Dec 18 - Assignment 3 - Final Unit Plan

Hi Susan,

Here is the final unit plan and the lessons:

https://drive.google.com/drive/folders/1Lo_iAULqMFAmUt4eL3H_MX3Opc9r0mCp?usp=sharing

I will be replying to the comments you made last time in this post:

"Do make sure that the topics you are planning to teach are appropriate for the students' background and grade level. For example, induction and group theory are not typically taught in Grade 9 -- but you may be able to give introduce some foundational ideas from these topics iff you don't rush things or make assumptions about the students' background knowledge!"

We talked at the end of the class about how these topics are actually in the Mickelson textbook I'll be teaching from. It involves teaching induction in Grade 9, as well as deductive reasoning (Chapter 7). The end chapter (Chapter 9) has symmetry that is close to group theory and includes group theory notation although they don't talk about groups specifically.

"Your project is still quite vague and needs a lot of thought about what you will actually ask students to do. They will not have Zome tools readily available -- and Lego is limited by its construction. When you talk about symmetry, be clear about whether you simply mean bilateral mirror symmetry (which is probably too basic for the project and grade level), or all kinds of symmetry groups (which is probably too much for the class to take on), or some specific spot in between those two!"

Thank you for the feedback. I was not clear on what is meant by symmetry. I've added several details on the project and how the students will be assessed using a strength based model.

"What homework are you planning to assign, that you expect to take up at the start of each class? I would NOT make a break so early in the class -- you've barely gotten started, so don't disperse the energy already at that point! I'd save a break for at least 50 or 60 minutes into the class."

I've removed the early break and added a homework section in the lesson plans.

Your lesson ideas are still very sparse and not defined enough at the moment, and will need more thought. Some of the activities in different parts of the lessons (like the Thinking Classroom and Scale Factor sections in 9.1) seem like a repeat of the same activity, at least as they are described at the moment. 

I've re-written them so it's clearer. The thinking classroom part focuses on whether "pi" exists for other shapes. i.e. if there is a universal scale factor for squares or triangles. The other part "Scale Factor" focuses on simply finding scale factors of arbitrary shapes, which are not necessarily squares or triangles. The textbook offers different polygons and even fully drawn out objects.

"I like the outdoor embodied activity idea, and need to see it in more detail."

I've added more details.

"I worry about the totem pole symmetry idea in the third lesson as it seems to be mentioned in a superficial way as it stands right now. However, with some research, this could be developed into something more meaningful and profound, and perhaps a real carving project (individual or collaborative) with a local carver and real wood could be a way of bringing true Indigenous ways of learning to your class? Or there may be other artistic media like painting or printmaking that could do something similar...something to consider."

I agree. I've replaced it with an arbitrary/necessary topic instead.

 

Dec 18 - Final Reflection

I learned a lot of puzzles and ways to challenge students. I really enjoyed writing the letters to myself. I learned a lot about the curriculum as well. I would have perhaps preferred the final assignment to be spaced out more, and not at the end. It would've helped with my practicum if it was sooner.

Dec 8 - Math Party

 https://www.ams.org/notices/200902/rtx090200212p.pdf

Dec 6 - Assignment 3 - Draft

This Google Drive folder has the 3 lesson plans and the unit overview:

https://drive.google.com/drive/folders/1Lo_iAULqMFAmUt4eL3H_MX3Opc9r0mCp?usp=sharing

Dec 2 - Dave Hewitt on Arbitrary vs. Necessary

I remember watching an interview of Richard Feynman where he mentioned that when he was a kid, he figured out his own way (invention) of doing logarithms and he made up his own notation and names. Then, when he tried to explain it to other people he realized it's important to have names for things that everyone agrees on. This is a good reason why we have to teach the "arbitrary". As much as I'd wish the nomenclature be changed, we still have to communicate to each other and we have to teach it. This is the same case with mathematics conventions, and defining certain concepts in some way, for example negative numbers being to the left on the number line.

I agree with the idea of not teaching "necessary" aspects as "arbitrary". I do think that a lot of teachers do this however. I made it my goal to guide the students to derive everything, and not just give out formulas. I think it's possible with most mathematical concepts in high school to do this, and most derivations don't require much sophistication.

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.