ªì¤p¼Æ¾Ç¾Ç²ß§xÃø¡G¤@­Ó±Ð¾Ç»²¾É³]­p­Ó®×

ªì¤p¼Æ¾Ç¾Ç²ß§xÃø¡G¤@­Ó±Ð¾Ç»²¾É³]­p­Ó®×

°¨²Q¯ô ­»´ä®ãÆW«H·R¤p¾Ç

¶À®a»ï ­»´ä¤¤¤å¤j¾Ç±Ð¨|¾Ç°|


	
ºK­n

ªì¤p¼Æ¾Çªº¾Ç²ß¡A¹ï¤@¨Ç¨àµ£¨Ó»¡¤wºc¦¨¤@©wªº§xÃø¡C¥Ñ©ó¤@­Ó¦b±Ð
¾Ç¹ê²ß´Á¶¡½í¨ìªº­Ó®×¡AIJµo°_§Ú­Ì¶i¦æ³o­Ó±Ð¾Ç»²§U³]­pªº±´°Q¡C
­º¥ý§Ú­Ì±N¹ï¤@¯ë¾Ç²ß§xÃøªº²[¸q§@¤@°ò¥»ÄÄÄÀ¡AµM«á¦A°w¹ïªì¤p¼Æ
¾Ç¾Ç²ß¡A°Q½×¤@¯ë­pºâ¯à¤O¥¢±`ªº±¡ªp¡A¨Ã«ü¥X¼Æ¾Ç¾Ç²ß¥»¨­ªº¤@¨Ç
¯SÂI¡A¥t¥~¤]¹ï¨ãÅé±Ð¨ã¹B¥Î©Ò¯A¤Îªº°ÝÃD¶i¦æ¦A«ä¡C¤å³¹ªº¤U¥b³¡
¤À«h¥H¥H¤Wªº²z½×¤Î¬ã¨sµ²ªG¬°°ò¦¡A¤ÀªR¤F¤@­Ó¾Ç²ß²³æ¥[¼Æ¦³§x
Ãøªº¤@¦~¯Å¾Ç¥Íªº¨ãÅ鱡ªp¡A¨Ã±Ä¥Î¦æ¬°¥D¸qªº¼Ò¦¡¡A¥H½Ò·~¤ÀªRªº
¤èªk¬°«ü¤Þ¡A³]­p¤F¤@­Ó»²§U±Ð¾Ç³æ¤¸¡AÂǦ¹¨ó§U­Ó®×¤¤ªº¾Ç¥Í­«·s
´x´¤¦³Ãö¼Æ¾Ç·§©À¤Î¹Bºâ¡C³o­Ó³]­pÁö¥¼¦³¾÷·|³q¹L¹ê½î¦Ó±o¨ìµû
¦ô¡A¦ý¥ç¤£¥¢¬°¤@­Ó»¡©ú¦p¦óÀ³¥Î²z½×ª¾ÃÑ©ó¨ó§U¾Ç²ß§xÃø¾Ç¥Íªº¨Ò
¤l¡C

¦^¡m¼Æ¾Ç±Ð¨|¡n²Ä ¥|´Á¥Ø¿ý
ªì¤p¼Æ¾Ç¾Ç²ß§xÃø¡G¤@­Ó±Ð¾Ç»²¾É³]­p­Ó®× °¨²Q¯ô ­»´ä®ãÆW«H·R¤p¾Ç ¶À®a»ï ­»´ä¤¤¤å¤j¾Ç½Òµ{»P±Ð¾Ç¾Ç¨t ¡u§Ú»{ÃѤ@Áû¦æ¬P¡A¤W­±¦í¤F¤@¦ì¬õÁyªº¥ý ¥Í¡C¥L±q¨S»D¹L¤@¦·ªá¡F¥L±q¨Sª`µø¹L¤@Áû ¬P¡F¥L±q¨Ó¨S·R¹L¤@­Ó¤H¡C¥L°£¤F§@¥[ªk¤§ ¥~¬Æ»ò¤]¨S°µ¹L¡C¦Ó¾ã¤Ñ¹³§A¤@¼Ë¤@¹M¤S¤@ ¹Mªº»¡¡G¡y§Ú¬OÄYµÂªº¤H¡A§Ú¬OÄYµÂªº¤H¡I¡z ¦Ó¥L«Ü¤Þ¥H¦Û»¨¡C¦ý³o¤£¬O¤H¡A³o¬OĨۣ¡C¡v Antoine de Saint-Exupéry¡m¤p¤ý¤l¡n ¤Þ¨¥ ¡u¾Ç²ß¡v¬O«ü¸g¥Ñ½m²ß©Î¦]¸gÅç¦Ó¨Ï¤H¦b¦æ¬°¤W²£¥Í¸û«ù¤[©Ê§ï Åܪº¤@ºØ¹Lµ{¡A¤]¬O¤HÃþ¥Í¬¡¤¤³Ì´¶¹Mªº¬¡°Ê¤§¤@ (³\¤Ñ«Â¡A1986¡F ¤ý§J¥ý¡A1987)¡C¬G¦¹¡A¥¿­±¦Ó¦³®Äªº¾Ç²ß¹ï¤@­Ó¤Hªº¦Û§Ú¦¨ªø¤Î§ï ¶i³£¬O·¥¬°­«­nªº¡C¦Ó¾Ç²ß¥ç¬O§Ú­Ì¨C­Ó¤H³£¦³ªº¤Ñ½á¯à¤O¡A¥u¬Oµ{ «×¤W¦³®t§O¦Ó¤w¡C¦¹¥~¡A¥¦¤]¬O§Ú­Ì°ò¥»ªº»Ý­n©MÅv§Q¡C¬G­Y¦³¤H¦] ºØºØ¤£¦Pªº­ì¦]¡A¨Ï¥L­Ì¦b¾Ç²ß¤W¥X²{§xÃø¡A¦]¦Óªýê¤F¥L­Ì¥¿±`ªº ¾Ç²ß¡A¥O¥L­Ì¤£¯à±q¤¤¦³©Ò±oµÛ¡A©Î»â²¤ºç¤¤ªº¼Ö½ì¡A¹ï¥L­Ì¥H¦Ü¬O ¾ã­ÓªÀ¸s¨Ó»¡¡A³£µ´¹ï¬O¤@ºØ·l¥¢©M¤£¤½¡CµM¦Ó¡A¨C­Ó¤Hªº¾Ç²ß¯à¤O ©Î¦b¤£¦P¤è­±ªºªí²{¦³©Ò®t²§¡A«o¤S¬OÃø¥HÁ×§K©M¤£ª§ªº¨Æ¹ê¡A©Ò¥H ¦p¦ó§ä¥X­Ó§O¾Ç²ßªÌªº¾Ç²ß§xÃø¡A¨Ã¹ï¤§¤©¥H¾A·íªº­«µø¤Î»²§U¡A¨Ï ³Ì²×¯à¥O¥L­Ìµo´§¨ä¼ç½è¡A¹ê¦b¬O­È±o±Ð¨|¤u§@ªÌ¥[¥HÃö¤ß©M²`¤J°Q ½×ªº½ÒÃD¡C¦Ó§Ú­Ì­Y¯à¦b¤@­Ó¤Hªº¨àµ£®É´Á¡A³o­Ó¾Ç²ß­è°_¨Bªº®É ­Ô¡A¤w¯à°w¹ï¨ä¾Ç²ßªº§xÃø¡Aµ¹¤©¾A·íªºÀ°§U¡A¥²¯à¦¬¨ä¨Æ¥b¥\­¿¤§ ®Ä¡A¹ï¨ä¤é«áªº¤ß´¼µo®i¥ç±N±a¨Ó³Ì¤jªº§U¯q¡C¥»¤å¥¿¬O­n°w¹ïªì¤p ¼Æ¾Ç¾Ç²ß§xÃøªº¤@¨Ç°ÝÃD¶i¦æªì±´¡A§Æ±æÂǦ¹¯à¥Oµ§ªÌ¥»¨­¤Î¨ä¥L¼Æ ¾Ç±Ð®v¹ï¦³Ãöªº½ÒÃD±a¨Ó©Î¦h©Î¤Öªº±Òµo¡C §Ú­Ì­º¥ý·|¹ï¤@¯ë¾Ç²ß§xÃøªº²[¸q§@¤@°ò¥»ªºÄÄÄÀ¡AµM«á¦A±´°Q ªì¤p¼Æ¾Ç¾Ç²ß©Ò¯A¤Îªº¤@¨Ç°ÝÃD¡C¦Ó¬°¤F¯à§ó¨ãÅé¦a±´°Q³o¨Ç°ÝÃD¡A §Ú­Ì¿ï¥Î¤F¤@­Ó¨àµ£¸û®e©ö¦b·í¤¤¥X²{¾Ç²ß§xÃøªº½dÃ¥ ¢w¢w ²³æ ¥[¼Æ­pºâ ¢w¢w §@¸û²`¤Jªº°Q½×¡C¿ï¾Ü¦¹½dÃ¥ªº­ì¦]¡A¬O¦]¬°µ§ªÌ¤§ ¤@´¿¦b¤@¦¸±Ð¾Ç¹ê²ß¤¤¡A¹J¨ì¤@­Ó¦b¼Æ¼Æ¡B¥[´î¼Æ¹Bºâªº°ÝÃD¤W¡A§¡ ¦³¾Ç²ß§xÃø±¡ªp¥X²{ªº¾Ç¥Í¡CÁö¦]¬O¦¸¹ê²ßªº®É¶¡¤Óµu¡A¥u¯àªì¨B´x ´¤¨ì¤@¨Ç¦³Ãöªº¸ê®Æ¡A¦Ó¥¼¯à¯u¥¿¹ï¥L§@¥X¸Ô²Ó¤Î¾A·íªº»²¾É¡A¦ý³o «oIJµo°_§Ú­Ì¹ï¦³Ãöªº¾Ç²ß§xÃø°ÝÃD¡A²£¥Í¶i¤@¨Bªº¬ã¨s°Ê¾÷©M¿³ ½ì¡A¥H¦¹§@¬°¹ï¦³Ãö°ÝÃD§@§ó¨ãÅé©M²`¤Jªº¬ã¨sµJÂI¡A¨Ã¥B°w¹ï­Ó®× ±´°Q¥i¦æªº±Ð¾Ç»²¾É¤èªk³]­p¡AÂǦ¹±a¥X¤@­Ó²z½×À³¥Îªº¹ê¨Ò¡C ¾Ç²ß§xÃø ¤@ª½¥H¨Ó¡A¤H­Ì¹ï¡u¾Ç²ß§xÃø¡v(learning difficulties / disabilities¡F ¤¤¤å¥Îµü¤W±`»P¡u¾Ç²ß»Ùê¡v¤@µü¤¬¥Î) §¡¦³¤£¦Pªº²z¸Ñ¡A¦U¬£ªº¾Ç ªÌ¡A¦p¯«¸g¥Í²z¾Ç®a¡B¤ß²z¾Ç®a©Î»y¨¥¤ß²z¾Ç®aµ¥¡A³£¹ï¥¦½á¤©¤£¦P ªº©w¸q¡C¦ý¤@¯ë¨Ó»¡¡A¾Ç²ß§xÃø¥i³QÂk¯Ç¬°¨â¤jÃþ¡G¤@¬°°¾­«¯f²z¾Ç ªº»¡©ú¡A«ü¥X¦³Ãöªº¾Ç²ß»Ùê¸ò¤¤¼Ï¯«¸g¨t²Î¦³Ãö¡A¬O¾÷¯à¨ü·l«áªº ²§ºAªí²{¡F¥t¤@Ãþ©w¸q«h°¾­«¦æ¬°ªº´y­z¡A»P¥Í²z¦]¯À¨S¤Ó¤jªºª½±µ Ãö«Y (³\¤Ñ«Â¡A1986¡Ap. 17¡F¤ý§J¥ý¡A1987¡Ap. 353)¡C¦Ó¥»¤å«h ¥u°w¹ï«áªÌ ¢w¢w °¾­«¾Ç²ß¦æ¬°ªº´y­z§@±´°Q¡A¥H«K¯à¹ï¦b¾Ç²ßªº¦æ ¬°©Î¹Lµ{¤W©Ò¥X²{ªº»Ùê¤Î¦³Ãöªºªí²{¯à¦h§@ÁA¸Ñ¡A±q¦Ó³]©w¦³Ãöªº ±Ð¾Ç¦w±Æ¥H§@»²§U¡C ÁöµM¡A¾ÇªÌ­Ì¹ï¦]¦æ¬°¦Ó²£¥Íªº¾Ç²ß§xÃø¤]¦³«Ü¦h¤£¦Pªº²z¸Ñ¡A µM¦Ó¡A·í¤¤«o¦³µÛ¤@­Ó¦@¦PÂI¡A´N¬O¥¦À³Âk¤J¯S®í¨àµ£±Ð¾Ç¦Ò¼{ªº¤@ Àô¡A¦ý«o¦³§O©ó´¼¯à¤£¨¬ªÌ¡B±¡ºü§xÂZªÌ¡BµøÄ±©Mťıµ¥¯à¤O¤W¦³¯Ê ³´ªºÃþ§O¡C¥L­Ìªº´¼¤O¸Ó¦³¤¤µ¥©Î¥H¤Wªºµ{«×¡A¦ý«o¦]¾Ç²ßªº¹Lµ{¥X ²{°ÝÃD¡A¦Ó²£¥Í¾Ç²ßªº»Ùê¡A¨Ï¾Ç·~¦¨´N°¾§C¡C²¨¥¤§¡A´N¬O´¼¤O»P ¦¨´N¶¡ªºªí²{¥X²{®t¶Z (³\¤Ñ«Â¡A1986¡App. 30-31¡F¤ò³s¶ó¡A1991¡A pp. 3-4)¡C ¦Ó¦b¦³¾Ç²ß§xÃøªº¨àµ£ªº¯S¼x¤è­±¡ABateman¤ÎGearheart³o¨â ¦ì¾ÇªÌ¹ï¦¹§¡¦³·¥ºëÅP¦Ó²M´·ªº¬É»¡¡A¯÷¥H¦¹¬°¥Nªí¨Ã¤À­z¦p¤U¡C Bateman ¥D­n¥H¤U¦C¯S¼x§@¬°©w¸q¡G ¡u¾Ç²ß»Ùê¨àµ£Åã¥ÜµÛ­ÓÅ骺¹w¦ô¤§´¼¼z¼ç¯à»P¹ê»Ú¤§ªí²{¤ô·Ç ¤GªÌ¶¡¦s¦³±Ð¨|·N¸qªº®t¶Z¡A¦¹®t¶Z²{¶H¸ò¾Ç²ß¹Lµ{¤§°ò¥»²§ºA ¦³Ãö¡A......³oºØ²§±`ª¬ºA¨Ã«DÁõÄÝ©ó¤@¯ëªº´¼¯à¤£¨¬¡B±Ð¨|©Î¤å¤Æ ­é¹Ü¡A¤]¤£ÁõÄÝ©óÄY­«ªº±¡ºü§xÂZ¡A©Î·P©x§@¥Î³à¥¢¡C¡v(Bateman, 1965¡FÂà¤Þ¦Û³\¤Ñ«Â¡A1986¡Ap. 31) ¦Ü©óGearheart§â¦³Ãöªº¯S¼x¤À¬°¨â¤jÃþ¡G(1) ¦@¦P¯S¼x¡G¾Ç·~»Ù êªÌªº´¼¤O¤Î·P©x±Ó¾Uµ{«× (sensory acuity) ¥²¶·¬O¥¿±`ªº¡F¨ä¾Ç·~ ¦¨´N¥²¶·¬O§C©ó¦Û¤vªº´¼°Ó¡B¦~ÄÖ©M±Ð¨|¾÷·|©Ò´£¨Ñªº¤ô·Ç¡A§Y©Ò¿× ¡uÅãµÛªº±Ð¨|®t¶Z¡v(significant educational discrepancy)¡C(2) ¥i¯à²£¥Í ªº¯S¼x¡G¥i¯à¥X²{¬¡°Ê¹L¦h©Î¹L¤Ö¡B¯Ê¥F°Ê¾÷¡Bª`·N¤O¹L«×©Î¯Ê¥F¡B ª¾Ä±©Î°O¾Ð¤O²§±`¡B¨ó½Õ§@¥Î¯Ê¥F¡B©T°õµ¥ (³\¤Ñ«Â¡A1986¡App. 31-32)¡C °£¤F¤W¦C¤@¨Ç¥Í²z¡B¤ß²z¦]¯À¥i¯à¦b¾Ç²ß¹Lµ{¤¤¾É­P¾Ç²ß¦]Ãø¡A ¾Ç²ß¦¨ªG±j®t¤H·N¥~¡A§Ú­ÌÁÙÀ³ª`·N±Ð¾Ç¤è­±ªº¦]¯À¡A½Ñ¦p±Ð§÷¤Ó ²`¡B±Ðªk¤£·íµ¥¡A­P¨Ï¥¼¯à°t¦X¨àµ£ªº¤ß´¼µo®i¡A³£¬Oºc¦¨¾Ç²ßªÌ¦³ ¾Ç²ß§xÃøªº¥i¯à¥~¦b¦]¯À (¤ò³s¶ó¡A1991¡Ap. 3)¡C´N±Ð¾Ç¤Î±Ð§÷³] ­p¦Ó¨¥¡A³oÂI¬O¯S§O­È±o¥[¥H¯d·Nªº¡C ­pºâ¯à¤O¥¢±` ¥H¤U§Ú­Ì¶°¤¤°Q½×¦b¼Æ¾Ç¾Ç²ß½d³ò¤º©Ò¥X²{ªº¾Ç²ß§xÃø¡C©Ò¿×­p ºâ¯à¤O¥¢±`¡A¥iºÙ¬°¹Bºâ¯à¤O»Ùê©Î¥¢ºâ¯g (dyscalculia)¡A¬ã¨sÅã¥Ü ³o¤è­±ªº¾Ç²ß§xÃø©¹©¹»P»y¨¥¯à¤O¥¢±`¦P®É¥X²{ (Chinn & Ashcroft, 1993; Geary, 1994)¡C¤£¹L³o¶W¶V¤F§Ú­Ì¦b¦¹ªº±´°Q½d³ò¡A¼È¥B±q²¤¡C §@¬°¤@­Ó¾Ç²ßªº¾Ç¬ì¡A¼Æ¾Ç¦³¤T¤è­±ªº¯S¼x¤×¨ä®e©öºc¦¨¾Ç²ß¤W ªº°ÝÃD©Î§xÃø¡C²Ä¤@¡A¼Æ¾Çª¾ÃѦ³«Ü±jªº¶¶§Ç©Ê¡A¾Ç²ß¤º®e¤j³£»Ý­n «Ø°ò©ó¥ý«e¤£¦P³¡¤Àªº¤w¦³ª¾ÃÑ¡F²Ä¤G¡A°£¤F¶¶§ÇªºÃö«Y¥~¡A¤£¦P³¡ ¤Àªº·§©À©Î¹Bºâ§Þ¥©©¼¦¹¬Û³s¡Aµ²ºc²Õ´©Ê«Ü°ª¡F²Ä¤T¡A¬O¼Æ¾Ç¦Û¨­ ¦^·¹ (reflexive) ªºµ²ºc©Ê¡A§Y¥Ñ¤w¦³ªº³¡¥÷²Õ¦¨ªº¥þÅ驹©¹·|±a¨Ó¹ï ­ì¨Ó³¡¤Àªº­«·s²z¸Ñ¡A³oÂI¦b¾Ç²ß®Éªº«ä¦Ò´£¤É·|¦³³Ì©úÅ㪺¤Ï¬M¡C ¼Æ¨tªº³v¨B»{ÃÑ´N¬O¤@­Ó²³æªº¨Ò¤l¡A¥Ñ¦ÛµM¼Æ¶}©l¡A¨CÂX¥R¤@¦¸ªº ¼Æ¨t³£·|±N¥ý«eªº¼Æ¨t¥H¬YºØ·sªº¤è¦¡©M·N¸q§l¯Ç¶i¥h¡C¦]¦¹¡A Bruner (1960) ´£¥XªºÁ³±Û¦¡½Òµ{ (spiral curriculum) ±Ðªk¡A¨ä¹ê»P¼Æ ¾Çª¾Ãѵ²ºc¬Û·í§k¦X¡C¾Ç¥Í¥i¥H³z¹L±q¤£Â_´£¤Éªº¾Ç²ß¼h¦¸¡A²`¤Æ¹ï ¦U­Ó¼Æ¾Ç·§©Àªº»{ÃÑ¡C ¾Ç²ß§xÃøªº§Î¦¨¡A°£¤F¦]¬°¼Æ¾Çª¾ÃѪº°ò¥»µ²ºc¯S¼x¥~¡A¼Æ¾Çªº ¨ãÅ餺®e¤]¥]§tµÛ¤@¨Ç»P¾Ç²ß§xÃø¦³Ãöªº¦]¯À¡C¬°¤F­nÀÀ©w¾A·íªº±Ð ¾Ç»²§U³]­p¡A¥H¨ó§U¦³¾Ç²ß»Ùꪺ¾Ç¥Í¡A¥²¶·¥ý²z²M¦b¼Æ¾Çªº½dÃ¥ ¤¤¡A¦³¦ó¾Ç²ß§xÃø¤Î¨ä§Î¦¨ªº­ì¦]¡A¤~¯à¹ï¯g¤UÃĦa§@¥X»²§U¡C ²³©Ò©Pª¾¡A¦b¼Æ¾Çªº¾Ç²ß¤¤¡A©¹©¹²o¯A¨ì­n¨Ï¥Î¼Æ¾Ç¤¤ªº¶H¼x²Å ¸¹¡A©Î¯A¤Î¼Æ¶q»PªÅ¶¡Ãö«Yªº´x´¤¤Î¹B¥Î¡A¬G¼Æ¾Ç¾Ç²ßªºµo®i¥i¤À¬° ¤T­Ó¼h­±¡G¼Æ¾Ç¤§¤º¦b»y¨¥ (inner language)¡B¦¬°T¯à¤O (receptive ability)¡Bµo°T¯à¤O (expressive ability) (³\¤Ñ«Â¡A1986¡Ap. 278)¡C¦Ó¦b ¥H¤W¦U­Ó¼h­±¤¤¡A¥i¯à¥X²{ªº¨ãÅé²§±`¯S¼x¦p¤U[1]¡G (1) ª½±µ¯A¤Î¼Æ¦r·§©À»P²Å¸¹¤§¹B¥Î¤Wªº¯à¤O¥¢±`¡F (2) ª¾Ä± ¢w ªÅ¶¡²Õ´¯à¤O (visual-spatial organisation) ªº¯Ê³´¡F (3) ²£¥Í¨­Åé§Î¶Hªº§xÂZ¡A¦p¤£¯àÃѧO¦Û¤vªº¤â«ü¬°¦óª«¡F (4) ±`¦³¤è¦V·Pªº²§±`¡A¤À¤£²M«e«á¥ª¥k¡A¹ï©ó¦a¹Ï¤@Ãþªí¥Ü¤è¦¡¾\ Ū¤W¦³§xÃø¡C ¥H¤U¦CÁ|ªº¬O¤@¨Ç¸û¨ãÅ骺¦æ¬°ªí²{[2]¡G (1) Ãø«Ø¥ß¼Æ­ÈªºÆ[©À¡F (2) ÃøÁA¸Ñ¼Æ¼Æªº¯u¸q¡A¦p¥u­­¾÷±ñ¦¡ªº°á¥X¼Æ¦r¡A¦Ó¤£ª¾¨ä¯u¸q¡F (3) ÃøÁp¦Xťıªº¼Æ¦r·§©À»PµøÄ±ªº¼Æ¦r²Å¸¹¡A¦p¯àÅ¥²M·¡¼Æ¦rªº¦W ºÙ©Îµo­µ¡A¦ýÃø¥H»{¥X¨äªü©Ô§B¼Æ¦r¡F (4) Ãø§â°ò¼Æ (cardinal number) »P§Ç¼Æ (ordinal number) ªº·N¸q¤À ¿ë¡F (5) Ãø¥Î±½µøªº¤è¦¡¼Æ¥Xª«¥óªº¼Æ¶q¡A¦Ó­n³v­Ó¼Æ¤~¥i±o¥X¨ä¼Æ¡F (6) Ãø»{²M¼Æ¶qªº¦u«í­ì²z (conservation of quantity) ©Î¥i°f©Ê (reversibility)¡A¦p¤£¯à²z¸Ñ¨â­Ó¤­¤¸´N¬O¤@­Ó¤Q¤¸¡F (7) Ãø»{ÃÑ¥[´î­¼°£³o¥|­Ó²Å¸¹¤Î¨ä¹Bºâªº·N¸q¡F (8) Ãø²z¸Ñ©Î°O¾Ð¹Bºâ®Éªº¤@¨Çªk«h¡A¦p¥|«h¹Bºâ®É¶·¥ý­¼°£¡A«á¥[ ´î¡F (9) Ãø²z¸Ñ´ú¶qªø«×¡B®e¶qµ¥­ì²z¤Î¤èªk¡F (10) ÃøÃѧO¦a¹Ï©Î¨ä¥L¹Ï§Îªº«ü¥Ü²Å¸¹¡C ¨ä¥L¥i¯à¥X²{¾Ç²ß§xÃøªºªí²{¡AÁÙ¥]¬A¦bª½¦¡¹Bºâ®É¿ë§O¤W¤U¥ª ¥kµ¥¤è¦Vªº¹Lµ{¦³©Ò¯Ê¥¢¡B¹ï§Ç¦C©Î¦¸§Ç¦³¯S§O§xÃø (¨Ò¦p±N64¼g¦¨ 46¡B¹Bºâµ{§Ç¤£¯à¨Ì¦¸§Ç¼ô°O)¡Bµu´Á°O¾Ð¤Îªø´Á°O¾Ðªº¯à¤O§¡¦³¯Ê ³´¡A¥H­P¼W¥[¤F³B²z¹Bºâ®ÉªºÃø«×¡B¼Æ¾Ç¦Wµü¤Î²Å¸¹ªº¯S¦³·N¸q¦³²§ ©ó¤é±`¥Î»y¡B­Ó§O¼Æ¾Ç²Å¸¹¦³¤£¦P·N¸q (¨Ò¦p2+3©M +3¤¤ªº¡u+¡v¦³ ¤£¦Pªº·N¸q)¡B®v¥Í¤§¶¡»{ª¾Ãþ«¬ (cognitive