The Breakthrough in Algebra

Algebra is a learned skill and can be taught just as effectively as any other learned skill. Teaching a skill requires patience and the realization that understanding of concepts is not a prerequisite of the initial development of skills: understanding often follows the ability to do rather than precedes it.

Speaking a mother tongue is a learned skill that is mastered by the quick and the slow, by the gifted and the nongifted, and by both logical and illogical thinkers. People in any of these categories can also become bilingual in the proper environment. Ask an eight-year-old child of a Vietnamese refugee a question in either Vietnamese or English, whichever you prefer. If it is your wish, he will reply in Vietnamese to questions in English and in English to questions in Vietnamese. He has learned the skill of expressing his thoughts with facility in both languages. One never attempts to relate the fact of mastery of these languages to the intelligence of the child, or to confuse this mastery with a presumed mastery of logic by an eight-year-old. The child simply speaks two languages.

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John Saxon

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Algebra is a learned skill and can be taught just as effectively as any other learned skill. Teaching a skill requires patience and the realization that understanding of concepts is not a prerequisite of the initial development of skills: understanding often follows the ability to do rather than precedes it.

Speaking a mother tongue is a learned skill that is mastered by the quick and the slow, by the gifted and the nongifted, and by both logical and illogical thinkers. People in any of these categories can also become bilingual in the proper environment. Ask an eight-year-old child of a Vietnamese refugee a question in either Vietnamese or English, whichever you prefer. If it is your wish, he will reply in Vietnamese to questions in English and in English to questions in Vietnamese. He has learned the skill of expressing his thoughts with facility in both languages. One never attempts to relate the fact of mastery of these languages to the intelligence of the child, or to confuse this mastery with a presumed mastery of logic by an eight-year-old. The child simply speaks two languages.