Final Reflection

Over the last few months, I've appreciated the progression, engagement, and diversity of ideas in this course a lot. I've learned how to develop lessons for mathematics education in a creative way and become more cemented in my teaching identity. Math has always been able to lend itself to more interdisciplinary ways of structuring classes, and yet, it's so easy to get caught up in the lecture style that has less efficacy in inspiring today's students. That led to why I really loved the activities we were able to try in the garden. Having the opportunity to try outdoor-learning with a STEM (inspired) class made it seem a lot more achievable, and I'm so much more likely to try recreating that experience for some of my future students. 

Unit Planning Assignment

 Here's my unit plan:

https://docs.google.com/document/d/1JNjxshJjMJXSZ9j-RJCnmm3froVigO2DyjOH8ubrpIE/edit?usp=sharing

Reflection: Wagner & Herbel-Eisenmann on textbooks

I thought a lot about what a math textbook meant to me as a high school student. Unfortunately, it was nothing close to what teachers or authors may have intended- it was simply a place where homework problems came from, with a cool fact here and there. My sisters, both AP Math students, also agreed that their textbooks did not mean very much to them, simply a responsibility to keep it in good condition until the end of the year. 

On one hand, that meant that we relied a lot more on the teacher's notes and other contents to succeed during the year, but on the other, the textbooks don't seem to have served their purpose. 

Reflection: Mihalyi Czikszentmihalyi's TED Talk on Flow

During his TED Talk, Mihaly Csikszentmihaly reflected on many moments where meaningfulness in life was separate from materialism. At some point he remarked, "whether it's mathematics or music, it takes that long to be able to change something in a way that it's better than what was there before," in regards to a level of commitment, creativity, and expertise. With comfort in creativity, one can embrace challenges and attain 'flow.

Dave Hewitt and Mathematical Awareness and Fractions Reflection

Here was my attempt to the activities proposed by Dave Hewitt in the video:

Reflection: “Arbitrary and Necessary Part 1: a Way of Viewing the Mathematics Curriculum” by Dave Hewitt

The irony of this reading was that in order to understand the terminology, “arbitrary” and “necessary”, I had to memorize Hewitt's definitions because it wasn’t a natural deduction for myself. I thought of “necessary” in terms of having to lay the groundwork with definitions, and “arbitrary” as the formulas (because quantities are unspecified). That initial confusion helped drive the argument home though, because sometimes the point is to memorize properties and function to succeed in appropriate contexts. 

"The Giant Soup Can of Hornby Island"

I found that estimating the volume of water in the Giant Soup Can Tank a very similar problem to that which would be solved in a Physics class. Fermi Problems are generally used to estimate the order of magnitude for a quantity in a given space. These problems usually have very flexible approaches, because the end goal simply justifying the closest possible guess. 

Pro-D Day Plan and Reflection

 For the Pro D Day on October 20th, I attended UBC's "Introduction to SOGI in the K-12 Context." It was a really informative workshop, and I took away a lot of ideas on creating safe spaces in the classroom.

Battleground Schools Reflection

 "Battleground schools" by Mathison and Ross was a very enlightening read. I was not aware of the many pushes in mathematics education over the years, assuming that it stayed relatively constant until the most recent curriculum shift. I think that view was partially motivated by conversations from my elders. My family received a standard British Education in the Caribbean, and likewise with our friends from the UK, India, Hong Kong, etc. From those discussions I had understood that the North American Education system was slightly lower in some respects to the British System, but didn't know of the movements that polarized educators- especially for math! I thought that the shifts were in connection to subjects such as language arts, English, Drama, Music, Social Studies, etc.

"What is meant by 'curriculum'?" Reflection

Throughout Eisner’s, “The Three Curricula That All Schools Teach,” I found myself in agreement with the descriptions of the three curricula. Eisner mentions how students who graduate from secondary school spend 12,000 hours in school settings, which is a considerable amount of time for their exposure and compliances to the goals of the curriculum. 

Group Teaching Activity Lesson Plan + Post-Lesson Reflection

LESSON PLAN:

Here's the lesson plan for Chernie, Esther, and I's lesson: 

https://docs.google.com/document/d/1JHQ12-x3AkxAMUZgkpAem8jumMaeLTv4V2e1efBVf2I/edit?usp=sharing

Our topic is Introduction to Slope for Grade 10 Foundations and Pre-Calculus. 

