Students Learning without Algorithms

In the article some advantages to teaching math without telling the students the proceedures or even the right answers is that they will thik things out for themselves. This is an advantage because the students can become good problem solvers and learn how to fish (do math) and not be handed a fish (given the answers.) As in the case of the article where the students were asked to divide 1/(1/3).

A disadvantage to not telling the students the right answers and the procedures is that if they are getting the right answers for the wrong reasons this can de detramental to their learning because they will not know the proper way and later in their math carreers because their foundation is sandy, they will fail bif time. We can see this by the 2 different trains of thoughts the children had when asked to divide 1/(2/3).

Von Glasersfeld and Constructivism

I wish to discuss what Von Glasersfeld means when he talks about constructivism. He uses this term contruct knowlege as opposed to aquirering or gaining knowlege is to show that knowlege is something that we bulid on that we "construct." It conjures up the image that knowlege is something we must buld from the ground up and not something we can add to our arsinal of learning or take in through some other means. To construct knowlege is to go through life and based on your experiences know things the way you do. Experience plays a vital role in constructing knowlege. If your knowlge is that women are pretty, it because you have experienced what ugly to you means and you know what pretty to you means based on your experience with what it means to be ugly or in other words not beagtiful. The conditions in which we construct knowlege is when we come across something that challenges what we know by showing us a case were our knowlege does not hold, and we make changes to our knowlege and come to know something new based on the thing that caused us to question what we thought we knew. This is also the same reason Von Glaserfeld refers to knowlege as theory because a theory is something we believe and think we know to be true but there is a chance it is false just like with our knowlege. The reason knowlege is viable rather than correct is that being viable allows knowlege to adapt and evolve with our experienceses and and it is not fixed and unchanging with what is what is implied when one says knowlege is correct.

Assumng I believe in Constructivism (shich I do) I wish to also say how it would effect my role as a teacher. Hypathetically If I were a teacher and asked my students to turn there home work in at the end of class because I had a knowlege that some students came late to class and they might like me better as a teacher if I did not penalize them for being late. In so doing I have the experience that the students will then procrastinate their homework assignment and do it while I am lecturing, that would challenge my knowlege and I would adjust what I know, (Construct my knowlege) so I would ask for their home work at the beginning of class so a.) People might be on time. and B.) They will pay attention to me during class. This is a constructivism view point because I am able to change what I know, what I know bases on my experiences and what I know is viable meaning it is a theory that based on my experience with the class, I know is a wrong theory and I must make changes to make it a more correct one.