Blog Entry Five

In Warrington's "How Children Think about Division with Fractions" she describes many different positive things that come from teaching through constructivism, without teaching the mindless algorithms often involved in mathematics. One of the advantages that she described was that the children were learning to think for themselves. She recalls one time when one of her students went against both her classmates and even her teacher to state what she believed to be the correct answer. She was confident in her beliefs and figured that the way she got her answer was correct and made sure the class knew. Another advantage she points out is that the children were able to work with each other and think of their own ways to see patterns. When she shared the story problem of seeing how many 1/2 lb bags you could make out of 5 3/4 pounds of peanuts, one girl realized that if you double everything, easier numbers are available to do the math with. Simply comparing and seeing that her answer was right helped her to become confident in her thinking style. I agreed with both of these advantages and one advantage I saw was that, the children were really learning how to do these. Down the road they would not forget the "rules" because they put in the effort to figure them out by themselves.

Although the advantages are strong, there are a few disadvantages to the system. One clear disadvantage, is that the students were not told the right answers. Although this may seem like a great idea, because the students would have to be confident in what they thought, they could never really know if what they were doing was completely perfect. An example of this is 4 2/3 divided by 1/3. This problem is a little bit more challenging, and the students wondered when it was all said and done which answer was correct. Without a concrete answer, they just had to accept what they were thinking. ALthough a majority of the students probably did understand, there is a great chance that some of the students did not completely understand, and that would be what they always remembered. So, there are definite disadvantages to the system as well.

#4 ... Constructivism

In von Glaserfeld's paper "Learning as a Constructive Activity" he defines and explains in detail his thoughts and meanings to the term "constructive knowledge". The key word of this is constructive. He does not believe that people just take in what they hear. Rather, when learning, humans filter things through their mind and use their own experiences to make sense of things. They construct the idea of what they are hearing in their head. One example he used that made it clear to me was with the word 'mermaid'. No one has really met a mermaid, but with a description of it being the head of a human and the fin of a fish, one is able to construct or put together the pictures and create a mermaid in their head. One last important detail of constructing knowledge in the paper is, that the way things are constructed is from prior knowledge. Each time something is learned it can then be used to help construct another idea.

If I whole heartedly believed in constructivism, I would implicate it in my classroom in two ways. First, I would prepare each lesson with the perspective of the age of the students I was teaching in mind. There is a great chance that the things I would know would be drastically different than the things that the students would know. I would need to make sure that the concepts I were teaching would be possible to piece together with the students knowledge. Second, I would be sure to describe things a variety of ways. There is no way I could find a way to teach that each student would be able to construct an idea. So, if I taught things a few different ways, there would be a better chance of everyone understanding.