Assignment #4

In von Glasersfeld's paper on constructivism, rather than making the claim that we acquire or obtain knowledge, he states that we "construct" knowledge through our experiences in life. His use of the word construct helps us see what he is meaning. Just as a construction worker uses a blueprint, or knowledge gained beforehand, to build a house, so do we 'construct' our view of the world through experiences we have had in the past. Continuing the analogy, one does not build a house starting with the roof. A solid foundation is necessary for the walls, doors, windows, support beams, and roof to stand. So it is with our knowledge, we only know the things that we know because of the foundations that we've had. Also, just as a worker has his own 'best' method of construction, so too do we form our own 'best' ideas of what the difference between truth and error are. And, just like the construction worker, we don't change our ideas of truth until we're presented with something that provides a clear counter-example to what we believe. Thus, von Glasersfeld is making the argument that the only way we know things is through experience; hence, it's impossible for us to know the 'truth.'

One important implication that constructivism has on mathematics is how it points out the fact that just because I view a topic one way does not mean that everyone views it the same way. I know that as I have tutored, subjects that I have found to be quite simple to understand, such as rules of exponents, others have really struggled with. After reading this article I've come to learn the importance of trying to see through my student's eyes. Trying to really see where they're coming from and what 'baggage', whether good or bad, they're bringing with them to the proverbial table. As I try to learn more about how people view various aspects of math, I can then modify my teaching to fit into their world views and ideas. By doing this, I can help them create a more accurate view of math and how it works.