In one of our meetings, as this module is supposed to give us some insight in pyschological theories to the way someone learns, we tried to pinpoint which theory on how we learn was as close to the way we expect our target audience to use. Katina helped us out and mentioned metacognition.
Having learnt a little about metacognition, I decided to do some further research to see how relevant metacognition really is.
To start off, a definition:
"Metacognition is recognition on the part of the learner that learning has taken place, or is taking place. It involves understanding and appreciating the factors that make learning possible and one's own strategies and processes of learning...". www.assessnet.org.uk/mod/glossary/view.php
This is a very common cognitive process with problem-solving in mathematics. When someone reaches a problem in maths, they consciously acknowledge the problem and manages to find a way to overcome it as a consequence.
I read a few chapters of the book "The Handbook of Research on Mathematics Teaching and Learning" -
http://books.google.co.uk/books?id=lLeo33Tvz9
UC&printsec=frontcover&dq=metacognition&lr=
&source=gbs_summary_s&cad=0#PPP1,M1
In chapter 15, it goes into a large amount of detail on how "problem-solving must be one of the fundamentals of teaching mathematics in schools". Although this is not chipped in stone gospel words of wisdom, the opinion of the author does have a valid point. Solving numeric problems is the best way to learn the very fundamentals of mathematics. This gives us even more reason to carry along the same track we are on already in terms of how to structure the learning element of the game.
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