From reading this article, the main argument that it is addressing is dichotomies surrounding mathematics education in North America. It is certainly interesting (and a bit scary!) to know that there are math teachers out there, either elementary or secondary, who are successful in mathematics learning and teaching, and yet the reason they are so successful in math purely because they have been "memorizing" algorithms and concepts in their brains without much sense on "why" they worked or why they are as they are. Interestingly, if a math teacher carries this sense of learning in his or her classrooms, there would be a chance that their students would also carry this mindset of math learning. This can be shown in their ability to educate themselves on how to interpret math. Most of the math education reforms, the Progressivist movement, the New Math Reform, and the "Math Wars" of NCTM, gave me new insights into their different ways of teaching and learning in that specific period of time. But I think that math learning over time is starting to focus more on the importance of real-life applications and what students can do with math in the future instead of just simply memorizing everything that deemed important.
From looking at the table between Conservative and Progressive stances in mathematics education, I think that I fit under the Conservative view more than Progressive view, depending on the level of schooling I had done in the past as a student. When I was younger, I attended part of elementary schooling in China and part in Canada. My perspective of math learning in China was highly conservative. Teachers would be drilling concepts and math formulas into my brain without necessarily telling me why that is. Interesting fact about me is that I used to really dislike math when I was younger because I was just not getting the concepts! However, as I came to Canada, this level of learning and assessment changed slightly. Math is no longer just about working by yourself, timing your arithmetic abilities in under 60-seconds and getting all the right answers. Some of my Canadian math teachers do focus more on the "why" and the "how" instead of focusing a lot on getting the answer. There were more collaborations and group work involved, which is what I want accomplish as a math teacher in the future as we live in the time of change and advancements.