External Representation - Printable Version +- Teach the Brain Forums (https://www.teach-the-brain.org/forums) +-- Forum: Teach-the-Brain (https://www.teach-the-brain.org/forums/Forum-Teach-the-Brain) +--- Forum: How the Brain Learns (https://www.teach-the-brain.org/forums/Forum-How-the-Brain-Learns) +--- Thread: External Representation (/Thread-External-Representation)

External Representation - Karldw - 17-07-2005 Time for some fun. The following comes from an LD site. Ask and I will tell you where but for now I want to focus on the concept. “Examining the use of external representations and their effect on solutions to problems in informal or formal tests and homework, might reveal to teachers the way that their students solve problems. These entities known as external representations are used when an individual solves a problem and shows his working out of the problem. These entities include: words, abbreviation, symbols, letters, lines, pictures and ideas. Knowing the external representations a student uses to solve problems could assist teachers in designing teaching materials and strategies to help their students, particularly those with dyslexia.” This works the other way also. When you teach you usually induce an external representation of the problem into the student. This is particularly true in things like word problems in maths. The induced representation can effect the students ability to solve the problem. There may be unnecessary information. There may be multiple ways to solve the problem. Are these consistent? There may be multiple answers to the problem. How can you tell? What is the cognitive difficulty of the problem? How can you change and/or measure the level of cognitive difficulty? These are all matters of cognition which is what education is about. With external representations we can begin to evaluate the characteristics of an internal/external relationship in cognitive processing such as the properties of the internal and external structures and the cognitive benefits of different external representations. This allows us to begin to assess more effectively how technological innovation in external representations should be approached. The following is a problem by cognitive scientists Johnson-Laird and Byrne about “setting a table”. Try to solve the problem and see if you can incorporate an external representation of the problem that will help you see the answers to the above questions. 1.The fork is on the right of the spoon. 2.The fork is on the right of the cup. 3.The knife is in front of the cup. 4.The plate is in front of the fork. What is the relation between the plate and the knife? Let us know what you think the answer to the problem is and also what you think the answers to the above questions are. Extra credit – Is it possible to place the cup anywhere you wish relative to the plate and why? External Representation - Karldw - 19-07-2005 I had a direct contact related to the above post. To make everyone feel better she stated, “I attempted the problem you presented in the forum. I enjoy these, they keep me thinking. But, I had a problem with the semantics on this one. I'm not sure what is meant by 'in front of'”. This is a reasonable question. The clue comes from the name of the problem - “setting a table”. You must deduce from this that the problem is essentially a two dimensional spacial problem. This is critical to the graphical solution that I use. There is no given coordinate system so you are free to use your own except that it could effect the logic of your answer. She also says that she is familiar with “graphic organizers (what I believe you call external representation).” “Graphic organizers” are a more or less generic term that is common for k-12 teachers. It is used so broadly that it is hard to extract a commonality other than “graphic”. I generally work with what I call linear graph techniques which has a well defined confusion in the field of mathematics. I used the term “external representation” because it expresses a cognitive way of thinking. This is described in the document below Shin, Sun-Joo, Lemon, Oliver, "Diagrams", The Stanford Encyclopedia of Philosophy (Winter 2003 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/win2003/entries/diagrams/>. “Diagrams or pictures probably rank among the oldest forms of human communication. They are not only used for representation but can also be used to carry out certain types of reasoning...” There are various approaches to the use of diagrams. One is the philosophy of mind and cognitive science. Another is diagrammatic reasoning where it can be shown that there is no intrinsic logical difference between symbolic and diagrammatic systems. The “Diagrams” article says: “The following quotation from Chandrasekaran et al. [1995, p. xvii] succinctly sums up the distinction between internal versus external diagrammatic representations: External diagrammatic representations: These are constructed by the agent in a medium in the external world (paper, etc), but are meant as representations by the agent. Internal diagrams or images: These comprise the (controversial) internal representations that are posited to have some pictorial properties. ...logicians focus on external diagrammatic systems, the imagery debate among philosophers of mind and cognitive scientists is mainly about internal diagrams, and research on the cognitive role of diagrams touches on both forms.” I was very pleased to see the association between “external representations” and “graphic organizers”. For those of you who are familiar with graphic organizers this is a good place to start. This is in essence what I am talking about. I will continue to say “external representation” because I want to emphasize the philosophy of mind and cognitive science on this forum.