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Riemann's Contribution to Flight and Laser Fusion

Riemann's Contribution to Flight and Laser Fusion

Riemann's Contribution to Flight and Laser Fusion

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on development of deductive reasoningabilities?2. If you regard logic as essential <strong>to</strong>mathematics <strong>and</strong> science, how do yousuggest one develop logical, analyticalabilities?3. When you advocate developmen<strong>to</strong>f creativity do you considerlearning of problem solving heuristics(strategies) as useful? How would yourecommend they be learned/developed?4. Do you know of any books orprograms that would be helpful indeveloping logical analytical skills <strong>and</strong>problem solving strategy development?Rick SilversFayetteville, N.C.To the Edi<strong>to</strong>r:As a math <strong>and</strong> science teacher, Ifind myself in accord with your ideasrelative <strong>to</strong> education, government,<strong>and</strong> so on. My question is what bookscould you recommend covering thephilosophy <strong>and</strong> approach <strong>to</strong> teachingscience <strong>and</strong> math that best gets awayfrom the present trend that's killingthe intellect of our young people?J. Mulholl<strong>and</strong>Anchorage, AlaskaTo the Edi<strong>to</strong>r:Children do not have the resourceof experience <strong>to</strong> think like adults.Why does it take so many words <strong>to</strong>say "learn by rote first"? The theoryof math's construction can be learnedlater after we have more resources<strong>and</strong> then, at that, many may neverneed learn it.We certainly don't learn <strong>to</strong> drive acar by first taking it apart bolt by bolt<strong>to</strong> see what makes it work.I hope after four generations ofexperimenting the educa<strong>to</strong>rs will finallyrealize they had better get back<strong>to</strong> teaching a basic fundamental educationfirst or we may have <strong>to</strong> reinventthe wheel.Not "New Math," but "BackwardsMath"!John C. CarlsonOrangevale, Calif.To the Edi<strong>to</strong>r:I recently received the May issue of<strong>Fusion</strong>. I was very disappointed. Onpage 37 there is a discussion of Chomsky<strong>and</strong> Piaget. The author states,"Chomsky also divorces languagefrom mind." Yet the entire contributionof Chomsky <strong>to</strong> linguistics hasbeen <strong>to</strong> explore those ways in whichlanguage adumbrates the structure ofmind.In his book Language <strong>and</strong> Mind,Chomsky states: ". . . it is fair <strong>to</strong> supposethat the major contribution ofthe study of language will lie in theunderst<strong>and</strong>ing it can provide as <strong>to</strong> thecharacter of mental process <strong>and</strong> thestructures they form <strong>and</strong> manipulate."I received my PhD in linguisticsfrom Ohio State, with a dissertation inthe theory of transformational syntax.Since I know that linguistics has beenseriously misrepresented in yourmagazine, how can I trust your articleson math <strong>and</strong> physics?Dr. Ronald L. NeeldNew Orleans, La.The Edi<strong>to</strong>r RepliesThere is a better kind of mathematicsthan either the antimath of the"New Math" or the rote memorizationadvocated by the "back <strong>to</strong>basics" movement. For several thous<strong>and</strong>sof years, a Pla<strong>to</strong>nic current inscience—represented by Pla<strong>to</strong> himself,Archimedes (but not Euclid),Leibniz (but not New<strong>to</strong>n), <strong>and</strong> Riemann(but not Maxwell)—has no<strong>to</strong>nly taught mathematics using thismethod but has been responsible forall the major advances in mathematicalscience.The Pla<strong>to</strong>nic approach <strong>to</strong> education(sometimes called the Socraticmethod) starts from the realizationthat the subject of education is theprocess of concept formation. That is,a true teacher does not teach information,but rather, the self-knowledgerequired for a student <strong>to</strong> recreatethose ideas for himself. Ateacher must teach what Pla<strong>to</strong> calledthe "hypothesis of the higher hypothesis"—themethod of self-consciouslygenerating quantitatively new knowledge.<strong>Contribution</strong>s <strong>to</strong> the FEFare tax deductible!There are many useful <strong>to</strong>ols in theteacher's armamentarium, includingalgorithmic methods <strong>and</strong> deductivelogic, but these are not the subject ofeducation. They are tertiary aspects ofsome disciplines, instead. When these"logical" <strong>to</strong>pics are turned in<strong>to</strong> thesubject of education, as is the essenceof Piaget, Chomsky, <strong>and</strong> linguisticsgenerally, not only is education destroyed,but also the capabilities forcreative thought in the student aredemolished.Pla<strong>to</strong>'s dialogues remain the bestsource of education in this method—especially the Timaeus, the Sophist,<strong>and</strong> the Parmenides. There have alsobeen inspired applications of goodteaching in many other books, <strong>and</strong>the FEF is preparing a curriculum forscience <strong>and</strong> mathematics based onthese his<strong>to</strong>rical materials as part of itseducation campaign.Oc<strong>to</strong>ber-November 1981FUSION 9

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