Dec 19 - Final Reflection

Skemp's article differentiating instrumental and relational mathematics stuck with me throughout the term, and not just in this course. It gave a name to a problem I'd been encountering within my tutoring job, and I think other readings ran in parallel with it. This course also showed me a plethora of different ways to go about teaching mathematics, and while I likely won't use some of the more artistic ones, it was still worth being exposed to them just in case. 

I have a couple suggestions for this course in the future:

Drawing from the course outline, I wish we had spent more time discussing the curriculum and how to structure units around it. My understanding is the BC curriculum is intentionally vague to provide teachers with autonomy, but that can be intimidating for new teachers. Even just spending time talking about the blog post we made about pathways would have helped.

Speaking of blog posts, I think more time should be spent discussing them in the following class. Perhaps even a summary of the key ideas we were intended to gain from each post. 

Dec 18 - Unit and Lesson Plans - Second Submission

I have added sample questions, a sample quiz, and created the Summative Assessment Document

The Unit Plan document: 

https://docs.google.com/document/d/1ccA1JGbQPJxJm-Z-byaKnTpg9peIr8D-Qp2aYnR4lug/edit?usp=sharing

The Lesson Plan document now has sample questions, as well as a sample quiz at the end and the assessment breakdown:

https://docs.google.com/document/d/16f3Y9nwGtMTvgIpm78j8oPvfI4iUaI7El1w1kUyFAdg/edit?usp=sharing

The Summative Assessment Project:

https://docs.google.com/document/d/1_ceXKY1W4pq4mtdK7G9GkJw-IqCdW6wEz0u2hLfgMjU/edit?usp=sharing

Dec 13 - Favourite Math 'Thing'

For my favourite math 'thing' I will put forth two answers, one older and one new, with an overarching theme.

My initial post for this was going to be the YouTube channel 3Blue1Brown, which explains all kinds of mathematical ideas and relationships in fun, usually visual, ways.

Based on Susan's suggestion I also checked out Vi Hart's YouTube Channel, I scrolled through it for awhile to find something to start with, and I discovered a video about dragons! Not just any dragons, but fractal dragons, which were discovered during a quest to not learn logarithms! Needless to say I was hooked and watched all 4 videos in this mini-series, which ended with a very clever explanation of logarithms.

So while I put forth a YouTube channel and a YouTube mini-series as my answer to the question, I think my real favourite math 'thing' is the variety of ways that exist to explain (or teach in our case) the same mathematical idea.

Dec 6 - Assignment 3: Unit Plan and Lesson Plans - First Draft

 Unit plan:

https://docs.google.com/document/d/1ccA1JGbQPJxJm-Z-byaKnTpg9peIr8D-Qp2aYnR4lug/edit?usp=sharing

Lesson plans:

https://docs.google.com/document/d/16f3Y9nwGtMTvgIpm78j8oPvfI4iUaI7El1w1kUyFAdg/edit?usp=sharing

Dec 2 - Arbitrary vs Necessary

 

Hewitt's discussion of arbitrary vs necessary components of mathematics seems to me to parallel the idea of inquiry vs instruction. We as teachers should not be instructing and informing our students about things which they could instead discover for themselves, given sufficient conventions and an appropriate task. My SA during my short practicum spoke about this idea, and instead of instructing her Math 9 class about similar triangles, she gave them an investigation to perform, whereupon they would discover that the two triangles were proportional. I personally, and I assume I'm not alone in this, am guilty of telling students to "think about it" in regards to them forgetting something arbitrary, because I didn't want to "give them the answer". In situations like this, context is extremely important, and I will certainly work to become more aware of what the student's knowledge gap is, so I can react appropriately. As it pertains to lesson/unit planning, Hewitt's argument makes the case for using inquiry methods to teach any and all necessary curricular components. This seems a daunting task, but if the outcome is increased student engagement and retention, its hard to argue against it.

Nov 30 - TPI Test

 

Hurray for consistency! It turns out I value nearly everything equally, which I'm not too surprised about, I want my students to both understand mathematics and grow into critical, compassionate citizens. I'm also not surprised that Social Reform was the lowest. While I think its important to challenge societal norms, in my teaching style I hope that occurs as a result of a successful mathematics education, rather than a direct result of said teaching. 

Its worth noting that the "Reflecting on Your TPI Results" section suggests taking note of B-I-A discrepancies of 3 or more; which occurs for me in all but the apprenticeship category. Three of those four gaps are of the minimum value of 3 points, so I'm not too concerned about being an inconsistent teacher. I will also point out that my answers to the Action subsection were almost entirely "Usually" because I feel like I don't have quite enough experience to base my answers on pure reflection. 

Nov 23 - On Textbooks

As a student I always considered my textbook as primarily a source of practice problems, and as a secondary source of information if I didn’t understand something my teacher taught. I don’t think I ever paid much attention to the verbs and forms address, though they still could’ve had a subconscious effect. 

As a teacher I understand the importance of how language can create or prevent connections between students and the subject material. I still think the primary purpose of a textbook (or workbook in the case of gr8 and 9) is as a supplemental source of knowledge and a source of practice problems. 

But in the age of Khan Academy, Wikipedia, etc., I don’t think it should be the only approved supplement. I would in fact argue that textbooks, as a printed resource, are slow to change and adapt to new ways of teaching mathematics, such as the concept of a “thinking classroom”, and so reliance on them should be reduced. They are certainly more accessible for students, due to being provided by the school, but as I saw in my practicum, funding to replace them needs to be found as they age. In the Pre-Calc 11 class I observed, the textbook was supplemented by a duotang containing lessons, practice problems and even practice tests on topics and content which were absent from the textbook. Its creation and use were more economical than purchasing a new textbook every so many years. All of this is to say that a student’s primary source of learning and knowledge should be their teacher, and a textbook used as a supplement should be on the same level as any other vetted resource.