Response to Stephen

"Were it to seem 'viable' to a student that 1+1 came out to some other figure, would a teacher be in a position to correct them under RC theory?"


You have to accept certain "truths" in order to do math. 1+1=2 means nothing unless you accept certain postulates as true. So, if a student refused to do math because he or she did not accept these postulates, then I think that would be supported by a radical constructivist. However, I am less sure about what a radical constructivist would think of a student who came to the conclusion that 1+1=3 after accepting the postulates. It seems hard to argue that that could be correct. I think there is value in the notion that "objective truths" that we take for granted (such as 1+1=2) should be challenged. However, in every area of life, we must accept certain "postulates" in order to function. I wouldn't even be writing this if I was a radical constructivist because, for all I know, nobody in this class actually exists and my blog will never be seen by anyone. For my own benefit, I have to just accept that there is a reality outside of my own perceptions.

Question: Is it valid to reject radical constructivism solely because it makes it very hard (or maybe even impossible) to function normally in society?

Response to Ed

"Should schools be concerned with the physical and emotional well-being of their students as well as the intellectual?"

Yes. Schools (at least the public schools that I attended) usually show an interest in more than just the intellectual development of students. Much time is devoted to the students' development of morals and values (we had "Character Development" sessions in middle school, which was supposed to teach us how to be good people). More obviously, most schools require physical education up to a certain age. Since people younger than 18 typically spend most of their time in school, it makes sense for schools to take responsibility for more than just mere intellectual development. Between going to school, doing homework, after-school activities, and parents' busy work schedules, it is unrealistic to assume that parents will teach their children values outside of school. Schools should probably take responsibility for the development of students in most areas, such as intellectual, emotional, character, and yes, physical education. However, the way most schools go about physical education is problematic. Most people have horror stories about "gym class" from when they were younger. Sports are supposed to be recreational, so it seems odd to force somebody to do something for fun. Since sports are just one of many ways to get physical activity, I think there should be a broad range of physical activity for students to chose from. For example, MCLA requires 2 physical education classes, but I think our school has a lot to choose from, so there is something for everybody. Of course, you need a bigger budget to have more options for physical education, which many schools probably cannot do.
Question: Should schools teach morals and values to their students?

Knowledge=Justified True Belief

Today in class, we discussed the theory that knowledge is a justified true belief. How do we know when something is true and justified? I think that most of the things students learn in school is not true or justified to them. For example, a student learns about World War II. How does the student actually know if what he or she is learning is true and justified? How do any of us know that events in history as we know them are true and justified? We believe them, because trusted authority figures tell us that these events happened a certain way. But since we have not experienced these things, we cannot know if this "knowledge" is true and justified. It seems to me that the only way for a belief to be justified is if one has experienced something in the world to confirm the belief. So, a justified belief is really only justified for the person who has experienced something that justifies the belief. Therefore, most of the things we learn in school are not justified true beliefs to the learner. So, knowledge claims are obviously beliefs, and they can be justified through experience.
Question: How can a knowledge claim be proven true?

Math and Constructivism

As I read about constructivism, I began to think about how it could be applied in the classroom, and I think that constructivism would be a good approach to learning math. Many people seem to be frustrated and confused by math because it seems "made up". As someone who loves math, I have heard this so much from people. They feel like the rules of math are completely arbitrary, random, and just do not make any sense. I believe that people may feel this way because they have been taught a set of rules to memorize. Math is something that can be discovered, and I think what you learn is a lot more valuable if you discover it on your own. Instead of just teaching kids that 1+1=2, because that's just the way it is, kids should be able to explore math on their own and come to an understanding of the concepts. I know that the first time I was shown a hands-on, concrete example of the concept of pi, I was so amazed that I had been using pi for so long without having any understanding of it. And I immediately understood it after seeing it. This may be an example of different learning styles, but I think this approach would work with most people.

Question: Do constructivist teaching methods cater to certain learning styles?