Constructivism and Implications

Prior to the course, I did not know how to teach mathematics and I did not know how a student learned mathematics. I know I was taught to solve mathematics problems using algorithms and there has to be a better way. I am in the process of constructing new theories of constructivism and how it works. I am learning, the constructivist’s method nurturers the student’s developmental understanding by building from his or her previous knowledge. I see the role of the teacher as a facilitator of understanding through contextual tasks, group shared problem solving, and sharing the students invented strategies and refining the student’s understanding. This is a journey I am excited about.

The contextual tasks are engineered to connect the student with his or her past knowledge and letting a new understanding be constructed. If engineered correctly, the student will develop the understanding and be able to answer the how and why questions.

The implications I currently see are:

Letting go so the student can develop his or her understanding

Letting go of using algorithmic methods

The teacher’s new role as a facilitator of understanding

Engineering the lessons

Let the students invent new strategies

Creating a flexible classroom environment

In closing this blog, I know there will be more implications and I will add to the above list.

The New Math

According to the author, constructivist theory of learning suggests new knowledge is constructed by the student integrating new information with existing knowledge. That learning takes place as the students discuss and interact among themselves and the teacher assesses the students while they work in groups. The teacher uses the student’s work to demonstrate different problem solving strategies.

I think by engineering the lesson plan is an essential part of this technique. "Letting go" is another component.

The students and teacher relationship would be different because mutual respect would be apparent. The students would be enthusiastic about math. The learning experience would also be mutual.

Just a note: I assign tasks daily to my team. I have noticed my team members will solve the tasks in different ways. Sometimes, they will work in groups sharing ideas and then work on the task. At the end of the day the result is the task is completed; however, I sometimes question the efficiency. I also enlist the ideas of other team members collaborating on a solution to a problem. Sound familiar? Why can’t we apply this technique to a new mathematics teaching?

June 13th 2007

Reflection- I just realized today is a special day.