Blog #5

There are many advantages to teaching mathematics without using algorithms. One is that the students have to use their own logic to come up with ways how to do things and how to make sense of it. They have to go through an understanding and discovering process rather than a using process, using meaning using different rules and equations. The advantage of the teacher not ever telling if the answer is right or wrong is that the kids will continue to second guess their logic until they have come to a conclusion that it could not be any other way. This kind of teaching is also beneficial because it gets kids involved and interacting rather than just sitting and listening to a lecture.

The disadvantage to this is that kids may come up with the wrong answer, even after much work and debate on it. If the teacher never tells them it's wrong, they'll continue to do things wrong. I think that the better way to approach this kind of teaching is to sit back and watch the kids construct ideas and learn interactively but when they are sure that they have the right answer, but it is really wrong, the teacher uses questions to have them think through the spots that they went wrong. That way the students are still are able to use their own logic because no particular answer or process was given to them, but they'll be able to construct the correct processes and knowledge.

Glasersfeld meant by constructivism that we construct knowledge, it is not given to us, but rather it builds upon itself through experience and through different things that we've observed. We only learn that we are wrong when we experience a contradiction to what we had previously concluded. According to Glasersfeld, there is no truth because any thing considered "truth" is just something that has not been contradicted.

Knowing and understanding the principles behind constructivism helps me be able to better see how I need to approach things when I'm a teacher. I think it's really important to ask my students a lot of questions because I cannot assume that they have constructed the correct knowledge and the only way to find out if their thinking is correct is to ask them questions. I think it also helps me to realize that one thing needs to build upon the other through a variety of experiences because according to a constructivist perspective all knowledge is gained through experience.