Reflections on Flow

 I really liked how at the beginning of the talk he says "We talked to creative people - artists, scientist...". I always appreciate it when science is acknowledged as a creative endeavour - because it is really creative! I have experienced flow before, mainly when I'm creating art, but also when I am thinking about planning a lesson. I really enjoy thinking about how to present material - I actually think lesson planning is one of my favourite parts of being a teacher.  I have never experience flow while working on mathematics - I don't think that I'm a good enough mathematician. In the talk he discusses how it requires a certain level of skills to achieve this flow state - I think mathematics has always been a bit too challenging for me to really achieve a flow state while doing it. 

I don't know if students can achieve flow in a secondary math class. I think that if it were to happen students would have to be given a lot of time. When I think about the times that I have been in a flow state, it's been when I am working individually on something that I am very passionate about, and also when I have a lot of time to focus on that thing. I don't know that an 80 minute block is enough time for a student to get into a flow state. I read an article in one of my other classes 'The Seven Lesson Schoolteacher' by Gatto and he talks about how we're constantly teaching students that their work isn't important by stopping it every time the bell rings, and expecting them to abruptly shift their thinking onto the next task. I think that this effects students getting into the flow state - we've socialized them to drop their work, and we actually get mad at students when they want to keep working but we as the teacher want to move on. 

Textbook Reflections

I thought this reading was quite interesting. I have been on both sides, as the reader and the writer. I haven't written a textbook, but I did write a masters thesis, and when I did I was very intentional in the ways that I addressed the reader. As a student I was so frustrated by my math textbooks! I was so so so so so sick (cannot express this enough) of the textbook addressing the reader as "he". When I wrote my thesis I referred to the reader as "they", a gender neutral term. I also got frustrated when the textbook would refer to exercises as 'easy' and 'trivial', because a lot of the time, for me, they weren't. In my thesis I never wrote things off as easy and trivial. 

The examples given by the article were a bit surprising to me! I was surprised to find that the textbooks didn't use "I" or "we", as those are quite common math terms. Whenever I explain a math concept, I always use 'we' - e.g. 'now we divide by three'. I like this because it shows that math is collaborative - we are doing it together. As a high school student I never read the textbook, I only did the exercises. I do wonder what I would have thought as a high school student though. 

As a teacher I like using a textbook. I like textbooks because they organize the material for me, and they provide me with a starting point for how I will present the information and teach it to students. I also like the exercises in textbooks. I view textbooks as more of a teacher resource than a student resource at the high school level. I honestly don't expect the students to read the textbook - whether this is a good expectation or a bad one. 

My own real work math problem: Petersen Graph Wedding Arch

 This is real world math problem I had to do for my wedding last year! My husband and I both love math (we met in the math department), so we wanted to have something fun at our wedding that showcased where we met. We decided for our wedding arch to be the Petersen graph, but in the shape of a heart. (Based off of this drawing).

The whole thing was 6.5 feet tall. Calculate how long each piece should be in the final product. The curved lines will end up as straight lines. 

Here is a picture of the final product. My dad made it for us. 

(me and my friend taking pictures in front of it - we met through doing math research :) ) 

Soup Can Problem

 To solve this problem I began by researching. 

First, I wanted to estimate how large the length of the can was based off of how large a standard bike tire is. I found that the standard wheel size on a women's bike is 27.5 inches (https://www.femmecyclist.com/womens-bike-sizing/). I found that the length of the can was roughly 7 bike tires, making it 192.5 inches long. 

I then researched how big a normal campbells tomato soup can is. The AI overview on google told me that it was 4.125 inches tall. 192.5 inches divided by 4.125 inches gives a scale factor of 46.6 repeating. Given that a normal soup can is 3 inches in diameter, the big painted soup can is roughly 140 inches in diameter. 

I then looked up the volume of a right cylinder, V= pi*r^{2}*h. That means that the volume of the big soup can is 2963307.27 inches cubed. 

I then started investigating how much water it takes to put out a fire. I found that most measurements were in gallons, so I converted my volume to gallons and found that the tank should hold roughly 12828 gallons of water. 

From this website (https://kiserrenovations.com/how-much-water-is-used-to-put-out-a-fire/) I found that an 1,800 square foot, one story home requires around 600 gallons of water to put out. With ~12,000 gallons of water in this reservoir the firefighters could put out a lot of fires!

Arbitrary and Necessary

Overall I did not like this article. I felt that Skemp's article on relational versus instrumental knowledge stated these ideas in a better way. When we talk about instrumental knowledge, I think it's the use of 'arbitrary' knowledge. For example, students don't know why a negative times a negative is a positive, they just use it blindly from memory. I think that Hewitt would view this as a necessary fact, that is being taught in an arbitrary way. Whereas relational knowledge is having the deep understanding of why things work. What I gathered was that Hewitt's position was that teachers should be teaching the why, and not teaching necessary things as if they were arbitrary. 

I agree with this sentiment wholeheartedly, however Skemp's breakdown spoke to me more. I did not like in Hewitts article how he asserted that math lies in properties, and that it does not lie in the practicing of conventions. I thought that this was a very narrow view of mathematics, and devalued the work that goes into communicating mathematics. I believe that communicating math is doing math, and inherent to communicating math is using these set standards and conventions properly. You can have all the understanding in the world, but if you are unable to share this understanding, what is it worth? This devaluation of language reminds me of the hierarchy of academia - where sciences are put at the top, and 'softer' subjects such as english are put towards the bottom. I think all subjects are inherently intersectional, and almost tossing aside this aspect of math, to me, seems callous. 

As of right now, I don't think that this article will have an impact on my teaching. Like I mentioned, I totally agree with Skemp's article on relational versus instrumental knowledge, and I think allowing that to influence my teaching is better, because that approach doesn't devalue math communication in the way that I feel this article did. 

Provincial Wide Professional Development Day

 For the pro d day on Oct. 24 I attended two sessions on  on Fetal Alcohol Syndrome and how to be a more inclusive educator for students with fetal alcohol syndrome. I learned a lot! I’m happy that I attended. The thing that stuck with me the most from the info sessions was that it’s estimated that 4% of Canadians have FAS. That means that in every classroom there’s likely a student that has FAS. It’s good to be aware of this, and I’m glad that I am. 

Curricular Microteaching reflections

 I thought that our curricular micro teaching went well. I wanted to practice writing on the board while teaching, making sure that I didn’t talk at the board, and I thought I achieved that goal.

I think that our timing was off. We didn’t get to cover everything that we wanted, and I think we in general but off more than we could chew. For next time, I think planning to cover less material would be a good idea. I think I have a better idea now of how much you can do with fifteen minutes.