Statement
Reason
1. In an argument, all steps must be justified.
1. Definition of Argument
2. In real, adult arguments, such justifications
2. Definition of Justification
often take the form of cogent explanations,
appeals to agreed-upon facts, and clear, explicit
reasoning.
3. High schoolers are too simpleminded for such
3. Fundamental Axiom of Condescension
techniques.
Towards Young People
4. Besides, it would take too long for instructors
4. Overworked Teacher Postulate
to grade such arguments.
5. Instead, high schoolers ought to justify their
5. Property of Nonsensical Schooling
arguments by reciting the names of theorems
and axioms, invoked as if they were not logical
statements but magical spells.
6. Logic ought to be learned through two-
6. Theorem of Maximal Damage
column proofs.
Theorem #3: Two-column proofs are great preparation for the future.
Statement
1. High school ought to prepare students for
Reason
1. Definition of Education
their remaining years as scholars, and their
future decades as citizens.
2. Real mathematicians employ two-column
2. Theorem of Lies
proofs all the time!
3. Two-column proofs are also used in the
3. Theorem of Even More Lies
workplace and the political sphere. They’re
everywhere!
4. I mean, we wouldn’t be using such an artificial, 4. Definition of Wishful Thinking
opaque system for teaching logic if it didn’t have
some real-world utility, right?
5. Logic ought to be learned through two-
5. Axiom of Systemic Stubbornness in Education
column proofs.
High school students taking geometry 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!
How?
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.