The War On Abstract Thought
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Education theses gather dust; the damage they’ve inflicted is evident in the lamentable state of language and mathematical proficiency among the majority of students, documented year after year by much-maligned standardized tests. While SLL claims no expertise in the arcane field “Education” has become, it appears that the crippling of students’ minds has had two broad components: dispense with step by step learning and jump among steps, on the theory that as the later steps are learned, the earlier steps will somehow be mastered, and dispense with hierarchies, on the theory that everything is interrelated, so by teaching everything at the same time, the student learns everything.
Education theses gather dust; the damage they’ve inflicted is evident in the lamentable state of language and mathematical proficiency among the majority of students, documented year after year by much-maligned standardized tests. While SLL claims no expertise in the arcane field “Education” has become, it appears that the crippling of students’ minds has had two broad components: dispense with step by step learning and jump among steps, on the theory that as the later steps are learned, the earlier steps will somehow be mastered, and dispense with hierarchies, on the theory that everything is interrelated, so by teaching everything at the same time, the student learns everything.
"The journey of a thousand miles begins with one step." - Lao Tzu "You must learn to crawl before you can walk" (proverb)
I believe in Locke's "Tabula Rasa." Concept formation and abstractions must be preceded by cognition of perceptions and then concretes. to jump around and bypass the basics does not provide one with a solid foundation upon which they can rely upon their new abstractions. Concepts “represent classifications of observed existents according to their relationships to other observed existents.”Ayn Rand Concept formation requires the omission of measurements, but includes all other similar characteristics. A chair is a chair no matter how large or small. Once the concept is established a word (Chair) is the symbol, the expression of the concept. this is how we best learn... one percept built upon the next in a hierarchy. I suppose some extraordinary people may be able to jump forward and fill in the blanks later, but without a step by step building upon prior knowledge most will be left at a disadvantage and likely to develop false premises.
Respectfully,
O.A.
The beauty and power of math is how each piece of new knowledge builds upon the rest and how it was discovered and can be and was derived from what came before. When understands this one becomes mathematically aware and literate. But this is almost never taught in school.
Instead we dump one disconnected technique after the other on students and have them apply these rote learned techniques to countless problems with not a clue of where the technique came from, how it works, how it was derived. This makes math deadly boring an completely opaque. It turns most people off tremendously.
Building a body of understanding and fluid ability to work with the key abstractions - to think in that domain - this is what is very important for being a capable and employable adult in our increasingly technological world. All the rote memorization in the world will not get one there.