Flow

Have you experienced a state of flow through certain experiences? 

I have experienced flow when rock climbing. I enjoy climbing the different routes and working out both my brain and body. I will run into obstacles both mentally and physically as I climb. But the challenge, as well as the music in the background, keep me going until 2 hours have passed and my hands are blistering.

What prompts it? 

My rock climbing flow is very inline with the videos we watched on the idea of Flow. I will keep trying harder and harder problems, but eventually I reach a point where I can go no further and don't have either the technical skills nor the expertise to solve a problem. I lose all flow as my self-efficacy of the task at hand drops. Once I feel like the task is so challenging that no amount of effort can solve it, my engagement drops.

Likewise, if the gym is ever so busy that I can only squeeze in to do the easy routes, I also don't enter into a state of flow. The task is not challenging enough and so I do not end up engaging with it.

Is it sometimes connected with mathematical experiences?

One can definitely use math while in flow while rock climbing. Recognizing the distances between holds and using spatial awareness to project one's self on the wall are two ways my mathematical mind gets activated in flow.

On a more general note, I often find that when I am facing a challenging math problem, I often enter into flow. The only issue with my current sources of math problems is that I find them either too challenging or too easy. But on the occasions where I find a perfect problem I can lose and entire day playing with it.

Class Summary/ Blog Reflection

 Looking through my blog posts, I have unlocked memories of the earlier days of this course when we were in the garden in the early fall days. I also got to take another look at the art projects that we did over the span of the semester. So much has happened that I can barely keep track of it all, so hard to process. But as I read the blogs I get to remember the things we did.

My favourite part of the course happened early on when we reading the Skemp article. By breaking the idea of knowledge into that of instrumental vs relational understanding unlocked something in my brain. It was a new way of thinking that had never happened before. Because of having this reading early on, I was able to see the lessons and projects through the lens of instrumental vs relational understanding, and that enormously helped me through the course.

I also liked the math art projects that were related to the curriculum we would be teaching in the schools. While we learned a lot of art ideas, it will be a bit of work to find the time to implement them in our classrooms. I would have loved more lessons like the GCF/LCM dances that I will be able to implement in my practicum seamlessly.

Unit Plan & Lesson Plans - Exponents and Prime Factorization

Sorry for the quality of the class notes, the pen did not convert to Google Docs well. During the classes, students will be given the blank notes at the start of class. As a class we will work through the notes together, with the green writing being the targeted information I want to convey with students.

Unit Plan

Lesson 1 - GCF/LCM

Lesson 1 - Class Notes

Lesson 2 - Prime Factorization

Lesson 2 - Class Notes

Prime Factorization Art

Lesson 11 - Encryption in Math

Lesson 11 - Class Notes

The way textbooks may position position mathematical learners

 This text highlighted some key examples of how different textbooks represent mathematical ideas differently. The ones that stood out to me were how absolute values, the binomial coefficient, and derivatives were all somehow represented with different lenses. It is expected that the arts will have different biases, but it is not expected for bias to emerge in STEM subjects such as math. Because bias is not expected, its presence is even more insidious.

I have talked about textbooks at great lengths with my SAs. In order to teach the current grade 10 curriculum, I require 3 different textbooks. This is because the curriculum keeps changing and the textbooks quickly become out of date. Because textbooks are static by nature they are not good teaching tools for the changing environment of learning.

My final thoughts on textbooks is that they teach material a certain way, and it might not line up with the way I view that topic of math. I will be biased in my own teaching, but I think that as an educator, it is better to teach well with your own bias than to teach a choppy, inauthentic lesson with someone else's bias. Students learn best from teachers who are passionate about the material, and that passion might disappear if I was forced to teach math in an inauthentic way.

Dave Hewitt & mathematical awareness

 In the videos we watched in class, the three things that made me stop and think were:

1) Hewitt's ideas that students will naturally find the correct answers, they just needed guidance to get there faster. That if left to their own devices, mathematical thinking comes naturally, it is only that the pace needs to be quickened

2) The idea of a group choir makes a lot of sense. I especially enjoyed that for tricky answers the unison would break and then the group as a whole would understand that further thought had to be put into this question.

3) I loved that Hewitt did not tell his students what was right and what was wrong, he was only a guide. He was constantly asking if the students thought they were right. In honesty, I remember being a student and being decently upset with teachers who did this. I remember feeling cheated, why was I doing their job for them? But i recognize now the significance of framing the relationship with students in this way.

I think that the fraction problem is a great inquiry problem that doesn't have any correct answer, at least not at the start. It is obvious that Hewitt has a particular fraction in mind, but by framing the question in terms of multiple steps, students feel much more agency. Just finding a fraction in between 5/7 and 3/4, there are infinite answers. By making the problem more concise, he is controlling which fraction the students give as an answer, but it still does not feel like agency is removed from the student.

I have already incorporated group choir into my teaching because I felt like it is a good way for students that have self doubts to more easily play along; they are just one voice in a group of 30. It make me happy to see that someone so professional as Hewitt approves of this teaching style.

Hewitt Arbitrary vs Necessary

 After reading this article, issues that I ran into during my practicum were voiced. I was tasked with teaching the equations of lines, but ran into difficulties quickly. I thought that I would have been able to just share my knowledge with my students. However, I ran into needing to know a bunch of different forms of the lines. For example, I needed to teach that "General Form of a line is 0 = Ax +By +C where A B C are all integers and A is non-negative."

I marked tests and found that many students did not exactly follow these rules, and felt bad that I had to take marks away for these mistakes. I am happy that I now know that these rules were arbitrary, and this exemplifies why there was so much friction between me and this issue.

The most annoying aspect of this experience is that students were so busy learning these arbitrary rules, that they did not understand the necessary concepts of lines being a relationship between x and y. Students would remove x and y just in order to make the equation look more like General Form.

When I teach my classes, I am going to focus on necessary knowledge and prioritize it. After students understand necessary concepts, I will teach them the arbitrary rules.

Oct 20 Pro-D Day

Last Friday I attended the BCMAT conference in Surrey and it was an amazing experience.

My first session was about a teaching style called argumentative thinking. Using this routine, students are pushed to argue their thoughts in front of the class. I like this routine because it promotes the competency of explaining ideas through mathematical language.

My second session was about Group Quizzes. This idea aligned well with my ideas of how teaching should be done. We have been taught that students learn well from each other, and when group quizzes are used they can supplement each other's knowledge. The only downside is that assessment becomes complicated because you are not assessing the individual. I think that a classroom breakdown should be group work at the start, then individual work to be assessed on afterwards.

My final class was about culturally relevant material. Unfortunately, this session did not teach what I was expecting from the summary. It did talk about the idea of a warm demander, which happens to be an idea that I had already researched myself individually. 

The best thing that I took away from this conference was the interactions I had with other teachers. I did not feel like a lesser person there. I asked questions that were relevant and did not stick out. My confidence increased drastically after this conference, which is perfect for the start of my short practicum.