When I was a lad growing up on the prairies of northern Montana, I had the good fortune to attend a small high school (the student body was approximately 350) where something approximating a classical education was taught. The rural school district couldn't afford to hire faculty to teach astronomy, rhetoric, philosophy, or Greek ~ but we students did have access to physics, chemistry, biology, American and world history, English literature, Latin, sociology, music, drama, and every math from algebra through geometry to trigonometry.
We also had dedicated teachers who introduced us to the tools we would need to branch out into the world. This morning I was reminded of those resources when I came across a NYTimes article, A Picture of Language. The writer introduces us to parsing, the first system for analyzing syntax, developed in 1847 by W.S. Clark. She then proceeds to a much simpler and more useful system, sentence diagramming, developed by Alonzo Reed and Brainerd Kellogg in 1877. It is the latter system which I learned under the able tutelage of Mr. Morgan Sherlock. (Click on the above diagram example to enlarge)
Diagramming a sentence is easy and fun, rather like solving a puzzle. For those of us who are visual learners, It is an ideal approach to understanding the relationships between words within a sentence, and translates to understanding other, more complex relationships between ideas within almost any academic discipline. You'll find a simple introduction here, and a collection of instructional videos here.
Alas, sentence diagramming has fallen from favor in many schools. What a pity. As Reed and Kellogg put it in the introduction to their grammar text, sentence diagramming "teaches the pupil to look through the literary order and discover the logical order. He thus learns what the literary order really is, and sees that this may be varied indefinitely, so long as the logical relations are kept clear .... The diagram drives the pupil to a most searching examination of the sentence, brings him face to face with every difficulty, and compels a decision on every point.
In short, it is one route for learning to think, critically and systematically. When our children are supplied with calculators, smart phones, computers, and the Internet, perhaps thinking has become passe. Verbal and written expression has become dumbed down. Math skills are waning. Small wonder that many students from the U.S. are falling farther and farther behind students from other countries in the sciences, the arts, and yes, writing a coherent sentence.