Course Reflection

 I have thoroughly enjoyed this course in this semester. The most rewarding part of the course is witnessing the transformation of myself through out the course. One big idea I took away from this course is that all roads lead to Rome. There are so many correct ways of doing things which lead to the same result. Seeing my colleagues in this class doing things in so many creative ways really opens my eyes to the world of teaching. Over the course of this semester, I was impressed times and times again by the work done by them. Through working on puzzles like the lockers problem, the dish problem, geometric puzzle and the giant soup problem, we can see how different people use different ways to solve the problems. I believe that this course really taught me to be open-minded and humble that Math can be done in a lot of different ways (A lot of interesting and fun ways too!)

Another thing I learnt in this course was collaboration. I really like the presentation by Asha because I had the chance to work with her during my 2 week practicum. Her vertical whiteboard classroom really emphasizes on collaboration among her students. You can see students teaching each other and this actually give them a sense of purpose. This bolsters their intrinsic motivation in the subject which increases their interest in the topic. It is no longer the old fashion way of lecture and notes. Before coming into this class, I really had no idea of how to teach other than the way how I was taught back in high school. And after going through these 3 months, I know that I do not want my future students to go through the same boring way of learning Math (And no wonder why so many people have Math anxiety).

I wish that this class was done in person since it allows more time for collaboration and group work. It is a shame we had to do it online. But we tried our best to mimic a real classroom and I learnt a lot from Susan and my fellow TCs and for that I am really grateful. 

Unit Plan

 Here is the link to my unit plan:

https://drive.google.com/drive/folders/1gykWJ6TtVYKSi8KAiyU-4MgzX3EjFeK5?usp=sharing

Math Party

When I hang out with my friends, some of us in the group always like to share jokes and riddles, some of which are Math related. I think I would just share one of my favourite ones for our Math party on Monday:

10 prisoners were sentenced to life in prison. However, the judge decided to give them one last chance to save themselves by playing a game with them. First, the judge would line them all up in a single file. Then he would place either a black hat or a white hat on top of each prisoner's head. One by one, and starting from the last person in the row, they had to guess the colour of the hat on top of their own heads. The prisoners who guessed right would be freed, those who guessed wrong would be thrown into jail.

Note the following:

- Each prisoner could only say one word to guess and it was either "black" or "white". If what the prisoner said matched with the colour of the hat on his head, he would be set free. A prisoner could not say anything else other than "black" or "white".

- The last prisoner in the row could see everyone in front of him (including the colours of their hats), the 9th prisoner could see everyone in front of him (including the colours of their hats) and so on, until the 1st prisoner, who could not see anyone in front of him.

- A prisoner could not see the hat on top of his own head.

- Before the game, the prisoners did not know how many black and white hats there were, that is, there could be 5 blacks and 5 whites, 2 blacks and 8 whites, 10 blacks or even 10 whites, just to name a few combinations.

- Before the prisoners lined up, they got together and discussed strategies of how they could play this game

Question: What is the strategy that can save the most number of prisoners? How many prisoners can you save using this strategy?

Unit Plan 1st Draft (Quadratic Functions and Equations)

 Unit Plan:

https://docs.google.com/document/d/1HYrWjJkAm2MfM2AVoFYThNSk9YB_ndS2dxJ01XN5teo/edit?usp=sharing

Lesson Plans:

Factoring Review, Solving Quadratic Equations graphically and by factoring:

https://docs.google.com/document/d/1QfmeRszBGUW1AHM-3mZBWsOsxG2ZvjD4RLuqAsBlrnM/edit?usp=sharing

Quadratic Functions in Vertex and Standard Forms:

https://docs.google.com/document/d/1NuKXqWOSTOwVs0GvQ9JnsUkHTd2-pWp_avdfpCEN5Rw/edit?usp=sharing

Completing the Squares and Application Problems:

https://docs.google.com/document/d/1rDOte_SXXtAZIwDPDdbVyCtKT2cEyCa9GN9pnL0xI_M/edit?usp=sharing

Arbitrary vs. Necessary

After reading this article, it makes me reflect on how I can improve on giving lessons to my high school Math students. A lot of times, maybe due to time limitations, we tend to just give too much information that we think are arbitrary to the students. But in fact they can be worked out using arbitrary concepts. This means we are basically giving too much information to the students. They are suppose to learn the topics themselves with our guidance. For example, when we are doing exponents, the arbitrary is the exponent notations and the definition: " a number to the power of 2 means the number multiplied by itself". Then from there, a lot of the exponent laws can be derived from this arbitrary definition of exponent. Of course most students require guidance from the teachers to arrive at all the exponent laws (unless your students are very smart). From this example we can see that learning a mathematical topics does not require teachers to lecture for the whole class. All we have to do is give hints and guidance so students arrive at the desired theorem or learning outcome. 

Another thing is some concepts were taught during previous grades and those topics become the "arbitrary" topics. Teachers do not have to go over how we derive those laws and theorems again. That is why you do not see high school Math teachers teaching students simple adding and subtracting of whole numbers. These are conventions that students have learnt and acquired when they were in elementary school. 

Overall, I feel that to teach a Math class effectively, we have to differentiate the arbitrary and the necessary. I think that we spend less time talking about arbitrary and instead focus on the necessary to foster a thinking class. As teachers, we have to come up with good guiding questions so students can make good use of the arbitrary to derive the necessary, ie. the learning outcome.

Teaching Perspective Inventory

To be honest, I am not surprised by this result. All along even when I was tutoring my students, I focus on nurturing and encouraging them. I am not the kind of teacher who always demand academic excellence in all areas from my students. I look at what they are good at and interested in, then I provide guidance for them to be good at what they love to do. Also it is no surprise my social reform scores the lowest because I do not really focus on educating my students to change the society. I nurture students to excel in what they love doing but I really do not tell every single student that they are here to bring about changes to the system. This is just not the focus of my teaching. 

Another thing that catches my attention is, I am after all still a novice school teacher (even though I have done tutoring for quite a number of years now), so we see that most of my bars are just a few points shy of nurturing. This is because as a novice teacher, I want to do a bit of everything. I have yet to develop my own teaching philosophy or identity. So maybe after a few years of teaching in school, I may see my dominant teaching perspective to stand out even more. 

Thinking about math textbooks

 I think Math textbooks are like guide books where wordings are unbiased and non-personal. Official documents like an insurance policy, land owner certificate and electronic appliance user manual have really formal wordings. Math textbooks are kind of like that, but without all the jargons. One good thing about it is there is no ambiguity. After all we do not want students to misunderstand so the wordings must be precise. But one trade off is lack of context. Math textbooks are full of proofs and theorems, you do not see connection to the real world (the examples they use are mostly unrealistic). I think they make textbooks this way so teachers do not depends solely on it when teaching the class (At least I will not). Teachers are the ones who need to make connection between the math and the real world. During my 2 week practicum, I learnt that students learn the best if they can connect the idea they learn in school to their daily lives. Therefore, math topics like financial literacy are amongst the most popular among math students.

I see teachers are using the textbook less nowadays. They may based their explanation of theorems and concepts on the textbook, but teachers like to use real life examples as much as possible. As I mention earlier, students like real life example a lot  because for them, that is the best way to learn. The section I may use from the textbook is the practice questions. I may assign homework from them as well. However, as we have more advance technology and more online resources, I see the reliance on textbooks is diminishing. There are more innovative ways of presenting a lesson than using a dull textbook. Nowadays I see students only use the math textbooks when they need to check on a certain formula or work on their homework.