Assignment #5

Throughout Warrington's paper, she has many advantages and disadvantages to her idea of teaching children mathematics without procedures or algorithms. One of the advantages to this style of teaching is the idea that children, when they understand how to do problems, it will have been from their own thought process and would have created thinking in their part to get to an answer. An example of this is when she would ask fraction/division problems without teaching the children the "invert and multiply" rule. This then connects to the advantage of children having part of a relational understanding of the procedures they are creating in their head. Another advantage is Warrington's idea of constructivism of teaching the children new concepts by starting with a topic or concept they've already learned. As Warrington states, this helps them understand the new concept better because they are starting with something familiar.

Besides the advantages of Warrington's style of teaching, there are also many disadvantages. One of those is her idea of children not acquiring knowledge from other people. Yes people will think about things and come up with their own consensus on a concept or topic, but they need the influence of others in order to create their own ideas. Another disadvantage is how Warrington doesn't give the children answers. The procedure on how the child got to the answer is important, but informing them of the correct one is also important so they can move onto another problem and feel like they are understanding things correctly. The last disadvantage I believe Warrington has in teaching this way is that it takes the children longer to understand a procedure when they have to create it with their own knowledge. Many children think differently than others and may not have the prior knowledge enough to create that procedure on their own. Thus, if children are taught the correctly through relational understanding, they would learn the procedure as well as why they are using it for specific concepts or problems.

Assignment #4

Throughout his paper, von Glasersfield gave different ideas and points to what constructivism is. The main idea that he followed and presented throughout the paper was the idea of construct knowledge. Construct knowledge is the idea that all knowledge we obtain is built upon previous knowledge that we have: it isn't created or acquired. He then describes how knowledge is constructed by the experiences we have in our life. Through these experiences we go through, there is then a truth to the knowledge that has been constructed. This truth is the reality of life around us. It can only be changed or our opinion of this knowledge being true only changes when we go through other experiences to counteract the truth that has been made by previous experiences.
In taking constructivism as a true idea and correct perspective of knowledge, an implication in teaching situations that could be used to teach mathematics would be the importance of creating experiences or life situations in the classroom These children then will use those experiences as truth for ideas and concepts in math. Besides creating experiences (such as different problems or examples) to acquire knowledge, one should also build on the experiences one is having in the outside world around them. By looking at mathematics in the world outside the classroom, children would then create a sense of truth to concepts and laws given them. It also would be important to build on knowledge and understanding the children already have constructed, such as in other mathematics classes. In doing all this, constructivism is being used by knowledge being built on knowledge that has already been created as true through prior experiences and then new experiences are being created or brought to one's attention by seeing them inside and outside the classroom.