40. Exhaustive Exercise Databases

Students should have access to a virtually limitless number of exercises in math, science, language, and other subjects. These exercises should be divided into narrow categories, each of which emphasizes one particular aspect, potential point of confusion, or certain stage of problem-solving that is prone to causing confusion or mistakes in the subject being taught.

Perhaps the internet the most practical and lowest-cost place for such exercises to be made available to those who need it. All school textbooks and school bookstores should be required to list such websites in a place easily visible to students.

The idea is to provide students with access to a flood of sample problems, organized by category, so that they could practice working through any formulas, concepts, rules or specific portions of them which they do not quite understand. These exercises should be designed so that every possible snag that a student may face could be resolved by having that student work through a series of exercises specifically designed to pull that student through that snag with an understanding of how to resolve that snag in a variety of different situations and contexts. Studies should be made on where students have problems or become stuck, and a series of exercises should be created to specifically deal with each of those problems. For example, if a student has trouble subtracting from rounded hundred numbers (such as 300) because of the borrowing functions that must be performed, there should be a whole set of exercises listing hundreds of similar math problem that, while using different numbers, share the property that borrowing must be performed from rounded hundred numbers.

Other exercises could focus on helping English students identify specific parts of speech like subjects, nouns, adjectives, adverbs, prepositional phrases, etc., within sentences. Students could even diagram whole chapters of books to practice this skill. The learning of scientific formulas and chemical equations could also be enhanced in a similar manner.

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