The Trivium
Dorothy Sayers wrote that we often succeed in teaching pupils subjects but fail in teaching them how to think. They learn everything except the art of learning. It is as though we teach a child to memorize a nice song to play on the piano without ever teaching him the scale or how to read music!
Read Dorothy Sayers complete essay “The Lost Tools of Learning,” at http://www.gbt.org/text/sayers.html.
Grammar Stage: Students learn the principles, rules and facts of history, science, math and every subject. Much of this should be accomplished while children are young and enjoy memorization!
Logic Stage: The second step in learning is logic - the correct way to reason and to analyze arguments in every subject area. Largely overlooked today, this skill is taught most earnestly beginning in the junior high years when children love to debate. Formal logic and geometry and classical foreign languages are useful for teaching this. Lively debates are often planned in science and other classes.
Rhetoric: A student is trained to write and present his ideas in a sophisticated and effective manner. This should be emphasized in high school. But elements of it begin even in first grade and earlier as children learn to talk clearly and confidently in front of the class.