Medha Sharma 342

  From Fibonacci Curved Kites to Our Own Mathematical Art Piece Medha Sharma, Joshua Kanaganayagam, Helen Chen  For our project, we chose Gauthier Cerf’s Curved Kite Fibonacci Spiral . We chose this piece because it showed us a different way of visualizing the Fibonacci sequence. We were familiar with the usual Fibonacci squares and the resulting spiral, but Cerf’s work showed us how the Fibonacci sequence could be used to make various other geometric constructions while still creating a beautiful art piece. This combination of math and art made us curious about how it was constructed and how we might use the same underlying ideas to make our own artistic design. Reverse Engineering the Original Artwork Before creating our own piece, we first tried to understand the math behind Cerf’s curved kite. Each curved kite was constructed from circular arcs, and an interesting property we discovered was the relationship between its dimensions and area. Understanding how these individua...

One section of the reading that made me pause was Eisner’s analysis of the implicit curriculum regarding reward structures in early childhood education. Eisner cites research by Mark Lepper demonstrating that extrinsic motivators, such as star charts, smiling faces, and golden tickets, risk conditioning students to become "reward junkies". Over time, these external payoffs can dampen a child's intrinsic curiosity and replace self-directed initiative with passive compliance. As Eisner notes, students quickly adapt by "studying the teacher" to determine the bare minimum effort required to secure a specific grade, asking procedural questions like "How long does the term paper need to be?" rather than engaging deeply with the material. However, reflecting on classroom practice, I see a necessary nuance here: extrinsic recognition and positive reinforcement can also serve as vital sources of encouragement, particularly for young learners building confiden...

I had so many questions and thoughts while reading this article, but the ones which kept me thinking and questioning our education system are:  (Page 390)  A particularly striking point was how standardized tests are designed to filter out certain curriculum content. When students successfully master a concept and consistently answer a question correctly, test creators discard that item because it fails to "discriminate" between high and low achievers. Essentially, the assessment is continuously adjusted to guarantee a consistent failure rate. This raises several questions: Do test makers simply discard content because a large majority excels at it? Rather than dismissing these successes, why isn't there an effort to build upon those foundational skills? What is the ultimate purpose of learning these concepts if they are eventually deemed unworthy of assessment? (Page 396)  Dewey’s thoughts on challenging obedient students really stood out to me. While I agree that high a...

 

My Favourite teacher: My high school math teacher in grade 11 remains my greatest role model. What set him apart was his authentic persona; he struck a perfect balance between maintaining firm classroom decorum and building approachable, casual relationships, even joining us for a game of volleyball. His clear instructional style and vivid language left a lasting impression, to the point that I still find myself using his phrasing with my own students today. Most importantly, he ensured every single student felt seen and heard, regardless of their academic standing or learning difficulties. He also fostered genuine independence by trusting us during assessments, leaving the room to instill a sense of personal accountability for our own learning. My Least Favourite Teacher. My least favourite educator was my grade 7 math teacher. Looking back, her instruction felt constantly rushed, and there was a noticeable bias toward top-performing students during lessons and assessments. Since I w...

 Reading Skemp’s analysis highlights three key moments that demand a pause. The first is his framing of "understanding" as a faux ami (pg. 1), revealing that teachers and students often speak entirely different languages under the same word. Honestly, I never thought about how it impacts learning before reading this article.  The second is the striking observation that " ‘Well is the enemy of better,’ and if pupils can get the right answers by the kind of thinking they are used to, they will not take kindly to suggestions that they should try for something beyond this" (pg. 5) . This underscores the psychological friction teachers face when students resist deeper conceptual thinking because surface-level rules yield immediate success. And I think, even sometimes, teachers lack tools to assess if their understanding is instrumental or relational unless they encounter a problem-solving situation and fail.   Lastly, his cognitive map analogy, where instrumental lear...