Adding the Ineffable to an Algebra Class

"In teaching as in few other fields," writes Rosetta Marantz Cohen in her introduction to A Lifetime of Teaching: Portraits of Five Veteran High School Teachers, "the life makes itself manifest in ever?/aspect of the work." To understand the careers of devoted and successful teachers, Ms. Cohen followed five exemplary yet quite different high-school teachers, profiling each in intimate, day-in-the-classroom detail. One of the teachers, Carl Brenner, is a 28-year veteran of Alamos Heights High School in San Antonio and the author of four popular mathematics texts. In his personal and low-key, yet academically demanding style, Mr. Brenner helps prove a central thesis of the book: that it is ultimately the teacher, not the method, that forms the cornerstone of a student's educational experience.

The following excerpt gives glimpses of how Mr. Brenner, whose favorite expression is "convince me," builds...