| “A problem well-defined is
half-solved.” John Dewey The special theory of cognition (STC) is introduced within the context of an intuitive problem: a problem where both the concepts and language for manipulating those concepts needs to be defined. The theory addresses the question about how different conceptual and representational systems influence a student’s ability to solve problems: “We all believe that they do, and authors show that they do, but none show how they do. (James Kaput)” The STC is used as a basis for analyzing a problem and showing the alternate solution pathways. These pathways are then matched to solutions. The presentation will have more meaning if you take some time out to work on the problem below. The Missing Piece of the Puzzle The first row is a sequence of jigsaw puzzle pieces. Which puzzle piece in the second row logically comes next in the sequence?  An acceptable solution to this problem requires (a) a detailed description of the ideas used and how they are used and (b) alternate solutions. It is important to take your time and keep track of the kinds of activities you engage in. It’s not really important to either solve the problem or get a correct answer. What is important is to be aware of the kinds of things that you are doing. |