Final Course Reflection

 

This course has been an incredible journey, one that has reshaped the way I see Mathematics education and my role as a future teacher. Reading back at my blog posts, I can identify numerous areas where my understanding of mathematics as a whole and how students receive mathematical instruction has evolved. The biggest think might be recognizing the critical difference between relational and instrumental understanding. Skemp's ideas about the satisfaction that comes with relational learning deeply resonated with me and made me think about my own experiences as a student. I’ve come to realize that the moments I truly enjoyed math, and perhaps the ones that sparked my love for the subject, were when I understood the "why" behind concepts. This understanding is something I hope to prioritize in my future classroom, even if it requires a little more time and effort. Since reading this article, I have also began to see how teachers in my practicum school use the different instruction methods and how the students reach to them.

Another key lesson I learnt was through Eisner’s discussion on the subtle yet powerful messages embedded in the curriculum and materials. It reinforced the responsibility we hold as educators—not only to teach but to be intentional about what and how we teach. Lockhart’s critique of traditional math instruction further pushed me to think about making math engaging and relevant to students’ lives. While I disagreed with some of his points, his emphasis on creativity and inquiry has inspired me to integrate more real-life connections and necessary knowledge into my lessons. Geometry, in particular, feels like an area ripe for exploration in this way. Combining math with other subjects like history and art is another idea I’m excited to experiment with, as it offers a holistic view of concepts and sparks creativity.

As a suggestion for future years, I think it would be helpful to include more examples of how to implement relational understanding in diverse classroom settings, particularly when dealing with time constraints and diverse levels of learners. More discussions on integrating math with other disciplines could also be beneficial. Overall, this course has been a deeply reflective and transformative experience, and I am leaving with a clearer sense of how I want to teach and inspire my students.

Sequences Micro Lesson Reflections

 

Overall, I feel that our micro-lesson went well and engaged students in helping them meet many of the objectives we defined. There are some overall themes from the feedback that I noticed.

1. Clarity of Presentation & Activities and Learning Objectives Addressed and Met
   Some feedback indicated that while the activities were engaging, the clarity of the lesson could have been improved. While I was happy with the natural flow from the drumming activity to the introduction of sequences, I think that some more time to connect the activity to the concepts being taught would be beneficial.

2. Explaining Concepts
   There were a few moments where the explanation of concepts could have been clearer. I made the mistake of saying r represents rate instead of ratio, which may have also added to the confusion. Next time, I would include a brief step-by-step breakdown of how to identify and calculate the common ratio, explaining the underlying concepts more and with additional examples.

3. Drumming Activity
   The drumming activity was well-received and enjoyed by all. It set a lively tone for the lesson and about the connection between rhythms and mathematics. It would be useful to build off of this exercise in future classes where more patterns and sequences would be introduced. The teacher can build up to include more diverse rhythms or variations, like tripling or halving beats even further or in varying ways. This would deepen the connection between the auditory patterns and the mathematical being introduces..

4. Time Management and Consolidation
   As always, the timings don't go as planned. I felt like we had to rush a bit  at the end, with little time to review key points. Next time, I would plan better and be sure to at least include a clear summary at the end to help students see how patterns in sequences connect to real-world examples like music and science. This would solidify and further their understanding and make the lesson more meaningful.

Workplace 10 Unit 3: Trig

       

 Please click the links to access the documents.

     Unit Plan

     Lesson 1

    Lesson 5

    Lesson 7

MicroLesson Teaching Plan: Sequences PreCal 12

Please access through the link:

https://docs.google.com/document/d/1MBxwKz5iexRaJV0zTaUb-8RIJEwPlx25/edit?usp=drive_link&ouid=114344616397971363305&rtpof=true&sd=true

Pro-D Day: Assessment Workshop

 

I attended a workshop on assessing students’ thinking and processes rather than just their academic abilities. The session was very hands on and looked deep at strategies like using rubrics, think-alouds, and concept mapping to evaluate how students approach problems and make decisions. We explored frameworks including Bloom’s Taxonomy and practiced creating open-ended questions that encourage students to explain their reasoning. I benefited greatly from a hands-on activity where we assessed sample student works. This helped put the ideas into practice and improve my process  immediately, because I was able to stop and ask questions as needed from the presenters.

What stood out most to me was how small changes, like asking “How did you come to this conclusion?” instead of “What is the answer?” can have significant impacts on how the students react and in encouraging critical thinking. I was surprised by how much I hadn’t considered the value of observing and supporting students as they think through challenges. Moving forward, I want to work on creating my own rubrics to evaluate thinking skills and experiment with giving more meaningful feedback that helps students grow as thinkers. This workshop left helped transform how I viewed "good academic outcomes" for students, and it inspired to make my assessments more purposeful and student-centred.

One particular point that I related to strongly was a side point discussed in the workshop about how students retain information. The presenter's shared a chart showing how students retain different modes of content. It was integrated into the workshop to show that if we use different instructional modes, it will make the assessments more suitable and tailored for each student. I always knew that discussions and engagement was crucial to learning, but this was the first time I saw it structured and could see the importance of each.

 

https://remixculture.les.middcreate.net/blog/blooms-taxonomy-remixed/