Micro-teaching Reflection

Self- and Peer-evaluations

    A big idea I learned from this activity is that it's very easy to get myself engaged in teaching the content because we chose a topic that we are passionate and have knowledge in. This made me realize how important it is to have passion and solid knowledge in what you are teaching (whether it's teaching/training a skill at work and tutoring academic subjects, to explaining someone about the details of some breaking news), to be an effective instructor for your audience. If I'm not having a fun time talking about something, how would it be possible to keep the students engaged in what I say? Not everything teachers teach is "fun" (like certain historical events, since those should be treated in a respectful manner), but the significance of being able to show how much we care and think it's meaningful will reach the audience. In the math context, this definitely reaffirmed my values as a teacher, on the importance of mastery while creating a positive learning environment for all students. 

    My micro-teaching lesson went smoothly, having enough time to go through the key slides and information needed to complete the assignment at the end. I think the layout of the lesson was very clear, especially because I took the time at the start to go over the lesson objective and learning objectives with the students. While teaching, I noticed that all of my students were very engaged in the content. With this, I made the choice to allocate more time to the end-of-class activity. The choice to make this change ended up being successful, even though I made the decision on the spot. I'm happy that I was able to make flexible decisions as I saw how the students were doing. 

    One thing I should work on is my voice projection, especially when we have many groups talking at the same time. I've always had a hard time adjusting my volume to the adequate loudness of the environment, since I either speak very very loud in a large room to teach karate, or I talk softer with my friends in a smaller group setting. I hope I can practice this during our other teaching opportunities in the program or during the upcoming short practicum. Something that I could have added to my lesson was another very small check-in question or activity. This could've been a short Check-Your-Understanding question mid-lesson to connect with students and see if they are on the right track with the material. Even if I didn't have to use this check-in question, I could have added a slide just in case I had students who were struggling to understand the lesson. 

Micro-teaching Lesson Plan

 

Locker Problem

 

Math Art Project (Group Response)

Group members: Damanjit, Elvie, Helin, Yuki

Original Artwork and Artist: Flowering Grid by Eric Gjerde by Tejom Patel

    After our group collectively chose this artwork as our project topic, we faced a big issue of not having resources that lets us perfectly remake the original artwork. The artist, Tejom Patel, had creatively expanded their flower tessellation (based on Eric Gjerde’s work), by adding different folds to produce a new, unique piece. We started off attempting to perfectly mimic Patel’s art. However, due to our lack of knowledge on how the folds and designs work, we had to start off by choosing a design that had guides and tutorials. This was the Spread Hex Tessellation.

Similar to the original artwork, we kept the idea of hexagons and reflectional symmetry, but folded a tessellation where the hexagons overlap and pile up.

Here is the link to the video tutorial of the spread hex tessellation: 

https://youtu.be/3BTu2Hih39A?si=jRJpq3Fw6cG6oauz 

    Through our research phase, we came across Eric Gjerde’s book Origami Tessellations: Awe-Inspiring Geometric Designs. This resource provided detailed folding tutorials for many origami tessellations built from triangles, squares, and hexagons, and also explained key techniques such as Pleat Intersections, Triangle Twist, Square Twist, and Hexagon Twist. With this reference, we gained a deeper understanding when looking back at our own work, and it also gave us the idea to design an activity more suitable for a short classroom session.

    Our interactive activity with the class was a hands-on origami activity where each student folds their own piece of flower that will then combine to create a big multi-piece flower tessellation. Since abstract origami tessellations take a long time to fold, we designed it such that all prep is done (fold lines created beforehand) and students are to follow instructions while helping each other to collectively create one piece of art with the class. 

Note: We will post a picture of the complete class tessellation tomorrow

Here is the link to the origami flower we made in class:

https://youtube.com/shorts/tQMteMhp1Dk?si=Hxtkz7Yhg_-RoIt7 

    In addition to experimenting with hexagon-based tessellations, our group created a variation called the Layered Compass, which is folded from square paper rather than a hexagonal grid. This shift gave us a chance to explore the mathematical flexibility of tessellation design. Whereas hexagons naturally lend themselves to 120° rotational symmetries and interlocking flower-like patterns, the square base highlights 90° rotations, reflections, and layered symmetry. By adapting the same folding principles—pleats, twists, and repeating units—to a different polygonal foundation, we were able to compare how tiling properties change with shape and how symmetry groups are expressed through origami art. Using square paper also made the process more accessible, since it is a common format and easier for classroom folding activities. Through this variation, we not only made the project our own but also deepened our appreciation of tessellations as a versatile mathematical art form that can be reinvented through creative folding choices.

