This article brought an interesting question to my mind. How much of what we have learned could help or hinder what we learn next? Our previous knowledge could effectively help in constructing a new knowledge and our nature as human beings is to build new knowledge on what we’ve already learned and retrieve information from the past to help us understand the present situation. At the same time, previous knowledge could obscure what we are ready to accept and learn. We become bounded with what we know.
How much is too much?
When our mind is cluttered with knowledge, we sometimes miss the obvious and when we are used to complexity, we forget about simplicity. I connect that to how sometimes kids solve a new problem in a very creative way just because they do not have any previous knowledge regarding that problem.
The French author Antoine de Saint-Exupery says: “Grown-ups never understand anything for themselves, and it is tiresome for children to be always and forever explaining things to them. “
As a teacher, I believe that some basic knowledge about a topic is required. Yet, I need to take advantage of what my students don’t know and have them spend a big part of their time in a mathematics classroom exploring ideas and using heuristic problem solving. I want to encourage their creativity and their ability to challenge some rules and break some limits. In my classroom, I want to see fearless young mathematicians.
That was a great question that came to mind. I think it is very true, especially for myself, I tend to over think problems a lot and it is because I have too much knowledge in my head. I like how you mentioned that we have to take advantage of what our students don't know and use it for their own benefit, obviously they need to have some prior knowledge. But it is amazing as to how with some math problems you don't need to know much in order to attack the problem and solve it. We should teach students that if you have a mind you can problem solve. This confidence should be instilled in them in our math classes. Great idea Feda. :)
ReplyDeleteYes, the question of mental clutter is an interesting one. Sherlock Holmes would be proud. I think it is definitely valuable to have students confront something of which they have no prior knowledge. The pure creativity that ensues is an excellent learning experience. However, I wonder if we as teachers sometimes ruin these exercises with clutter.
ReplyDeleteExample: we introduce something brand new and get the students to invent possible solutions. This is a valuable exercise that forces them to think and be creative. We then get them to share their methods with each other. For a student who has just engaged in a great effort to generate his own understanding, is bombarding him with the other students' explanations (which may differ greatly from his own) just cluttering his mind?
I like your perspective on creativity and the connection you make with prior knowledge, Feda. However, my biggest challenge in math (especially senior) is to teach something new that does not require prior knowledge. In fact, I find that students may be more free and open to creativity once they have a solid foundation for learning.
ReplyDeleteSo, I guess there is a difference with having your mind cluttered with instrumental vs. relational knowledge and can see how the former can be in the way of creativity.
Hi Feda,
ReplyDeleteYou brought up an interesting question. We always attack problems with more complex manner (which we have learned) while that problems could be solved in very easy way. As the example is given in the article, Friet,who has not learned much in the class, came with more simplified solution.So, it is an interesting question that how much knowledge is too much?