Final Reflection

This course helped me shape my teaching philosophy in the math curriculum. The math art project helped me understand the strong correlation between math and art. I did not know that art exists in mathematics to this extent; seeing the beauty of this relationship made me want to implement art in my lesson plans. I believe that teaching mathematics through art could be a fun and engaging activity that will even help students be less fearful of the subject. Further, microteaching and group curricular lesson plans were very practical assignments. They helped me understand what I needed to be aware of and what I needed to work on as a teacher. Learning about the BC curriculum also helped me understand what I needed to focus on for my lesson plans. The hidden curriculum was eye-opening for me; I learned the importance of focusing on a student's development as an individual. I also felt privileged working in BC as it focuses on student's skills and helps them in personal, social, educational, and workplace contexts. The difference between arbitrary and necessary is now something I value when planning my lesson plans. I want my students to develop their awareness, creativity, and logic in mathematics and problem-solving. Finally, the unit plan project was a practical and resourceful guide for my extended practicum. As I was creating the unit plan, I focused on my experiences from my short practicum from what was effective. It was also a helpful experience because I got to think about diversifying my lesson plans, which was something I needed to work on after my short practicum. 

Unit Plan

Unit Plan 

Textbooks

As a teacher, I learned that I need to be aware of the textbooks I use in class and their linguistic choices. For example, I was not able to realize the difference between exclusive and inclusive imperatives before reading this article. It was interesting to think that these linguistic choices will not only help students reflect on their independent work, but think about their mathematics in the community. This will positively affect their involvement in class and enhance their mathematical thinking. Further, I learned that I need to be aware of the language I use when I give out my own instructions as well. As a student, I believe I will find myself reflecting on my thinking if I am given instructions such as "describe the pattern" or "suppose you use" instead of "make a table" or "graph your data." The verbs such as make and graph are very straightforward and require no thinking. However, describe and suppose are verbs that allow me to expand my thinking process. 

I personally do like textbooks as I believe they offer a guideline for teachers. However, I don't think I will be relying on them too much. Many textbooks that I encountered contain a lot of exclusive imperatives. Further, I think I will be able to allow students to reflect on their mathematics in the community if I give them personalized instructions that contain inclusive imperatives. Finally, I also need to be aware of what textbook I choose to use in class. I would prefer to use textbooks that have a separate section for problem-solving and applications (ex. MathQuest - I examined this textbook last class) as they allow students to make connections and understand relationships between math and the world.

Flow

There were many times when I experienced a state of flow. The model of flow was very relatable and made sense to me right away. When I encountered math problems, I felt all the different emotions that were listed in the model, so I knew what it felt like to be in a state of flow. This was possible when my challenges and abilities were balanced out. It always felt good to be in a state of flow as I was completely involved in what I was doing and I was able to experience a meaningful study session. Hence, I believe that it is possible to achieve a state of flow in secondary math classes. Teachers should implement challenging but not too challenging as well as fun activities. Deciding the difficulty level is challenging because everyone has different strengths and weaknesses. Hence, teachers should also prepare extending or easier questions just in case. Teachers should also know who their learners are in order to implement an appropriate level of difficulty. Lastly, teachers must make the assignments/activities engaging. They must be engaging enough to grab students' attention. Thus, when students are interested and are challenged enough, they will be able to get into the state of flow. 

Dave Hewitt

In the first video, I liked Dave's idea of using the entire classroom as a learning tool. His introduction to algebra and number line lesson was also taught by allowing students to speak in unison. This gave every student an opportunity to reflect on their learning. This made me stop and reflect on my role as a teacher candidate. However, as I was watching the video, I felt like the lesson was dragged on for too long. For example, I would implement more activities and foster group collaboration after a quick interactive lesson. Otherwise, if my lessons are too long, I believe my students will lose focus and interest. Another stop that was interesting was the concept of powers of the mind that was mentioned in the second video. He mentioned that there are different powers of the mind; one of them being memory. As teachers, we need to make sure that memory isn't the only skill that is being taught to the students. This is so common, especially in a mathematics classroom. It was also interesting to learn that we can learn a lot from little. His example of fractions made sense. We need a common name to add fractions and this can be easily explained with the concept of addition. I was able to learn that educating awareness is necessary instead of making students memorize information. I think Hewitt created the fraction problems to support awareness. This problem helped me understand how fractions work and that fractions can be equivalent even when they don't have the same denominator. These examples are crucial for students as they are able to build awareness in them. It will allow them to apply their knowledge instead of using their memory to solve it. Hence, I will need to be definitely thoughtful of the examples I give to my students in my teaching. 

I was able to find fractions between 5/7 and 3/4. Here is the work:

Arbitrary and Necessary

I was always aware of the difference between arbitrary and necessary realms in mathematics. As a student, I never understood why my teacher made me memorize formulas in a math classroom. It did not enhance my learning journey and made me spend less time practicing my logical and critical skills when solving a problem. As a math teacher, I need to make sure I am helping my students to practice their own awareness as this is a crucial skill in mathematics and problem solving. The article talked about a teacher informing their students that the angles of a triangle add up to 180 degrees. This example made me think about one of my lessons during my short practicum. I had to teach my students the quadratic transformations: stretch, vertical translation, horizontal translation, and reflection. However, my SA and I agreed that we did not want to tell our students what a, p, and q does in y=a(x-p)^2+q. Instead, we created an activity where students were able to investigate and play with Desmos, numbers, and tables of values to observe what each variable represents. Hence, this will drive students to use their awareness to come to their own conclusions. This also can be easily done through whiteboards. The day after I taught my students each of the transformations, I made them work in pairs and use the whiteboards to draw the graph of y=a(x-p)^2+q. The process of playing and struggling first before I gave them the lesson enhanced my student's understanding of this specific chapter. When I become a math teacher, I want to implement activities that will allow students to use their intuitive thinking to play and struggle before I give them my lesson. I believe that giving a lesson at the start of a class will allow students to practice developing their awareness instead of memorizing information.

Unit Plan Assignment

 I will be teaching Pre-Calculus 12 Trigonometry for my long practicum