미적분 교육

분류없음 2008/08/23 16:00 indices
Geogebra를 보면서 그 막강한 기능에 놀라웠다.
중고등학교 수학의 꽃은 미적분이다. 어쩌면 학교수학의 많은 부분은 미적분을 배우기 위한 과정일 수도 있다. 일본의 공문은 미적분을 가장 빠른 시간에 가르치기 위해 공문수학(구몬수학)을 만들었다는 이야기를 들을 적이 있다.
미적분은 중요하다. 그 아이디어의 찬란함과 더불어 계산의 편리성은 인류 문명에 이바지한 바가 크다. 영어로 calculus 즉, 계산술이라 불리우는 미적분.

사용자 삽입 이미지
(google image 중에서)

그렇게 중요하고 엄청난 일을 하고 있으며, 수학사에서 큰 부분을 차지하는 미적분이다. 또 아마도 '수학(mathematics)'라는 단어와 연결되는 대표적인 개념 이미지가 미적분과 관련된다.

하지만 그 미적분 중 많은 계산 부분은 이제 컴퓨터가 하고 있지 않은가? 컴퓨터가 없던 시절에는 어떤 양을 계산하는 계산 방법은 즉, know how는 중요한 지식이었다. 그러나 요즈음과 같은 세상은 know with, 창의적 사고가 강조되는 세상이고 이 떄에도 미적분의 계산이 그렇게 큰 의미를 가지는 지는 생각해 볼 일이다.
물론 생각한 사람들이 있었고, 그 결론은 계산 위주의 미적분 교육은 포기하더라도 미적분이 가지는 수학사적, 수학적 위치를 고려하여 계속 가르치고 배워야 한다는 것이었다.

그러나 아직도 허전한 무언가가 남는다. 잘 설계된 컴퓨터 환경의 사용법을 가르치는 것과 미적분을 가르치는 것 사이에는 어떤 차이가 있는가? 매뉴얼과 교과서 사이에 어떤 차이가 있는가? 차이가 있어야 할 텐데...

컴퓨터와 경쟁하는 교육이 결코 바람직한 것은 아닐 것이다.

다시 한번 컴퓨터와 함께하는 교육의 필요성을 느껴본다.
2008/08/23 16:00 2008/08/23 16:00
트랙백 83개, 댓글이 없습니다.

댓글+트랙백 RSS :: http://jmath.net/rss/response/19

댓글+트랙백 ATOM :: http://jmath.net/atom/response/19

트랙백 주소 :: http://jmath.net/trackback/19

트랙백 RSS :: http://jmath.net/rss/trackback/19

트랙백 ATOM :: http://jmath.net/atom/trackback/19

  1. Subject: Ephedra.

    Tracked from Ephedra. 2008/11/03 01:09  삭제

    Ephedra is it legal. Ephedra near herb. Yellow swarms with ephedra. Georgia ephedra lawyers. Ephedra ban illegal to posses. Firelean with ephedra. Ephedra.

  2. Subject: Generic for evista.

    Tracked from Lilly evista plea agreement. 2008/11/07 09:05  삭제

    Anchorage jack hit evista. Side effects of evista. Hodgkin's evista. Generic evista discount cheap. Generic name for evista.

  3. Subject: Horse porn beast porn zoo porn dog porn.

    Tracked from Animal sex zoo free porn bestiality horse dog. 2008/11/10 11:03  삭제

    Zoo sex pictures animal porn movies beast trailers. Porn animal free dog zoo. Zoo sex beastiality horse porn dog fucking.

  4. Subject: Zoo porn.

    Tracked from Zoo porn. 2008/11/11 09:49  삭제

    Zoo porn.

  5. Subject: Free zoo porn movies.

    Tracked from Free zoo porn movies. 2008/11/12 10:54  삭제

    Zoo sex pictures animal porn movies beast trailers.

  6. Subject: Bestiality zoo animal sex horse fuck dog porn.

    Tracked from Free zoo porn movies. 2008/11/12 19:16  삭제

    Zoo sex pictures animal porn movies beast trailers. Zoo porn. The petting zoo s stick figure hardcore porn page. Free zoo porn movies. Zoo porn animal porn horse porn.

  7. Subject: Pentermine great buy.

    Tracked from Pentermine great buy. 2008/11/13 08:06  삭제

    Pentermine great buy. Pentermine.

