Professor Suggests Principles for Teaching Proofs

February 17, 2010 

Writing in The Chronicle of Higher Education, Charles Coppin (Lamar University) offered advice on teaching mathematics. 

Coppin, who had participated in an MAA PREP writing workshop in 2008, said that teachers could apply the principles to any subject (algebra, calculus, developmental mathematics, humanities, etc). Encouraging and appealing to students' creativity, moreover, would help them gain confidence and become excited about mathematics. 

"They might even catch the bug to delve further into mathematics," Copping observed.

Coppin's advice included studying the masters to learn to write well. The same holds true for mathematics, he claimed. Students should participate in an inquiry-based class; study notes from such a class; and read Creative Mathematics (by H.S. Wall), Synthetic Geometry (by R. F. Jolly), and Foundations of Point Set Theory (by R.L. Moore).

Progress from the simple to the complex, wrote Coppin. Students should attain higher and higher levels of mathematical maturity, that is, apply different theorems, deal with numerous mathematical concepts, and develop imagination. 

Teachers should calibrate the Zone of Proximal Development. Defined by Lev Vygotsky, the ZPD is the intellectual gap that students must jump cognitively if they were to evolve to the next level of intellectual sophistication. 

Coppin advised teachers to write well. "When preparing notes for a proof class," he wrote, "craft them as if you are writing a masterpiece. Your students will notice the difference."

"Introducing students to the essence of mathematics, and its pervasiveness in all disciplines," concluded Coppin, "will help them start to become independent thinkers and masters of their own education. Students will be excited about mathematics and palpably more confident; those who are afraid of mathematics will be less so. The spirit of mathematics cannot be observed; it must be experienced firsthand."

Source: The Chronicle of Higher Education