Are Geometry Proofs Useless or Important?

The answer is both.

High school students taking geometry, including the new NYS Regents Geometry Course, will be doing lots of geometry proofs.

Geometry Proofs: Junk or Gems?“When will I ever use this junk?” will almost certainly cross their minds.

The answer is “probably never,” which clearly favors the “junk” designation in the title.

Then why make kids go through the ordeal?

The answer is that learning to do geometry proofs is a brain-boosting activity which helps make children’s brains better, permanently better!


Doing geometry proofs requires the brain to operate in new and complex ways, using seldom-used brain “real estate,” thus forming and reinforcing complex brain connections. Once developed, these neural connections remain, ready to “jump into action” in real-life situations, long after “CPCTC” has faded into mental oblivion.

Here are a few of the many thought juggling mental activities required when doing geometry proofs.

Organization. Doing proofs requires organization, requiring the brain to cultivate and improve neural paths in the executive function area. This involves sorting the given information, making diagrams, labeling, and keeping track of the progress throughout the task.

Logical thinking. Doing proofs requires logical thinking, a mental process that is rarely well developed in the younger high school students. The act of doing proofs provides a fine opportunity to develop, or improve upon, this valuable higher order thinking process.

Self-discipline. The mental and physical tasks required when doing proofs, e.g. making diagrams from sentences and symbols, planning, carrying out and coordinating all of the required activities, are unnatural, tedious, and difficult for many students. As a result, the students tend to develop a greater self-discipline.

Thus, doing geometry proofs is a “gem” of an activity because it is good for the brain; it helps make young brains better, permanently better!

So, contrary to Pink Floyd’s “Hey! Teachers! Leave them kids alone!” philosophy, espoused in their 1979 song “Another Brick in the Wall,” leaving kid’s brains alone would be a big mistake. Doing so would seriously compromise children’s brain development.

Consider passing this message on to the kids: Hey! Kids! Don’t forget to do your math homework, especially if it includes geometry proofs.


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