Writing Assignment 5

Warrington believes that guiding a classroom without the use of algorithms is the only way to go. This allows students to think on their own and explore math. When students know their teacher isn't going to feed them the right answers it requires them to dig deep into their own math experiences. This also helps students apply what they already know to new kinds of math. Students who come up with their own methods are more likely to retain this knowledge.
As much as I agree with Warrington, I also have many arguements. A whole new math system would have to be developed because although her method is more thorough, it is also much slower. I also feel that the bright students would benefit greatly from this experience, but those who struggle may end up trying to ride on their coattails, which can be difficult. I have had this experience where I have relied on my classmates to figure out how different theories can be explained.

Writing Assignment #4

Von Glasersfeld believes that all of our knowledge is constructed. Knowledge isn't just something that is given to us, but we must process information through our own filter system. We are constructing knowledge everyday in everything we do. Past experiences cause us to view new experiences differently than others who have similar experiences. Knowledge is more of a theory because we never know if what we know is reality. Our reality becomes what we construct through our experiences. Knowledge is viable because it seems to work until we hit a wall and then we must reconstruct it. Therefore, we can never really know if our knowledge is truly correct.
Math teachers need to keep this theory in mind when teaching. When giving examples, they need to be of the variety so that if students have constructed their knowledge wrong they can hit walls and reconstruct it. When teachers use examples that are always the same but different numbers or similar, it makes it more difficult to know if students are making up their own rules that are sure to fail them later on.