Adam Rodrigues - EDUC 450B Blog

  Topic: The relevance of proofs in secondary mathematics education. Guiding questions:  What are the benefits of learning and generating proofs or mathematical arguments? What are challenges to focusing on proofs in math education? (Such as teacher or student ability, for example) How to implement this in the classroom? How to integrate with curriculum and effectively instruct/coach students? Works Cited: Ball, D. L., Hoyles, C., Jahnke, H. N., & Movshovitz-Hadar, N. (2003). The teaching of proof.                             ArXiv:Math/0305021. http://arxiv.org/abs/math/0305021 • Ball et al. discuss the importance of making student argumentation and problem solving “public” in the classroom so that constructive feedback and learning can happen between students and student-teacher • The importance of how the need to prove is motivated (ie. from real problems or a challenge of how ...

I've been really busy over practicum and the last week so I'm just getting into the research and reading now. As I started the literature review, I have been considering switching to one of the other topics that I was initially considering. I want to make sure that the topic that I choose is meaningful to me and also has a good amount of existing literature available to learn from.  I have now collected 5-8+ articles in Zotero for each of the following broad research topics: - Conceptual thinking in math - Conceptual thinking in physics - Mathematical Proofs at the Secondary Level   I think I will revise my specific research question as I learn a bit more on the topic that I end up choosing through the literature review. I have a lot of work to do in the coming weeks, but from our recent reading, I know that this process is not linear, and it's okay to start with a period of intense thinking (even if productivity seems low). To connect the literature review to the "rea...

For my inquiry project, I intend to learn about optimal design for math problems that emphasize conceptual thinking more than algorithmic approaches. Some concepts that I wish to investigate within this topic are: The benefits of relational understanding Typical poor performance on conceptual questions in assessments Preparing students to succeed with these types of questions in assessments

In our discussion, a common thread that emerged was how practical constraints such as limited time, high volume of curricular content, or a quarterly system can affect teachers' ability to lead their students in creative science or mathematics. Further challenges to permitting creativity in science or mathematics also often come from the disposition of students, formed by their previous years of schooling and by the thinking of their peers and prior teachers. We discussed how teachers can try to reset expectations for themselves and their own classes that are realistic given the constraints in place, but also practice creativity in inventing ways to integrate creativity in their classes. This is usually harder to do than the typical cook-book type teaching, but arguably, essential for deeper student learning. 

One thing that stuck out to me from this article was how researchers (but also teachers and students) can often discount interesting observations before really knowing their significance. I really liked how Bavelas tied this thinking to an inappropriate application of statistical inference without knowing the underlying probabilities (p. 310).  Another stopping point for me was her adaptation of B.F. Skinner's words into a simple mantra for objective and effective research: "the subjects are always right" (Bavelas, p. 311). As someone with a background in the natural sciences, this seems like it should be an intuitive way to approach inquiry. Then again, when I reflect on my own the extent to which I allow my own biases and preconceived notions cloud my ability to engage in impartial observation, I realize how much I need to repeat these words to myself. Similarly, I think it is important to encourage students to approach inquiry from a humble perspective, rather than imp...

This short article stuck out to me for a couple of reasons. First of all, taking a class with Marina this term has helped me to see just how passionate she is about getting everyone to find interest in physics, and how that requires us to specifically encourage girls and other currently underrepresented populations in the field. She has told us in class before about how it was not uncommon for their to be many women working as physicists in eastern Europe and Russia when she was growing up. I found this particularly interesting because I never had even one female physics teacher or professor in high school or undergrad, and at least 75% of my classmates were men in undergrad. I wonder what caused the variance between cultures and also why "the percentage of [Canadian] women getting degrees in physics dropped from 30 per cent to about 12 per cent between 2000 and 2009". I think if we were able to uncover some of the reasons why there was such a decrease in female enrolment, pe...

For this week's response please, choose three quotes from the article (one each from the beginning, middle and end of the piece) and discuss them in terms of 'the tact of teaching' and teachers' practical wisdom (phroenesis) in classroom situations. How might one develop such tact and practical wisdom? How does this affect students, teachers and parents?  1. "Good teachers are intuitively aware that the daily activities of teaching and learning are conditioned by such subtle factors as the atmosphere of the school and classroom, by the relational qualities that pertain amongst students and teachers, and by the corporeal skills or embodied knowledge that teachers enact." (p. 5) 2. "What makes true reflection in action difficult is that life in classrooms is contingent, dynamic, everchanging: every moment, every second is situation-specific." (p. 12) 3. "If teaching is so embodied and so tied into the phenomenology of one's world, then it is n...