Blog Entry #5

Teaching mathematics to students without first telling them the procedures or even the right answer can be very helpful to a child's education according to Mary Ann Warrington. This method of teaching gives students the opportunity to construct their own knowledge with what they have been taught previously as well as through heated mathematical debates. Warrington spoke about how this kind of teaching environment gives the students more confidence and willingness to take risks by solving problems with their own devices. She talked about how constructivism brings forth intellectual autonomy. When children are encouraged to think for themselves they will develop much more successfully.

Although teaching in a constructivist manner has many advantages, there are some disadvantages that should be looked at carefully. If a teacher sits passively in the classroom observing the students as they construct knowledge, they could start to form false methods or procedures. Warrington stated that the teacher must understand each child's thought process and be able to carefully determine when and how to direct them to deeper and higher levels of thinking. During her experiences in the classroom, for example, when the class was working through the problem 4 2/5 divided by 1/3, the majority of the class was agreeing with a false procedure. If the one student who had done it correctly hadn't spoken up or figured the correct process out, then the entire class would have been in agreement with an incorrect method. Although constructing knowledge is extremely effective if done correctly, there is no way to force the children to come up with the right methods or procedures on their own. If they cannot figure it out on their own than the teaching method is useless.

Blog Entry #4

In Learning as a Constructive Activity, Ernst von Glasersfeld speaks of constructing knowledge rather than acquiring or gaining knowledge. In his article he mentions that the knowledge we have is continually built upon by the experiences we have throughout our life. Each experience that confirms our past belief adds onto our "knowledge" and we continue with this sense of truth that we call reality. Our view of this truth and knowledge only changes once we hit a wall and have experiences that contradict what we previously believed. Since our knowledge can always be changing based on what we see as reality, von Glaserfeld considers knowledge a mere theory. Everyone has different experiences, therefore there may not be any knowledge that is entirely correct, but rather viable and capable enough to get us through life successfully.

To use constructivism to teach my students math principles successfully, I would need to find ways for them to experience math on their own. If I gave them examples of activities outside the classroom that they were invloved in (such as sports or dealing with money) and incorporated mathematical principles (such as geometry or algebra), then my students would be able to construct their knowledge based on what they previously knew about these same activities. I also think it would be helpful for them to come up with their own story problems based on their own experiences, that way they can find their own "truth" to the mathematical scenarios.