  8. Subject: Free zoo porn movies.

    Tracked from Dog porn videos zoo porn videos animal porn videos. 2008/11/13 12:13  삭제

    Zoo sex movies and animal porn sites. Zoo porn. Zoo sex pictures animal porn movies beast trailers. Free zoo porn movies. Free zoo porn vids. Zoo sex beastiality horse porn dog fucking.

  9. Subject: Xenical.

    Tracked from Xenical. 2008/11/13 18:54  삭제

    Xenical.

  10. Subject: Zoo porn.

    Tracked from Zoo sex beastiality horse porn dog fucking. 2008/11/14 03:11  삭제

    Dog sex exclusive zoo sex horse porn only. Bestiality zoo animal sex horse fuck dog porn. Free zoo porn movies. Animal horse dog beast zoo porn sex cum fuck. Animal porn horse porn dog porn zoo porn search. Zoo sex beastiality horse porn dog fucking.

  11. Subject: Zovirax cream.

    Tracked from Zovirax. 2008/11/14 12:15  삭제

    Zovirax for cold sore. Zovirax cream. Zovirax side effects. Can zovirax treat genital heat rash. Zovirax.

  12. Subject: Ativan caffeine interaction.

    Tracked from Generic ativan. 2008/11/14 21:34  삭제

    Ativan. Ativan treatmenr for seizures. Ativan xr. Ativan xanax valuim trial pack.

  13. Subject: Lipitor.

    Tracked from Lipitor. 2008/11/15 05:44  삭제

    Lipitor.

  14. Subject: Negative effect of prozac.

    Tracked from Prozac nation. 2008/11/15 13:24  삭제

    Phentermine prozac. Tramadol soma zoloft prozac onlineprescription.md. Prozac use in dogs. Prozac side effects. Safely weaning off prozac. Prozac dangers. Prozac for dogs. Prozac.

  15. Subject: Adult zoo free thumbs porn.

    Tracked from Free zoo porn vids. 2008/11/15 21:24  삭제

    Zoo sex pictures animal porn movies beast trailers. Free zoo porn movies. Free zoo porn.

  16. Subject: Horse ass exclusive zoo sex horse porn only.

    Tracked from Adult zoo free thumbs porn. 2008/11/16 05:43  삭제

    Animal sex zoo free porn bestiality horse dog. Zoo porn. Animal horse dog beast zoo porn sex cum fuck. Free zoo porn movies. Free zoo porn vids. Free zoo porn.

  17. Subject: Cialis.

    Tracked from Cialis. 2008/11/16 16:27  삭제

    Cialis best price buy online. Liquid cialis. Cialis.

  18. Subject: Vicodin detox.

    Tracked from Vicodin statistics. 2008/11/16 21:17  삭제

    Vicodin. Information about vicodin. Vicodin at overseas pharmacies. Vicodin detox.

  19. Subject: Xenical purchase.

    Tracked from Xenical forum. 2008/11/17 05:18  삭제

    Xenical hgh phentermine quit smoking detox. Xenical. Xenical purchase. Xenical getpharma the real pharmacy.

  20. Subject: Side effects of adderall xr.

    Tracked from What is adderall. 2008/11/19 21:06  삭제

    Buy adderall. Order didrex adderall no prescription. Adderall.

  21. Subject: Adderall 7.5 image.

    Tracked from Adderall. 2008/11/19 21:55  삭제

    Adderall without prescription. Adderall side effects.

  22. Subject: Adderall.

    Tracked from Snorting adderall effects. 2008/11/20 15:40  삭제

    Buy wholesale adderall. Adderall xr.

  23. Subject: Dosing of amoxicillin for sinus infection.

    Tracked from Amoxicillin. 2008/11/21 08:15  삭제

    Amoxicillin.

  24. Subject: Doctors adderall.

    Tracked from Adderall xr. 2008/11/22 08:00  삭제

    Adderall abuse. Dosage and tolerance to adderall. Adderall. No prescription adderall.

  25. Subject: Phentermine no prescription.

    Tracked from Buy phentermine. 2008/11/23 07:31  삭제

    Phentermine hydrochloride. Phentermine phentermine. Phentermine. How does phentermine work. Phentermine pharmacy.

  26. Subject: Buy vicodin without script.

    Tracked from Vicodin detox. 2008/11/24 07:34  삭제

    Vicodin. Vicodin back pain. Vicodin detox. Vicodin withdrawal.

