The first thing that stopped me was the table of conservative and progressive stances on math education. The two stances have pretty much opposing arguments in every area of interest. Reading the table, I realized that I am very used to the conservative way of learning as in high school I was a student who only focused on the facts and algorithms that I was taught and was barely challenged to "present engagement with and development of mathematical modes of thinking that will expand [my] modes of thought and develop flexible problem-solving abilities" (p. 393). However, as a teacher candidate now I see how "progressive" the progressive stances are. Teaching students inquiry will have them focus more on their understanding of math than the abilities to solve problems. Given autonomy, teachers will be able to assess their learners' knowledge and skill levels better.
Another stop was the public criticisms of school mathematics in the late nineteenth century. The "rule of three" that led students to find solutions to proportional equations but failed to provide a "sense of why those particular procedures worked" is a technique that was particularly targeted by progressivists. Teaching students such techniques can sometimes be seen as a nonsense since it is just a technique that helps you find an answer and does not even require thinking or understanding. If students are only taught such techniques they will not ever learn how to explore and process new knowledge. They will just seek answers to problems not knowing or trying to know what those answers might imply or mean.
The third thing that stopped me was the role the media plays in our society. The framing the media uses has a great influence on how the public perceives things. It can sometimes deliver a false image of education system and change the point of view the public might have had on it. While playing a significant role in creating images of many things, the media should also reflect public opinion about those things. Holding its own biases and ideologies, the media cannot really reflect pure public opinion.
Thanks for these interesting ideas, Yeni!
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