Assignment #5

In Warrington's article, she discusses the importance of allowing students to think for themselves and come up with thoughts on their own rather than teachers telling them procedures. First, when students speak their thoughts they give the educator an idea of what needs to be taught and how they should teach it. This clarifies understanding and helps the teacher give the right prompts to allow students to conctruct a more correct interpretation of a concept. Also, students do not accept anything until they understand it and they have the courage to ask questions since that is the atmosphere of the classroom. Warrington illustrates this through the girl who stood up to her class because she thought the answer was 13 and 1/5 rather that 13 and 1/15.
Disadvantages include the time constraint. It takes much longer to go through understanding that procedures. Also, if the educator cannot create a safe environment where students feel comfortable asking questions, then this method of teaching will never work.

When von Glasserfeld uses the term "constructing knowledge" because, as he points out, each person's life consists of different experiences and different views on life. As one experiences a specific moment of "knowing" they can add that to their former knowledge and either change or build upon their previous thoughts or experiences with that subject or concept. This is why von Glasserfeld calls it contructing rather than aquiring--sometimes previous experiences may have led one astray in their "knowledge" and so when a knew experience occurs, they can break down their former knowledge and make the necessary changes (reconstructions) so their new knowledge now coincides with every one of their previous experiences. Because experiences play such a crucial role in constructing knowlege, then, since no one has had every experience possible, knowledge is relative and more of a theory than a pool of facts.
Understanding that knowledge is constucted is important to teach mathematics. With this understanding, I, as an educator, can teach one concept in many different methods rather than just expecting every student to understand from one method. Different methods will fit into different experiences students have had with a concepts. Also, I can try to see where or why a student's knowledge may be scewed or needs "reconstructing" according to what concept I am teaching and the method I am using to teach it. If I apply this idea of "constructing" knowledge, I will be able to communicate more clearly and accurately to my students.