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.
3 comments:
I am equally excited about these new theories (I know they are not that new, but they are new to us). Just think of all the knowledge that students possess that they can build upon. Yes, it may be very different from what we have, but much more real and relevant to them that any example we can give from our own past.
I can honestly say you are giving me a new appreciation for the way engineers think. :-) I love the detail and the preciseness of your statements. That said I think you hit the nail on the head. Einstein didn't learn all he knew from a teacher right? What if you have the next Einstein in your class? You don't want to be the teacher to stifle him. You want to be the one he thanks in his Noble Prize speech for letting him think for himself. I can hear it now...
I agree with your comments. I am also learning that I don't know how to teach mathematics. I look forward to implementing the constructivist methods in my classroom and seeing great results.
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