  27. Subject: Percocet addiction.

    Tracked from Canadian prescritions and percocet. 2008/11/30 06:47  삭제

    Percocet shipped cod no prior.

  28. Subject: Free ringtone.

    Tracked from Twilight zone ringtone free. 2008/12/02 03:28  삭제

    Free online ringtone sender via wap. Free ringtone. Free ringtone maker. Free ringtone downloads. Free lil boosie ringtone. Free polyphonic ringtone. Free prelude final fantasy ringtone.

  29. Subject: Free ringtone canada.

    Tracked from Rico suave free ringtone. 2008/12/02 12:09  삭제

    Free sprint ringtone. Free ringtone maker. Free ringtone downloads. Free lil boosie ringtone. Free ringtone uploader funformobile. Free danzig ringtone. Free ringtone music downloads. Free ringtone 3 c.

  30. Subject: Drug interactions amantadine percocet.

    Tracked from Generic percocet. 2008/12/06 16:18  삭제

    Compare brand name and generic percocet. Buy percocet online. Percocet. How to extract oxycodone from percocet. How long is percocet in your system.

  31. Subject: Golden casino online.

    Tracked from Golden casino online. 2008/12/07 13:52  삭제

    Golden casino online.

  32. Subject: Buy hydrocodone online discount cheap pharmacy.

    Tracked from Cheap hydrocodone online. 2008/12/07 22:31  삭제

    Drugs online cheap hydrocodone buy. Cheap hydrocodone. Cheap hydrocodone online.

  33. Subject: Brand ultram order ultram tramadol pain medicine.

    Tracked from Phendimetrazine order phentermine adipex tramadol. 2008/12/08 12:25  삭제

    Brand ultram order ultram tramadol pain medicine. Order tramadol.

  34. Subject: Phendimetrazine order phentermine adipex tramadol.

    Tracked from Phendimetrazine order phentermine adipex tramadol. 2008/12/08 21:38  삭제

    Order tramadol. Brand ultram order ultram tramadol pain medicine.

  35. Subject: I quit percocet.

    Tracked from Percocet. 2008/12/09 07:38  삭제

    Percocet dosing. Effects of long term percocet use. Percocet. How do you snort percocet. Percocet picture. How do i get off percocet. Percocet shipped cod no prior.

  36. Subject: Buy order phentermine diet pill.

    Tracked from Order phentermine diet pills fedex delivery. 2008/12/09 16:48  삭제

    Order phentermine.

  37. Subject: California casinos.

    Tracked from Online casinos www.free-onlinecasinos.org. 2008/12/10 01:19  삭제

    No deposit casinos. Online casinos. Casinos www.freeonline-casinos.net. Missouri casinos. Las vegas casinos. Free casinos online www.free-onlinecasinos.org. Casinos no deposit. Indian casinos. Louisiana casinos.

  38. Subject: Phentermine 37 5mg.

    Tracked from Buy phentermine online no prescription 37 5. 2008/12/10 11:17  삭제

    Phentermine 37 5mg. Phentermine 37.5 mg online prescription. Phentermine 90 37. for 80. Phentermine 37.5 mg without prescription.

  39. Subject: Miami south florida casinos aol city guide.

    Tracked from Bigcasinolist com a world guide to casinos. 2008/12/10 19:49  삭제

    Aicpa industry audit guide on casinos. Online casino guide and online casinos news. Bigcasinolist com a world guide to casinos.

  40. Subject: Ephedra.

    Tracked from Ephedra. 2008/12/11 04:32  삭제

    Ephedra.

  41. Subject: Buy percocet online.

    Tracked from Buy percocet online. 2008/12/11 06:45  삭제

    Buy percocet. Buy percocet online. Buy percocet online without office visit. Buy tylox percocet. Buy percocet and greece.

  42. Subject: Percocet.

    Tracked from Percocet without a prescription cheap. 2008/12/11 13:17  삭제

    Percocet signs of abuse. Percocet. Percocet dosing.

  43. Subject: Adderall.

    Tracked from Snorting adderall. 2008/12/12 07:01  삭제

    Adderall.

  44. Subject: Vicodin withdrawal symtoms.

    Tracked from Vicodin no rx. 2008/12/12 07:13  삭제

    How to get vicodin without a perscription. Vicodin detox. Re your vicodin refill is ready. Is it safe to snort vicodin.

