Blog #5

There are many advantages in Warrington's method of teaching math. One of the advantages is that students learn to associate the problem with real life situation. For example when the students gave examples of the a candy bar being divided or a pie shared among friends. This method of teaching makes students use what they already know to solve problems. Another advantage is that students learn to make logical leaps of understanding on there own. for example, when one of Warrington's students used equivalent ratios to make a problem easier to solve. This is something that will help students for the rest of there life when they are not dependent on a teacher to solve the problem for them.

I also think that there are many disadvantages as well to Warrington's teaching style. One of those disadvantages is that many of the students could be riding on the coat tails of the ones that really understand the topic. Meaning, several students who were struggling may have nodded there heads in agreement with the students who were passionate about their answers, without really understanding it for themselves. Also it is clear from the article that these students already understood fraction and many other mathematical concepts. I don't think this style of teaching would work for all subjects. It would be difficult to introduce new material and not let the students see patterns of how it works.

Blog #4

Glaserfeld had many reason for the theory of constructing knowledge. One of those reasons is that Glaserfeld used is that all the so called knowledge that we gain comes from our senses. Everyone interprets these senses differently and therefor we all construct our own ideas about what we have experienced based on our senses. If we were all acquired knowledge rather than constructing it. Then we would all have the same knowledge because it would be like the knowledge was handed out. If we were all handed a dollar then we would all have a dollar, but if we had to make a dollar then all of our dollars would be different. This is the theory behind Glaserfelds constructivism. That fact that we are all constructing knowledge makes knowledge itself become a paradox. For how can we know what is true knowledge if we are each building it up as we go based on our senses and past experiences. Glaserfeld mentioned that to truly view knowledge unbiasedly, we would need to know what we knew before we knew it. Which is of course impossible.

If I were teaching a math class and I believed in constructivism and I wanted to best help my students learn. I would give a test at the beginning of the year or at the beginning of the term that would help me understand the level that each of my students was at. This test would allow me to see the students work out problems. This way I could see how my student solve problems and get an idea of how they have built their mathematical knowledge. This test would also allow me to see my students past understanding and experiences with math. Since constructivism is always building up on past knowledge. I would be able to help my students by knowing where I should start building.