Most teachers of higher education have adopted a “here’s the problem, my student knows that already” type of approach to teaching. I learned this from Dr. Price. (key) He is a world renowned expert on the subject of educational philosophy and the author of a popular book on the subject, The Power of Conversational Hypnosis. I learned many things from Dr. Price and his work. Here are just a few that resonated with me.
“When an argument runs across a line of logic or fact, but cannot be applied directly to that line of logic or fact, it rests on a theory of validity–an appeal to a priori, or a credibility claim about the evidential basis for the argument. But when a student finds that a fact or argument can be applied directly to that same line of logic or fact, then it rests on a logical foundation that can be objectively verified.” (Price & van Benthem, 1986). This concept can be applied to an argument as well as a conclusion.
“A conclusion may be true, but it does not follow that the student must accept it as true.” (Price & van Benthem, 1986). This may sound like a platitude, but it is true. A student may find that a fact or argument supports a conclusion he already thinks is false, but he does not have to believe it to reach a conclusion that supports that conclusion. This is true of all kinds of reasoning.
“A student is not required to examine every aspect of the argument, but only the central point–the focus of attention.” (Price & van Benthem, 1986). A student is encouraged, not required, to examine every argument he writes about. (Even if he ends up defending that conclusion in the end.)
“To prove something is to show that it is possible. That which can be demonstrated cannot be proved.” (van Benthem & Price, 1986). This is a very good way to explain how diagrammatic reasoning differs from argumentative writing. A student who doubts a premise can reason from the premise to its negation, while a student who doubts the conclusion can argue from the negation to its affirmation.
Determining what to show is just one part of the exercise. In order to answer the question, “What should be demonstrated?” it is also important to decide what diagrammatic diagrams will be used. A student may choose to use graphs or charts, he may use lists, he may describe the subject’s arguments – in terms, so to speak – or he may describe his own arguments. The diagrams chosen will depend on the student’s style, the topic at hand, and the extent of his understanding.
One of the biggest difficulties encountered by novice students is to determine what is a conclusion and what is an argument. It is often difficult for a student to draw a line between these two things. To help with this task, a diagrammatic reasoning guide is often provided. These guides take the student through the different stages of argumentative discussion – from the point of view of the principal argument to the point of view of the defender – in such a way that both parties are portrayed graphically. This visual aid is invaluable because it allows the student to become acquainted with the various shapes, sizes, and colors that are associated with each stage of the argument. The resulting diagrammatic reasoning diagram may serve as a reference tool that will assist the student in deciding which arguments are valid and which ones are invalid, and thus that demonstrations will be most successful.