The Role of Logic in Teaching Proof (Epp, pp1) is centered on the “difficulties students experience in mathematics courses requiring them to write proofs, as observed by the author where her students showed “inability to precisely offer logical expressions to substantiate their mathematical arguments.” The students therefore, according to Epper appeared to be living “in a different logical and linguistic”, greatly different from hers and could not grasp the theoretical concepts in the course content.
According to the author, gauging the “truth and falsity”, of a theorems is a “complex cognitive activity”, a situation which do not necessarily need a background knowledge of the rational rule used in the arguments but the concept has to be applied to ascertain its validity.
However, many instructors fail to recognize the fact that most students lack such in-depth conceptualization especially in, “statements requiring proof by contradiction or proof by contraposition “while some students who indicate to understand the acceptable proofs are rarely eager to appreciate the need “for further verification.”
Existence of varied forms of mathematical reasoning including informal ways is identified as one of the reasons why students have such difficulty, especially due to the ensuing indistinctness in the “mathematical language” that leads to deliberate and arbitrary deviation from the fundamental meaning of a concept. Another source of illogical reasoning is exhibited when students “try to negate if-then statements”, like “negation of if p then q is simply p and not q”. The mathematical reasoning difficulty is also blamed on the previous method of delivery that was mainly based on concept generalizations that leaves weaker students disadvantaged.
The author suggest that there is need to incorporate the abstract rules of logic with the use of examples during teaching to initiate students’ eagerness to learn and master the concept at the very onset of introducing an area of study. I support this proposal since use of the non-mathematical examples would imply that the students need to develop and show valid case as a requirement for proving the algebraic concepts. To avoid wastage of limited time , teacher needs to first give a brief on the non mathematical examples and the grammatical syntax involved on a concept and then concurrently run the “principles of logical reasoning and the associated linguistic conventions” throughout the course coverage.
Epp, S. “The Role of Logic in Teaching Proof.” 2003. Retrieved February 4, 2009.Available