3 curricula all schools teachs

The first thing that made me stop and think is the idea that the honours classes can be a negative thing to students. At my school, we didn’t have extra credits for being in the honours program, but it was a more elite class. I was always really proud that I was in all the honours classes my school provided as well as French immersion. I know the other students saw me and my friends who were in all the same classes as smart, even without knowing our grades or really talking to us. I never thought of it from other students point of view if they wanted to get in, but didn’t. I’m also realizing how much of school is teaching children something specific unintentionally, and I need to keep those things in mind to make sure students have the freedom and creativity to learn the way that works for them. The article in general just made me stop and think about what we teach kids and why we teach them that way.

I think the new curriculum does a better job of being open and teaching students in a better way. I think it gives teachers the opportunity to be less strict and incorporate more into their classroom. I would love to be able to do units on art and music and with the new curriculum, I could work that in. I think the new curriculum gives us more opportunity to incorporate all the wonderful aspects of life into any subject that we teach. I also think that because it is so open, we have to be more careful about our own implicit biases and how we are teaching, and allow students to develop on their own with our biases having as little effect as possible.

Group Microteaching Reflection

I had a few takeaways from this teaching.
First of all, it was easier to look at the positives of the presentation and judge myself nicely when I presented in a group. Even though it didn’t go the way we had planned, I still felt like we pulled it together and I was happy with our group. Sue and Vincent were really great to work with, I felt we had similar values in teaching math, we cooperated well, and it was a really positive experience. I’m excited to have them both as colleagues in the future.

Secondly, we really just had too much information for 15 minutes. Looking back, it would have been wonderful to get the class more involved and have them discover the connections better, but we just ran out of time and didn’t get through everything we had planned. I know from this that I really need to work on my timing, especially for areas of math that I’m not as comfortable in, like trigonometry. Even after we cut down a lot of stuff we had intended to do, it still felt rushed and we didn’t get to all the activities we had planned for the class.

Thirdly, I’ve noticed a big difference in my confidence levels when I’m teaching vs presenting. In presentations, I’m nervous and unsure of myself, but in teaching all of that fades away. I’m excited for the practicum and to get started teaching. I want to practice with students and work on my communication skills. Even though I’m more confident teaching, I still always worry that I’m not explaining things in a way students understand. I’m looking forward to working on that and on timing my lessons and unit plans with an experienced teacher.

Overall, I really enjoyed this. I enjoyed learning from others and I really enjoyed working with Vincent and Sue. Actually, I’ve really enjoyed working with everyone I have been with so far in the math cohort. I’m excited for the future of math education and for working with teachers who share my values.

Group microteaching

https://docs.google.com/document/d/14_ELNbqpjlDr3S3QB8YEs5Ev5DmnBZ2Q/edit

A geometric puzzle

To solve this problem, I looked at a clock with markings for minutes. Since there are 60 minutes in an hour, I said 7 would be where 14 is on the clock, and what's across from that? 44 was across, so 44/2 is 22, and so my answer is 22.

An extension could be to have 40 or 50 markings instead of 30, those numbers don't go as well into clocks, which is a circle with markings that we are the most familiar with, so the students might have a harder time visualizing the answer.

An extension that has no right answer would be for example 31. Because the number of markings is odd, there is nothing across from any number. A harder extension would be with a bigger odd number, where it might not be as easy to see that there are no markings across from each other.

I think that there is some value in giving students impossible questions. I did a lot of disproving in the first few years of my degree. I learned to think critically and trust my gut, and to apply logic to show why something wasn't possible. My favorite questions were the ones that gave a statement and said prove or disprove. I think it's important to learn not to take things at face value and challenge what you read and what people tell you. I think it's important to be curious and question everything, and that that will serve students well in the future.

I'm not too sure about what makes puzzles geometric rather than simply logical. If I had to guess, I would say that I think geometric puzzles have a visual aspect to them that logic puzzles don't necessarily have. For example, I think this is a geometric puzzle because to solve it, I had to either visualize the circle or draw it out. With logic puzzles, I often don't visualize anything, usually I jot down some ideas, let them stew in my brain, and come back to it a few days later and solve it.

Battleground schools reflection

The first part of this article that really struck a chord with me was when it is talking about how many math teachers are really specialists in other subjects and don't understand math as well, and also about how people think that math is about memorizing and using formulas. I couldn't disagree more with this! The majority of people that I know that don't like math don't like it for this reason exactly. Their teacher didn't really understand what to do or how to do it, so if they had an original way of doing something, the teacher would mark it as wrong, and then the student gets fed up and starts disliking math. The dislike for math is, in my opinion, not without good reason. It has been separated from logical thinking and defining the world and now is only about doing well on tests. I am so grateful that I had wonderful math teachers in high school who really understood the topic and inspired me and other students to delve deeper. My grade 12 math teacher actually won a Prime Ministers award for teaching in STEM, and he is the one who inspired me and other students from the same high school, to get math degrees and to pursue teaching as a career. I am grateful to him all the time, especially now that I am in this program and can really see how amazing he is.

The part in the article about the Bourbaki French mathematicians wanting to stop teaching geometry and other visual representations of math blew my mind a little bit. To me, math is such a beautiful thing! Being able to see things represented geometrically really helps me understand them better. In the math art project, the one that struck me the most was the visual representation of irrational vs rational numbers. It is such a clear thing; oh this one has a pattern and all rationals will have some sort of pattern vs oh, this one is messy and hard to decipher, all irrational numbers will be this way. To me, teaching math in only abstract concepts will alienate a lot of students, and seems counterproductive to the goal of having more scientists and astronauts that was around at that time.

Microteaching reflections: Dutch Blitz

My biggest reflection on this teaching is that I think I am too hard on myself. I tend to think people aren't understanding me when they are following really well, and while I am fine with that during the teaching process, afterwards I am always thinking of different ways to teach it that would have been better. I also think in hindsight I could have picked a game with less rules. Although this game is my favourite, I know a lot of games that have less complicated rules.

I think my strengths here were timing and engagement of learners. I was able to explain the rules, we played a game, and then I was able to go over some extensions to the rules and right as I finished, time was up. I also felt that since it's a really interactive game and you always have something in your hands, that people were really engaged the whole time.

One thing I would change is that I wouldn't play the game next time. I debated a lot about playing and in the end, I decided to, but I think it would have been simpler if I hadn't, and that way I could have been more focused on the students and made really certain that everyone understood. I didn't notice one of the students had gotten confused until it was really too late to help them fix the error without starting the game again.

The dishes 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?

Taken from A puzzle from 4th century CE, China from the Sunzi Suan Jing 孙子算经

My first thought when reading this is that the number of guests must be a multiple of 12, since that is the least common multiple of 2, 3 and 4. 

My next thought was to write out that every guest had half a bowl of rice, one third of a bowl of broth and one quarter of a bowl of meat. Changing the wording helped me understand the problem better and find a formula to solve it.

I ended up with the equation:

guest + guest + guest = 65

  2           3            4

I simplified that and found that there were 60 guests total.

Microteaching lesson plan