The Reed-Kellogg system - Basic schemata

"Most methods of diagramming in pedagogy are based on the work of Alonzo Reed and Brainerd Kellogg in their book Higher Lessons in English, first published in 1877, though the method has been updated with recent understanding of grammar. ...
Some schoolteachers continue to use the Reed-Kellogg system in teaching grammar, but others have discouraged it in favor of more modern tree diagrams. However, these modern tree structures draw on techniques that were already present in Reed-Kellogg diagrams. Reed and Kellogg defend their system in the preface to their grammar:
The Objections to the Diagram.--The fact that the pictorial diagram groups the parts of a sentence according to their offices and relations, and not in the order of speech, has been spoken of as a fault. It is, on the contrary, a merit, for it 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 assertion that correct diagrams can be made mechanically is not borne out by the facts. It is easier to avoid precision in oral analysis than in written. 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.
... Reed-Kellogg diagrams abstract away from actual word order in order to focus more intently on how words in sentences function and relate to each other.
The Reed-Kellogg System. Simple sentences in the Reed-Kellogg system are diagrammed in accordance with the ... basic schemata" shown in this diagram example. [Sentence diagram. Wikipedia]
The example "The Reed-Kellogg system - Basic schemata" was created using the ConceptDraw PRO diagramming and vector drawing software extended with the Language Learning solution from the Science and Education area of ConceptDraw Solution Park.

This sentence diagram example was redesigned from the Wikipedia file: Examples of Reed-Kellogg diagrams.jpg.
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"Most methods of diagramming in pedagogy are based on the work of Alonzo Reed and Brainerd Kellogg in their book Higher Lessons in English, first published in 1877, though the method has been updated with recent understanding of grammar. Reed and Kellogg were preceded, and their work probably informed, by W. S. Clark, who published his "balloon" method of depicting grammar in his 1847 book A Practical Grammar: In Which Words, Phrases & Sentences are Classified According to Their Offices and Their Various Relationships to Each Another.
Some schoolteachers continue to use the Reed-Kellogg system in teaching grammar, but others have discouraged it in favor of more modern tree diagrams. However, these modern tree structures draw on techniques that were already present in Reed-Kellogg diagrams. Reed and Kellogg defend their system in the preface to their grammar:
The Objections to the Diagram. - The fact that the pictorial diagram groups the parts of a sentence according to their offices and relations, and not in the order of speech, has been spoken of as a fault. It is, on the contrary, a merit, for it 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 assertion that correct diagrams can be made mechanically is not borne out by the facts. It is easier to avoid precision in oral analysis than in written. 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.
These statements bear witness to the fact that Reed-Kellogg diagrams abstract away from actual word order in order to focus more intently on how words in sentences function and relate to each other." [Sentence diagram. Wikipedia]
The examples of Reed-Kellogg diagrams was created using the ConceptDraw PRO diagramming and vector drawing software extended with the Language Learning solution from the Science and Education area of ConceptDraw Solution Park.

"In elementary algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form
ax^2+bx+c=0
where x represents an unknown, and a, b, and c are constants with a not equal to 0. If a = 0, then the equation is linear, not quadratic. The constants a, b, and c are called, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.
Because the quadratic equation involves only one unknown, it is called "univariate". The quadratic equation only contains powers of x that are non-negative integers, and therefore it is a polynomial equation, and in particular it is a second degree polynomial equation since the greatest power is two.
Quadratic equations can be solved by a process known in American English as factoring and in other varieties of English as factorising, by completing the square, by using the quadratic formula, or by graphing." [Quadratic equation. Wikipedia]
The flowchart example "Solving quadratic equation algorithm" was created using the ConceptDraw PRO diagramming and vector drawing software extended with the Mathematics solution from the Science and Education area of ConceptDraw Solution Park.