"Epistemology is the branch of philosophy that seeks to define (knowledge), that seeks to explain what it means (to know) something, that seeks to understand how humans come to (know) things." [D.Q. from Green Book Article]
The positivist differs from the constructivist entirely. Positivist is the traditional way of teaching, and is based on fact. So to speak, this is the correct information on a topic because researchers and experts have concluded this. All knowledge is broke down into category's and should be stored in the proper folder. Different teaching styles can exist, but it all comes down to memorizing information that has already been learned and accepting it as the truth. Constructivist point of view on how one teaches knowledge is different. It goal is to focus on the routes to understanding a concept on your own through asking specific questions and analyzing. Instead of accepting information from an expert given, the constructivist cares about the student's abilities of understanding the process on how to arrive at the information given. Interpretations can be different between individuals, but each can explain the reasoning on how one arrived at there answer.
I have been taught my whole life from a positivist teachers point of view, so with that being said, I feel that I am more comfortable in that sort of learning environment, however in recent years (college) I have been adapting to a constructivist environment for specific classes. I do like the idea of the constructivist environment and the analyzing thought process, but I feel that is greatly depends on the topic at issue. Some information is better if based on pure factual information from the experts and can still be extremely useful. I don't like the idea of sacrificing the amount of categories studied to learn how to arrive at a conclusion for one category. The constructivist is beneficial, but not really applicable unless you are at the maximum knowledge of that subject and trying to disprove an expert or discover something else. The experts use a constructivist approach, but first already know all the positivist facts.
I think I learn best with the constructivist approach because the information sticks and if you forget, you can go through the process again. Where as when I am just taking in facts, information must be repeated to me several times and sometimes I still forget it.
The first point from my article is "the task of a constructivist teacher is to design experiences that will give students an opportunity to develop there own understanding of the data at hand ." [D.Q. from Green Book Article] The second point is that scientist exist in every category and subject matter. Research by experts pronounce the information in every field such as history, music, or math. "There is no distinction made in art history and chemistry textbooks to explain the different processes researchers used to determine the knowledge contained within the pages; each book presents both facts of the field." [D.Q. from Green Book] I think in my teaching, it will require a mix of both types of teaching for the student, because a lot of facts are very important, and knowing how to work through them understanding the reasoning behind the fact is also important. The amount teaching each type will vary with student feedback.
It is ok to mix styles...to a point. Some things as you mentioned have to be or are best learned from a positivst manner : This is an airplane
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However diversion from a planned route may not have such a concrete answer. There might be multiple airports that can be diverted to safely. However additional things must be found out such as fuel, etc. This is more of a contructivist method. I think both can be taught, however "experts" for either side would tell you differently.
Did you have any insights on the modalities article?