Adam Rodrigues - EDCP 342A Blog

What convinces (or doesn't convince) you in the authors' argument? I would have to say that the authors’ arguments were quite convincing to me personally, not only because of the points made and studies cited, but also because I am predisposed to agree based on my personal experience and observation. The main conclusions—that students must practice using multiple representations, that representation is a fundamentally social activity, and that instruction must use varying techniques—are in general agreement with what I have personally realized in my time as a student and my limited time as a teacher. Furthermore, the way that the authors used not only examples, but also real case studies, to support their points was effective in convincing me of their position. For example, Tchoshanov’s pilot study where three groups of students were taught trigonometry with controlled levels of representation (one group with just an analytic approach, one with just a visual approach, and one w...

  1. Writing about your favourite and least favourite math teachers -- and why. Favourite Teacher: I am quite lucky to have had many great math teachers over the course of my academic career, and perhaps this is one of the reasons why I am attracted to this particular occupation. If I must choose just one, I will focus on my grade 12 Functions teacher. I choose to write about him because he was one of the first math teachers that truly challenged me as a student, but simultaneously provided the support for me to succeed (and he sincerely wanted me to succeed). It was much more difficult to receive high marks in his class compared to the sections run by his colleagues, and so I, along with many other students, was initially upset by what seemed to be an injustice to us who were competing for university entrances and academic awards. However, as time went on, I quickly realized that this teacher pushed his students so that they would understand concepts more deeply, learn to be adapt...

 Reply to Jacob's group's response to question 1). The question: 1) What 'should' come first in learning math: instrumental or relational understanding? Why? In what contexts? Jacob's Group's Response: 1) We felt that there were pros and cons to both systems, but ideally the system would integrate relational and instrumental understanding together so that students both developed deep understanding for a subject alongside technical skills. Whitehead's theory of Romance, Precision, Generalization was discussed, focusing on making every lesson a combination of relational and instrumental. My reply: Hi Jacob, I very much agree with your group about the idea of integrating relational and instrumental understanding. I think instrumental understanding is practical in helping students to have efficient strategies to attack common problems. On the other hand, relational understanding will help to stimulate enjoyment of the subject and help students develop transferab...

Kelsea, Zach, and I designed and built the following templates for use in our math art assignment. Feel free to use them for your own enjoyment or educational purposes. Square Root of 2: https://www.desmos.com/calculator/0kw4kdsfqa Pi Circle:  https://www.desmos.com/calculator/wc3iclxffd Reflection: I found this assignment to be enlightening in that it helped me to be more creative with mathematics. I am have always found the creative side of math a bit more challenging than the analytical aspects. I think it is important to work on this part of mathematics though because creativity is essential to forming proofs, building, models, even suggesting propositions. It's also just really fascinating to expose the aesthetics of math through art!  Personally, I thought that our presentation had clear organization and an appropriate complexity of content. I think that our math art adaptation could be used in a high school classroom effectively to help teach concepts such as irrational...

In large part, I also share Skemp's preference for relational mathematics over the instrumental approach. As someone who enjoys the beauty of deep understanding and making connections in mathematics, I have always preferred this approach. Moreover, I have plenty of personal experience observing different students approaching mathematics with either relational or instrumental understanding as a subconscious goal, and the differences I've witnessed in both their enjoyment and performance favour those students who seek relational understanding. I have always aimed to teach math in such a way that would promote conceptual understanding in my students, and I have only taught in an instrumental way when there was a much greater immediate utility. It was interesting to stop and reflect about this a bit more consciously though by reading this article. The analogy that Skemp used, of finding one's way through a town, resonated with me in a particularly powerful way as I was able to ...

I really enjoyed working on this problem! I was reminded, however, about the importance of not leaving my work to the last minute, as I caught myself working on it late Sunday evening and didn't want to give up. I was able to solve it, and I've included my thought process below. I must admit that my justification may not be up to the spec of a number theory proof. 1. I first thought there might be some clever incorporation of binary numbers given the on/off character of the problem. I realized that any locker that had its state changed an odd number of times (including the first pass) would end up closed, and any one that had its state changed an even number of times would end up open. I then realized that I needed to think about divisibility but wasn't sure how to proceed. 2. Eventually, I decided to break down the problem into a smaller locker sample. I started with 10 lockers, and then scaled it up to 25 as I noticed a pattern emerge. I used a "c" to represent ...

 Hi folks, I'm Adam and here's a picture of me in my happy place. Looking forward to getting to know everyone! Adam