Nov 29 - TPI Quiz

I was expecting most areas to be close to each other as I believe in balance. On their website it says "from the Social Reform point of view, the object of teaching is the collective, rather than the individual." I actually believe that the collective is made up of the individual, so it's no surprise I scored low on this aspect. I also found it hard to see how some of the questions, which were obviously asking about the social reform quality, were related to math.

What struck me the most about this quiz is how the questions were worded. When I was reading the majority of them, "it depends" came to mind often. So I am not sure how accurate the results are.

Nov 22 - Math textbooks

While I believe that "Language indirectly indexes particular dispositions,
understandings, values, and beliefs", I don't have much to say as I, personally, was never bothered by any language used. In elementary school in Romania, actually most problems had weird impossible numbers, and it was only here in Canada, in grade 12 that I realized they were trying to make the problems realistic. In terms of the pronouns or other aspects it also never bothered me since I just focused on abstracting the meaning.

I think using textbooks is a good thing as long as the textbooks are good. By "good" I mean that they stimulate mathematical thinking which encompasses abstraction and generalization, among other things. There are many books with many examples, Gelfand's Algebra comes to mind. Developing spacial thinking and a geometric way of viewing things is a must therefore, studying Euclid or any textbook that goes through Euclid in a more modern way could also be a potentially good textbook.

Scale puzzle

 I used latex because it's hard to write math here:

I don't know how to solve this. I've tried multiple ways and I got stuck. There seems to be an infinite number of solutions. Perhaps a different way of looking at it might help, but I am not so sure at this time.

Nov 17 - Group microteaching reflection

I think we probably did way too much. In hindsight each of our areas that we touched on could easily have been made into a full lesson.

Maybe something simple with more interaction would've yielded more understanding in the student's case. It's easy to overwhelm them.

Nov 16 - Group Microteaching: Lesson Plan and Slides

Slides: https://docs.google.com/presentation/d/1hpTqnFjh0ofj-Sw_AmRU5kHEuvj5BaHSc36J5iUtKnM/edit?usp=sharing

Lesson Plan: https://drive.google.com/file/d/1fnjBjMaBmx8PTUXID_HcbPKpf1cl9cMB/view?usp=sharing

Nov 13 - Giant Soup Can

First I measured a Campbell's soup can. I got:

6.5cm diameter = can_diam

10cm length = can_length

Average bike height up to the saddle is 95cm (my bike).

From the picture it seems like the bike is 3 times smaller than the tank.

Therefore, the tank is 95*3=285cm tall. This would be the length of its diameter.

Let Diam_tank=285cm.

Since the tank has the same proportions as the can, we must find the scale factor.

Scale_factor = Diam_tank/can_diam =285/6.5=43.8 times.

Therefore let tank_length be the length of the tank.

We have tank_length=can_length*scale_factor=10cm*43.8=438cm.

Next to find the volume, we need to find the volume of a cylinder with the specified dimensions.

In this case, the volume of the tank = pi * r^2 * tank_length = 3.1415*1.425^2*4.38= 27.9 m^3

Google gives: Firefighters, on average, use nearly 3,000 gallons of water on a house fire. (Source: https://www.thisoldhouse.com/home-safety/21018283/what-really-happens-in-a-house-fire)  

This converts to 11.36 m^3 per house. So we can actually put out 3 burning houses!

 

I've chosen part (a) extending the puzzle.

In the Campbell Soup puzzle above we went from a small scale to a big scale. Now, we will go from a real life scale to a smaller scale. Look up the distance of all the planets in our solar system (including the sun) relative to the Earth and draw on an A4 paper an accurate scale of the solar system.

Nov 9 - Mihalyi Csikszenmihalyi - Flow

I believe we can promote "flow" by assigning meaningful problems, that are not routine. Thinking hard about a mathematical problem could push the student into the flow state. I've never experienced flow before while doing math, and Mihaly mentions that you need 10+ years of experience in a field and flow would come while doing something creative in math. It would be difficult to do this with students, since flow seems to depend on grade and mathematical maturity. However, creativity can be tapped into by assigning problems that require it.

In terms of activities, only group activities come to mind where students might feel immersed in the problem. Being surrounded by others and having a common goal (solving the problem at hand), could lead to flow. The problem of happiness comes from many things, which would include the general atmosphere of the class, and a desire to show up to class. Being an engaging teacher that cares, in my opinion, can go a long way when it comes to solving this issue.