These days, high school geometry is light on proofs, writes Barry Garelick on Education News. Students may know the sum of the measures of angles in a triangle equals 180 degrees, but most can’t prove the proposition.
If done right, the study of geometry offers students a first-rate and very accessible introduction to the nature and techniques of logical argument and proof which is central to the spirit of mathematics itself. As such, a proof-based geometry course offers to students—for the first time—an idea of what mathematics means to mathematicians, and how it is used. Also, unlike algebra and pre-calculus, since geometry deals with shapes, it is easier for students to visualize what it is that must be proven, as opposed to more abstract concepts in algebra.
Most geometry textbooks give students “one or two proofs that are not very challenging in a set of problems devoted to the application of theorems rather than the proving of propositions,” he writes. Many problems indicate missing angles or segments as algebraic expressions. It is, to quote Mr. Spock, “illogical.”