Warrington Paper

Some of the advantages of teaching the procedures or giving the correct answers gives the students the opportunity to think for themselves. In Warrington's paper she presented the students with problems without telling them what to do or how to solve it. She simply asked them what it meant to them and according to Warrington she states that children construct knowledge based on what they already know. So after she presented a fraction the students went on constructing knowledge about what they thought it meant based on what they already knew and in many cases they concluded correctly. Another advantage of this is that it encourages social interaction. When socially interacting with others it helps to bring more insights and helps to construct better knowledge because more minds are better than one. The students were able to put their ideas together and then conclude on an answer.

One disadvantage that I can see from this is that the children need to learn somewhat of the procedure and like in Benny's case, he was left to construct knowledge on his own and he came up with the wrong procedures and answers. That is something to consider, although the students are left to construct knowledge independently, they also need guidance to make sure they construct the right knowledge. Another thing, Warrington states that it is the responsibility of the teacher to provide learning environments, but how can the teacher know what a learning environment is that would suit each student? I think that that is a difficult thing to determine.

constructivism

von Glasersfled talks about "constructing" knowledge in the sense that it is more than the acquisition. He says that knowledge is that which human reason derives from experience. It fits observations. He also states that "the world we live in" is possible to be understood also as the world of our experience, as we see it, hear it and feel it. I think as far as constructivism is concerned, that "constructing" knowledge is gained through careful observation and then trial and error as opposed to the acquisition of knowledge which as I understand it is learning through what others have carefully observed and tired. Knowledge is such a profound concept when trying to think about it as something tangible and is called a theory because there is no real "proof" to it. There are so many different theories that remain only theories.

To me, if I were to apply constructivism to teaching mathematics, instead of teaching formulas and such I would have my students use objects like the blocks and shapes we use in class. I think that if they could carefully observe how and why concepts work using the blocks and shapes, it would create a better visual for them in their head. I think that it would help them to actually see why things such as division and multiplication work the way they do and not just to memorize them. I think this is compatible with a constructivist perspective because it seems to me to be more of constructing knowledge rather than me teaching and them acquiring.