or an area that can be improved.

I disagreed with his point, “The saddest part of all this ‘reform’ are the attempts to ‘make math interesting’ and ‘relevant to kids’ lives.’ You don’t need to make math interesting— it’s already more interesting than we can handle!”

A large portion of math is purely technical and can get very boring. One of the most frequently asked questions in a Math class is “Will I ever need this? Why am I spending so much time on something I will never use?” I have found that whenever I was able to make a  connection between the concept being taught and real life scenarios, my students were always engaged and interested in the topic.

Like Spemp, Lockhart’s emphasizes the importance of relational teaching over instructional. He encourages teachers to move away from only the “what” and to start including more of the “why”.

 

What Lockhart is saying Math classrooms are like.

 

What he says they should be like.

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