Math Art Project (Individual Response)

    This math art project with my group was a great start for me to think about how we can relate art pieces to math concepts and mathematical thinking. With the variety of choices off of the site provided by Susan, we were able to choose an art that we personally like and want to recreate, as well as seeing if the mathematical ideas behind the work is understandable for our level. By researching various ways to recreate our artwork, we came across many unique origami tessellation designs that range from simple to complex folds. When I played around with the Spread Hex Tessellation I made, I tried to incorporate my own folds and designs, which didn't end up symmetric and looked slightly off, so I had to stick to the original spread hex design. If I had more time to learn and discover more designs, I could have been able to make one that is unique to me and our group that is not on youtube or any origami textbooks!

    In the future, I would definitely want to incorporate these art projects as part of a couple of units in the curriculum so the students can develop creative thinking within a math class. Math is not all about algebra and graphs and problem solving, but it is seen in many designs around us. Everyone's interactive activity can be building blocks to any future hands-on activity that I can do with younger grades, leading to fun brain breaks and group activities. It will be a valuable learning experience for the students to shift gears from equations on paper to visually appealing artwork, opening up pathways in math education that it's not always the marks and test scores that hold meaning in math. Similar to what our group faced, the students will also have lots of freedom when selecting their artwork, and promotes personalization of the artwork. However, we must take into consideration that any interactive activity or project should have some connection to our curriculum, and be careful with time management so that students have enough lesson days to complete the curriculum in school. When certain activity instructions are difficult (like folding a flower with origami), it can be hard to have students pay close attention to the details and could end up having students give up or dislike the topic because it is "too hard and too time consuming" for them.

    I personally had so much fun being the student and doing the activity, while also being the teacher to help lead the activity. These opportunities are valuable since we get to see what it's like to learn crafts without prior knowledge, which helps with understanding frustration and satisfaction.

Favourite and Least Favourite Teachers

    My favourite math teacher was my high school teacher, who supported our transition from elementary to secondary school. They made math engaging with riddles, puzzles, and creative projects that made it easy to shift into a more structured academic learning. Grade 8 was overwhelming with emphasis on grades and tests, but this teacher kept a positive atmosphere, provided clear explanations, and was organized with schedules for each course, which all helped us navigate. Interactive activities extending from lessons included a hands-on art project (for geometry) and a cooking project (for fractions and ratios). Both were nice breaks from traditional assessments since we were not yet used to being tested or quizzed every week.    

    I don’t recall having a least favourite math teacher, but I did have a science teacher whose approach shaped how I think about the role of a teacher, classroom management, and building community. In this science 8 class, they emphasized the Cornell note-taking method and expected everyone to follow it strictly. Outside of class, many students were speaking about their frustrations on having to focus on how to take notes rather than the content itself. The teacher often checked our notes and called out those who struggled in organization, having quality work, and had a few blanks on their assignments. They offered very little support to the students, and they told other classmates to help get those students on track. This created stress, and ultimately discouraged some students from asking for help and having to deal with the power balance.

    Reflecting on these experiences, I’ve realized how crucial it is to learn from a variety of teachers and understand the student perspective of each choice the teacher makes. From my math teacher, I want to take away how they value creating a supportive, well-organized classroom that encourages creativity and collaboration to ease the transition from elementary to secondary. Of course, from my science teacher, I’ve learned the importance of respecting different learning styles and being the adult they can rely on when problems arise. Enforcing one method that I believe to be the most useful won’t result in successful students. Most importantly, I want to make sure that struggling students feel guided and supported by me as the teacher.

Reading Response: What is a 'Curriculum'?

    I didn’t realize until now that my elementary school also treated Art blocks as the ‘fun’ and academic blocks to need more intellectual attention and focus in my elementary school too. As a young student, I felt the same way; arts and crafts were exciting while literature felt tiring. I remember afternoons had a bit more focus on P.E., music, and arts, but I can’t recall if these were taught during the morning period. However, it’s very clear that we shouldn’t create a hierarchy on which courses are more valuable than others (while difficulties vary), and that art is another form of valuable thinking that leads to deep reflective practices.

    When I read the first paragraph under section on Null Curriculum, what came to mind wasn’t school but today’s media. Say, if your local or national media doesn’t report important global (or even specific local) events and situations, citizens remain uninformed and unaware. Omitting information can signal devaluation or ignorance, ultimately representing what the government or national media does not consider to be important.

    Before reading this article, I thought of ‘school curriculum’ as the component of learning that is well-planned for students, but this was only at the surface-level of what it represents. Learning doesn’t just come from what is explicitly taught by teachers in class, but everything that the student notices and doesn’t notice. Biases can never be fully removed, but there are still so many areas of the curriculum that could be reconsidered to enrich student learning if we can identify all components of the curriculum. Within time constraints on each subject, it’s difficult for administrators to design curricula that fully captures its meaning, and for teachers to integrate it into their lessons and classroom practice.