Final Unit Plan

 Hi all, 

Here is the link to my Unit plan, have fun reading!

 https://docs.google.com/document/d/1PIHB2QwOp-lclCX49-YmfVLkU54Dp0_-/edit?usp=drive_link&ouid=110552432786398953134&rtpof=true&sd=true

https://docs.google.com/document/d/1zSG84Q4QyacIjzEkmNxKIcap7egw5xPp/edit?usp=drive_link&ouid=110552432786398953134&rtpof=true&sd=true,

 https://docs.google.com/document/d/1sNonJjODNcdeiSzWlnjjLNddBkIpqLWV/edit?usp=drive_link&ouid=110552432786398953134&rtpof=true&sd=true,

 https://docs.google.com/document/d/1537Z412OWJTQJ0WeFTSOI8aGfAGlYZPb/edit?usp=drive_link&ouid=110552432786398953134&rtpof=true&sd=true,

Solution to soup can puzzle

To solve the problem of estimating the size of the giant soup can, I first researched similar large-scale soup can artworks around the world to understand the typical dimensions. By reviewing several examples, I discovered that these paintings tend to range in size from 10 to 30 feet in height, with 20 feet being the most common preference. Then, I started to estimating the size of the bike in the foreground as a reference point. By visually comparing the bike to the can, I could make a rough estimate of the can's scale, hypothesizing that it might be around 20 feet in height based on the proportion.

As a "student bird," I’m goal-oriented and eager to gather all available resources to solve problems efficiently. This is why I searched for examples of similar artworks. I also enjoy challenging myself to think critically, as I feel this is an area I can improve on. However, in reflecting on my "teacher bird" perspective, I recognize that my students would benefit more from engaging directly with the site itself. Conducting a hands-on investigation would offer a more authentic learning experience, allowing them to apply their skills in a real-world context and develop a deeper understanding of the problem-solving process. 

A puzzle  I always want my student to do is the Russian Block puzzle, where I would ask my students to come up as many as different ways to complete it. 

Micro-curricular teaching reflection

I have some valuable insights now about how I can improve my teaching approach in the future. One of the key takeaways is the importance of being more attentive to students’ reactions throughout the lesson. I realized that observing their body language, facial expressions, and engagement can give me immediate feedback on whether they’re understanding the material or if I need to adjust my approach. 

Another takeaway is that I need to ask more simple and low-stakes questions instead of diving too quickly into deep, philosophical ones. I found that asking more accessible questions helped gauge students’ understanding without overwhelming them. These types of questions also encourage participation , before I challenge them with more difficult ideas.

Lastly, I’ve learned to be more practical about time. Students don’t have long attention spans, especially with topics like fractions and percentages that can be abstract.  I need to be mindful of how much information I’m giving them in a short period. Breaking the material into smaller chunks and allowing for more interactive activities would help maintain their focus and engagement. 

Overall, I feel more confident in my ability to manage time and observe student understanding in future lessons.

Reflection on flow chart

The model of flow helped me understand the relationship between challenge, ability in order to achieve the experience of optimal performance. What I found interesting is the balance—neither too overwhelming nor too underwhelming. In the flow state, the full involvement, as seen in the zone marked "Flow" in the top right section of the chart, as I learned before in my psychology class in undergrad, is linked to a sense of happiness, focus, and confidence.

Reflecting on my personal experiences, I often find myself in a flow state during activities like spin class or pilates, especially when the music is loud, and the instructor is present guiding me through the motions. These exercises demand both physical and mental presence, allowing me to connect deeply with my body, pushing myself to focus entirely on the movements. For me, the mind-body connection is the key that unlocks flow. 