*Edit: October 16, 2023

Teaching Perspectives Inventory Reflection

 

Results from my TPI 

My results range in order as: nurturing, developmental, apprenticeship, social reform, and transmission. I was surprised that nurturing was dominant; developmental, apprenticeship, and social reform were present; and that transmission was recessive. It always seemed as though math teachers needed to have a higher balance of nurturing and transmission, so initially, I had trouble reconciling those contradicting results. Having reflected on my teaching experiences however, I realize that these results were very in line with my actual style. 

Micro-Teaching Topic + Lesson Plan + Post-lesson Reflection

TOPIC: 

 For the micro-teaching lesson plan activity, I would like to introduce: basic piping (decorating) techniques for baked goods. 

Math Art Projects & Reflection

Submission for the math art project.

The Dishes Problem

The problem: 

"How many guests are there?" said the official.

"I don't know," said the cook, "but every 2 used a dish of rice, every 3 used a dish of broth, and every 4 used a dish of meat between them". There were 65 dishes in all. How many guests were there?

Classroom talk on Skemp's Article

 On September 13th's class, our group responded to the following questions:

1) What 'should' come first in learning math: instrumental or relational understanding? Why? In what contexts?

2) What is our aim in teaching math: to teach fluency in procedures? To get kids excited about the possibilities in math? To help them have a deep understanding of some (or all) topics? How can we address all the goals that we (and our society in general) have for math learning? How to make principled choices about how we teach what, and when?

3) How can we, as mathematics teachers, work to improve the negative attitudes of math anxiety or math avoidance in our communities? Are these attitudes the same in all cultures, or could Canadian society learn more positive approaches to mathematics from other cultures?

Our responses were summarized on the blackboard: 

Letters from my future students!

Letter from a student who loved my class:

Dear Ms. Mohamed, 

Hope you have been taking care! 

I know it's been 10 years, but I really wanted to check in and thank you for my experience in your math class. Every so often I'll be minding my business throughout the day, and then I think, "oh look! So much math might have gone in to that" or "hmm, I wonder if that set of ideas came from a different origin place." I'm really grateful for the emphasis you placed on shifting our perspectives of math in the real world, and how much you passionately talked about different cultures, times, and people. You used to encourage us to share our math experience and our identity, and had so many thoughtful activities that facilitated that growth. I felt my confidence grow in your class, because I got to appreciate the subject I once hated and felt the satisfaction of all the mathematicians of the past cheering me on as I learned and mastered their topic of studies! 

Thoughts on Lockhart's Lament

I think that Paul Lockhart's, "A Mathematician's Lament", hit the nail on what mathematics education looks like from K-12. The examples of the musician and painter felt eerily familiar and I completely agree with him that students are generally taught to analyze the qualities and properties of concepts, without getting a chance to experience it in its full glory. The Fibonacci sequence, for example, is often blown over or briefly introduced as a series of numbers, but rarely is there a dedicated lesson highlighting the presence and applications for it in real life. The same thing can be said about prime numbers, where students understand that primes are defined as having factors of (1, P) - but they may not understand why that is important or what primes can do for us! Students learn about calculating the area of a standard parallelogram, but have they ever seen the application rhombs have to tilings? There is a significant disconnect between the mathematics that is taught in schools and the mathematics that many mathematicians interact with. This distance seems to deter students from the beauty of this study. 

My favourite and least favourite math teachers!

In terms of formal mathematics education, due to being a math major, I've had 20 MATH instructors during university, and another 8 during secondary school. I've also received assistance from my parents, some family friends, TAs and formal supports. So many have had a really positive influence on my journey, shaping the inner math teacher I hope to one day bring to the world! Others have, unfortunately, been examples of what not to do. 

Here were some of my favourites: 

The Locker Problem (1000 lockers edition)

Before attempting the problem, I thought the solution would have been a messy array of numbers that needed to be tracked via extensive diagrams. However, I began the problem by setting up 10 lockers, perhaps due to our connection to the base 10 system. Very quickly, it seemed that base 60 would be great for a more obvious illustration of the pattern since it has significantly more factors than 10. That level of effort may be commended, but would end up redundant.