  45. Subject: Adipexdrug addiction order phentermine online.

    Tracked from Order phentermine phentermine online. 2008/12/12 11:33  삭제

    Order phentermine gt buy phentermine online. Phentermine money order pharmacy online. Order phentermine uk. Order phentermine. Order phentermine phentermine online.

  46. Subject: Nexium.

    Tracked from Nexium. 2008/12/12 20:20  삭제

    Drug interaction between nexium and lorazepam. Weight gain and nexium. Generic nexium for sale. Nexium. Nexium damage. Nexium half-life. Nexium generic.

  47. Subject: Buy phentermine.

    Tracked from Phentermine for sale best buy. 2008/12/13 07:08  삭제

    Buy phentermine. Mg buy phentermine. Buy phentermine mexico. Buy cheap phentermine online. Buy phentermine on line. Where to buy phentermine without prescription.

  48. Subject: How to extract acetaminophen from percocet.

    Tracked from No prescription percocet. 2008/12/13 09:06  삭제

    Percocet online. Long term use of percocet. Canadian prescriptions and percocet. Percocet. Percocet vs vicodon. Percocet side effects.

  49. Subject: Difference between prilosec and nexium.

    Tracked from Nexium. 2008/12/13 17:44  삭제

    Nexium famotidine. Drug interaction between nexium and lorazepam. Nexium side effect. Nexium. The chemical formula of nexium. Generic for nexium. Information about nexium.

  50. Subject: Percocet 7.5.

    Tracked from Percocet verses lortabs. 2008/12/14 07:21  삭제

    Percocet withdrawal symptoms. Percocet. How to extract acetaminophen from percocet. How do i get off percocet. Percocet side effects. How long does percocet stay in your system.

  51. Subject: Best casino.

    Tracked from Best casino. 2008/12/14 09:25  삭제

    Best casino.

  52. Subject: Internet casino gambling online.

    Tracked from Online casino no deposit bonus. 2008/12/14 18:51  삭제

    Online slot machine www.casino-slot-machine.net. Online casino.

  53. Subject: Discount phentermine.

    Tracked from Discount phentermine. 2008/12/15 07:12  삭제

    Phentermine 37 5mg. Phentermine diet pills. Phentermine.

  54. Subject: Prozac.

    Tracked from Prozac mood disorder. 2008/12/15 09:28  삭제

    Side effects of prozac. Withdrawal symptoms from prozac prozac withdrawal. Prozac.

  55. Subject: Cheap payday loans.

    Tracked from Excellent resources blog archive payday loans. 2008/12/15 19:04  삭제

    Payday loans. Not paying payday loans. Same day payday loans. No fax payday loans. Payday loans for bad credit.

  56. Subject: No prescription vicodin.

    Tracked from Buy vicodin. 2008/12/16 09:57  삭제

    Lorcet vicodin online. Vicodin. Dangers of vicodin. No prescription vicodin. How to get vicodin without a perscription. Vicodin online. Vicodin no rx.

  57. Subject: Phentermine cheap.

    Tracked from Get cheap phentermine no prescription req d. 2008/12/16 13:06  삭제

    Cheap phentermine. Cheap phentermine no prescription. Buy cheap phentermine. Cheap phentermine diet pill.

  58. Subject: Casino.

    Tracked from Casino royal. 2008/12/16 21:51  삭제

    Casino. Emerald queen casino. James bond casino royal. Online casino. Casino royale trailer.

  59. Subject: Tramadol online.

    Tracked from Tramadol. 2008/12/17 07:27  삭제

    Tramadol 180. Comparative potencies of opioids tramadol. Tramadol.

  60. Subject: Is oxycodone or hydrocodone stronger.

    Tracked from Hydrocodone. 2008/12/18 09:55  삭제

    Hydrocodone. Buy hydrocodone online consultation. Www.bulevart.net hydrocodone-withdraw-symtoms.html.

  61. Subject: Percocet.

    Tracked from Percocet. 2008/12/19 08:25  삭제

    Percocet.

  62. Subject: Adderall.

    Tracked from Adderall without a prescription. 2008/12/20 08:04  삭제

    Adderall idiopathic edema. Adderall no prescription. Adderall. Lower back pain and adderall.

