Personal Learning theory
I personally think people learn through an unconscious process very much like the scientific method. They hypothesize about how the world should work, collect data, compare the data they have collected to see if it fits in their theory, and then revise their theory if they feel enough evidence has been found. In this way, people construct an understanding of the world around them using what they know as a basis.
Each piece of knowledge people gain has to be fit into their personal hypothesis. At first, people will "bend" their hypothesis to make facts fit which seem inconsistent, but eventually if enough contradictory data is collected, people are forced to revise their ideas. This is part of the reason why students have so much difficulty learning topics for which they do not have any background; they are constantly required to create and revisit their hypothesis, and to build theories about the information they are receiving "from scratch".
It is crucial during this process that the learner feels comfortable to make mistakes. Instead of feeling pressure to have exactly the right answer each time, learners must be willing to work through the entire process of learning. Although it is possible that an individual learner will have a theory which fits all the facts as they are collected, it is much more likely that conflicts exist between their theory and the data.
In the classroom, this is when we normally say that a student has "made a mistake", which is unfortunate language. Rather than criticizing students who have a cognitive discord occurring, we should encourage more reflection of the learning process, and provide opportunities to establish a new theory which fits the given facts and can be worked into the learner's personal theory of how the world works.
About David

David is a mathematics teacher and a learning specialist for technology at Stratford Hall in Vancouver, BC. He has been teaching since 2002, and has worked in Brooklyn, London, and Bangkok before moving back to Canada. He has his Masters degree in Educational Technology from UBC, and is the co-author of a mathematics textbook. He has been published in ISTE's Leading and Learning, Educational Technology Solutions, The Software Developers Journal, The Bangkok Post and Edutopia. He blogs with the Cooperative Catalyst, and is the Assessment group facilitator for Edutopia. He has also helped organize the first Edcamp in Canada, and TEDxKIDS@BC.
Disclaimer: The ideas discussed on this blog are my own, and in no way represent those of my employer.
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