Also, I’ve noticed that what I do before entering these activities plays a crucial role. I make it a point to praise myself for showing up, acknowledge my effort before I begin, which sets a positive tone that prepares me mentally for the experience. Afterward, I take a moment to thank myself for completing the task, reinforcing the accomplishment. This same mindset can be applied in a math classroom, where many students might struggle. As a teacher, it’s important to mentally prime students, encouraging them to approach challenges with a positive and open attitude. Another critical aspect of achieving flow in teaching is recalibrating lesson plans in real-time based on student reactions and understanding, as suggested by my practicum school teacher. Observing students’ engagement, adjusting the pace or content when necessary, and ensuring the challenge level is balanced with their abilities can help foster a flow state in the classroom.

Reflection on math textbooks

In Wagner & Herbel-Eisenmann’s work on math textbooks, I found it interesting that the authors suggest that textbooks have the potential to shape the learner’s identity, I believe the subject matter itself is subjective every learner's experience in education.

Reflecting on my own experiences, I’ve found that as a student, textbooks served as a reliable source for learning independently. They were a helpful tool for reinforcing concepts and understanding new ones. As a teacher, I continue to rely on textbooks to structure my lessons, check my own understanding, and find supplemental materials to enrich the class. However, I believe that every textbook has its value, and it’s essential for educators to use interactive methods to combine various types of textbooks. We should test them out, using our judgment to find the best fit for our students' unique needs. From my own experience in China, I witnessed students tearing textbooks after completing large-scale assessments, which signified how their attitude toward the textbook was shaped by the teachers’ approach. Instead of holding textbooks up as the authority, or the standard, it’s essential to see them as a starting point, a tool to share and build upon knowledge. This can be my personal challenge for the upcoming long practicum. Since I will be teaching knowledge heavy content (Calculus 12), I will be making observation of the student-textbook relationships and how they will affect students' learning. And for myself, I will find creative and engaging approaches to boost student' progress.

Response to arbitrary and necessary knowledge

Hewitt’s article highlights crucial distinctions between arbitrary and necessary knowledge and explores their subtle differences in how students acquire these concepts.

This reminds me of Building Thinking Classrooms, a book I’ve been reading. The first chapter serves as a guide for integrating non-curricular activities before starting a new lesson. These activities typically involve complex, thought-provoking, and highly engaging questions. Students draw on their prior knowledge, experiment with it, adapt it in new ways, and engage creatively with their existing mathematical skills. I find this process highly constructive for developing necessary knowledge, as students become active participants in their own learning, fostering a proactive and exploratory mindset.

After such activities, teachers can introduce a new lesson where arbitrary knowledge is taught. Because students are already in an intellectually active state, they are more receptive to learning and retaining arbitrary knowledge. They can better establish connections, create mental maps, and apply personalized methods to internalize the material more effectively. This sequence of active engagement followed by direct instruction supports a balanced learning experience, combining discovery and structured teaching to deepen understanding and retention.

Pro-D day reflection

 Last week’s Pro D event was an incredible experience! I attended the Culturally Responsive Pedagogy Symposium at the SCARF building, where I listened to insightful talks and discussions on various topics that are currently shaping education. 

In this post, I wanted to share a particularly impactful talk by Dr. Pamela Malins--"Facilitating Difficult and Sensitive Conversations." This session was especially thought-provoking and resonated with me on a personal level. Dr. Malins discussed strategies for leading challenging conversations in the classroom. As new teachers, we are increasingly encountering students from diverse backgrounds, which can present communication challenges due to language barriers and cultural differences. 

Dr. Malins introduced several practical techniques, including setting clear ground rules before initiating discussions, using evidence-based arguments, and ensuring that both teachers and students participate in an inclusive and respectful manner. By establishing these ground rules early, teachers can facilitate discussions that encourage thoughtful engagement. Additionally, she highlighted the benefits of using small group discussions and allowing time for reflection to help students feel more comfortable participating. 

Another key point she made was the importance of active listening. When facilitated effectively, active listening demonstrates empathy and fosters an inclusive, productive dialogue.

They are useful strategies that will go a long way in my teaching career, and I will remember them to apply them daily.