  63. Subject: Potent lortab percocet darvon.

    Tracked from Generic percocet. 2008/12/22 00:05  삭제

    Percocet. How long is percocet in your system.

  64. Subject: Phentermine.

    Tracked from Phentermine free shipping. 2008/12/22 09:33  삭제

    Phentermine. Phentermine ingredient.

  65. Subject: Lowest online phentermine price.

    Tracked from Phentermine capsule. 2008/12/23 19:52  삭제

    Lowest online phentermine price. How does phentermine work. Online phentermine.

  66. Subject: Phentermine mg.

    Tracked from Phentermine. 2008/12/26 01:46  삭제

    Phentermine. Cheap phentermine free shipping. Order phentermine phentermine online.

  67. Subject: Phentermine for sale best buy.

    Tracked from Phentermine buy phentermine. 2008/12/26 11:38  삭제

    Where to buy phentermine. Buy phentermine. Buy phentermine cod. Buy phentermine online with paypal. Buy cheap phentermine onli ne. Phentermine buy. Buy cheap phentermine on line now save. Phentermine buy cheap online.

  68. Subject: Phentermine overnight.

    Tracked from Generic phentermine. 2008/12/27 21:32  삭제

    Phentermine diet pills. Phentermine cod.

  69. Subject: Tramadol.

    Tracked from Tramadol. 2008/12/28 08:59  삭제

    Tramadol saturday delivery. Tramadol. Cheapest tramadol available online.

  70. Subject: Percocet extract how to shoot.

    Tracked from Side effects of percocet. 2008/12/29 06:52  삭제

    Effects of long term percocet use. Symtoms of withdrawl from percocet. Percocet addiction recovery. Percocet side effects. Benefits of percocet.

  71. Subject: Viagra.

    Tracked from Get viagra. 2008/12/29 07:56  삭제

    Viagra. Re viagra cello.

  72. Subject: Tramadol.

    Tracked from Buy tramadol. 2008/12/29 17:08  삭제

    Tramadol abuse pharmacy discounter. Tramadol. Tramadol medication.

  73. Subject: Tramadol.

    Tracked from Tramadol. 2008/12/30 07:59  삭제

    Tramadol.

  74. Subject: Detox signs and symptoms oxycontin.

    Tracked from Oxycontin. 2008/12/30 17:16  삭제

    Oxycontin withdrawl. Oxycontin. Atlanta oxycontin attorneys. Buy oxycontin without prior prescription. Oxycontin withdrawal home remedies.

  75. Subject: Soma.

    Tracked from Buy soma online. 2008/12/31 03:27  삭제

    Soma overnight. Soma side effects. Soma to florida. Soma. Soma beds.

  76. Subject: Vicodin.

    Tracked from Vicodin. 2008/12/31 07:01  삭제

    Vicodin.

  77. Subject: Fioricet medications.

    Tracked from Fioricet. 2008/12/31 13:29  삭제

    Fioricet order. Fioricet tablet. Fioricet.

  78. Subject: Buy valium.

    Tracked from Generic valium no prescription. 2009/01/01 06:54  삭제

    Valium 5mg how long in system. Zithromax with valium interaction. Side effects of valium. Valium.

  79. Subject: Adderall.

    Tracked from Average adult dose of adderall xr. 2009/01/01 07:24  삭제

    Adderall.

  80. Subject: Valium liquid form.

    Tracked from Valium causing depression. 2009/01/01 15:36  삭제

    Valium side effects. Buy valium c.o.d.. Valium.

  81. Subject: Pecocet.

    Tracked from Pecocet. 2009/01/02 17:47  삭제

    Pecocet online. Pecocet.

  82. Subject: Paxil withdrawals.

    Tracked from Paxil and insomnia. 2009/01/04 01:38  삭제

    Side effects from paxil. Paxil 30 milligram 60 prices. Paxil.

  83. Subject: Tramadol.

    Tracked from Tramadol. 2009/01/04 07:19  삭제

    Tramadol saturday delivery. Tramadol. Tramadol 100mg.

댓글을 달아 주세요

댓글 RSS 주소 : http://jmath.net/rss/comment/19
댓글 ATOM 주소 : http://jmath.net/atom/comment/19

◀ 이전페이지 1 ... 3 4 5 6 7 8 9 10 11 ... 24 다음페이지 ▶