Stocker

I acknowledge that today in my young adulthood I have more skills and confidence than I even know how to deal with and use efficiently, but a lot of this cultural and intellectual capital was not granted to me at birth and a lot of the knowledge that I use now is due to my interest and engagement with the world in a mathematical way. My aim as a secondary teacher is to teach mathematics as a means of acquiring autonomy, and to give my students access to a wider perception of the world as to make choices that will bring them to places of power and comfort based on their individual needs and wants. In particular, to use that power to challenge and question the world and it's social structures with logical justifications, ideally as a means of making it more equitable. Of course, each student is encouraged to use their aptitudes, passions, and energy in any way that they see will be an addition to their livelihood.
I imagine this textbook is an attempt at providing curricular resources for a hopeful emerging of the popular idea that mathematics, along with all other subjects at school, should be used as a means of empowering students to engage with the social structures around them and think critically about how to live in the world. I agree with a lot of the points raised in the introduction and of particular note the choice to use a quote from "Nel Noddings", quite possibly the Nel who questions the use of everything, at the beginning of the chapter;
 

I think there are clear relationships between logic, philosophy, sociology, and mathematics. These connections pose questions like why things work, how do we fix things, and where should I start? Questions of this sort are relative and each individual encounters different problems and challenges in the real world and engages with them relative to each of these unique experiences. The questions are common no matter how different the experiences, and thus providing opportunities for students' minds to reflect and think critically about the world in these ways is extremely important in the goal of "producing" intelligent and creative children. I imagine mathematics as a discipline that tries to model the world in a systematic way through defining rules from playing off of physical intuition and logic. When a student is doing mathematics the goal should be that they come to see the pieces in that model, why they work, and how it can perhaps be done "better" or more "efficiently" (and why it is important to define these parameters in a systematic or arbitrary way).

This textbook seems to provide concrete ways in which teachers teach concepts of social justice in their classrooms. I think it is certainly interesting to explore lessons of this sort, and it is becoming more welcome with the emergence of the new curriculum. I look forward to promoting my students to use their knowledge and skills to shake things up and make the world more fun.

Math Art Project Reflections

In the math art project myself, Jing, and Devon all had distinct and independent interpretations in how we can deconstruct interesting 3D objects into a set of simpler 2D constructions. I really enjoyed collaborating and discussing on how we can in-cooperate all of these unique perspectives and come full circle to illustrate how different kinds of art and structure can be creating through have a conceptual understanding of mathematics.

I personally decided to use my skills in programming, specifically Scientific Computing, to break up two shapes into a finite number of 2D cross-sections as a means of creating a blue-print for a sculpture. The sculpture I chose was a hyperboloid of one sheet (above: an image I generated of this surface using Matlab) inside of a sphere. Sadly, the glue I used was not strong enough (Rest In Pieces hyperboloid sphere) but I was able to perfectly construct the figure I had in mind. In our activity we illustrated that by going through a range for a specific variable, the choice of that variable being important based on the geometry of the surface, one can make physical sculptures of 3D mathematical surfaces defined using algebraic expressions. I think the use of art as an application for having a conceptual understanding of mathematics is interesting and can certainly be seen in the physical word with incredible works of engineering and design surrounding us. Art is more accessible than math as it generally is open-ended and doesn't require strict rules and generally is aided from a bit of chaos and creativity, but incorporating technical components into art can allow for very interesting pieces that are still equally prone to the chaos and creativity of art as it is very easy to make a single mistake and build off of it to make something unique and beautiful.

Micro-teaching feedback

Access to lesson plan: https://docs.google.com/document/d/1BorOSa41kvwdXHcyt5VCKaUzoGO8V8fJEW8xbw0sw2M/edit?usp=sharing

In this team-teaching I think Erika and I did a relatively good job trying to present something that seems technical and boring in a fun and interesting way. The activity related the representation of areas with unknown distances with the multiplication of binomials, ultimately allowing the student to understand the expression geometrically. We then did the algebraic explanation and looked at some applications when employing this formula and how there are different circumstances when we might use different of squares in order to change the expression such that the two terms are squared (i.e rationalizing the denominator using the conjugate).

After reflecting I don't think I would have done much differently. The activity went on a little bit longer than intended, but that was because we anticipated the students making the connections faster. Instead we took more time to ensure that everyone finished the activity and worked one on one with the students to guide and facilitate the completion of the proof. I think we rightly decided that the students would get more out of the lesson with a focus on the interactive aspect of the lesson. If this was my actual class, it would not be such a big deal that we did not cover every single detail that we had hoped to, and there would be an opportunity to review and bring it back to the big idea in the proceeding classes. It was a good experience to do the micro-teaching, and it solidifies my confidence and enthusiasm for teaching mathematics.