style) ¬O§_¬Û¾AÀ³¡A»P¤Î ¼Æ¾ÇµJ¼{·P (mathematics anxiety) ªº¼vÅTµ¥ (Chinn & Ashcroft, 1993, pp. 5 - 7)¡C ÁA¸Ñ¤F¥H¤W¦³Ãö¼Æ¾Ç¾Ç²ß»Ùꪺ¤@¨Ç¯S¼x«á¡A­±¹ï­Ó§O­Ó®×®É¡A §Ú­Ì«K¶·»{²M¾É­P³o¨Ç±¡ªp¥X²{ªº­ì¦]¡C³o¤j­P¥i±q¨â¤è­±¥h¤ÀªR¡G ¾Ç²ßªÌ¥»¨­ªº¾Ç²ß¹Lµ{©Î¯à¤O¾É­P¾Ç²ß§xÃøªº§Î¦¨¡F¼Æ¾Ç¾Ç²ßªº¤@¨Ç ¯S½è©M¯S¦³ªº¹Lµ{¡C«eªÌ¬O«ü¤@¨Ç¥X¦Û¾Ç²ßªÌ¥»¨­ªº¯à¤O¯Ê³´¡A¦p¼g ©ÎŪ¿ù¼Æ¦r¡A¨Ò¦p§â¡u3¡v¼g¦¨¡u e¡v¡F¤£ÃѤâ«ü¤§¯Ê³´¯g (finger agnosia)¡F¥ª¥k¤è¦V·P¥¢±`¯g (right-left disorientation) µ¥¯à¤O¤W¤§¯Ê³´ (¤ò³s¶ó¡A1991¡F³\¤Ñ«Â¡A1986)¡C¦Ó«áªÌÃö©ó¼Æ¾Ç¾Ç²ßªº¤@¨Ç¯S½è ©M¹Lµ{¤W¡A«e¤å¤w¦³°Q½×¡A¦b¦¹§Ú­Ì¸Õ¬Ý¤@¤UPiaget (1973) ©Ò´£ªº¤@ ¨Ç­nÂI¡G ¡u²¨©¿¤F¬¡°Êªº¨¤¦â¦Ó¥u°±¯d©ó»y¨¥¼h­± [ªº±Ð¾Ç]¡A¤×¨ä¬O¼Æ¾Ç ±Ð¨|¡A±N·|¬O¤@­ÓÄY­«¿ù»~¡C¯S§O¹ï©ó¦~¥®ªº¾Ç¥Í¡A§Q¥Îª«¥ó§@ ¬¡°Ê¹ï©ó´x´¤ºâ³N¤Î´X¦óÃö«Y (¥¿¦p [¥j] ®J¤Î¤Hªº¹êÅ禡¼Æ¾Ç ¥ç¤@¼Ë)¡A¬O¤£¥i©Î¯Êªº¡C¡v (p. 80) ¦b¸ÑÄÀ¼Æ¾Ç¸gÅ窺«Ø¥ß¹Lµ{¤W¡APiaget (1973) ¶i¤@¨B«ü¥X³o¨Ç ¬¡°Ê¸gÅ窺¿n²Ö¡B¤º¤Æ¡A³q¹L»P¼Æ²zÅÞ¿è¸gÅç¨ó½Õ¦Ó²£¥Í¤@ºØ¦³§O©ó ¤@¯ë±qª«Åé©Ê½è©â¶H¤Æªº·§©À§Î¦¨¹Lµ{¡A¤D¬O¤@ºØ¡u¤Ï·Ó¦¡¡vªº©â¶H ¤Æ¹Lµ{ (reflective abstraction)[3]¡A¥Ñ¦¹¤~¥i¥H¨Ï¬¡°Ê¸gÅç¦b¸û°ª¼h¦¸ªº ¤ß´¼¬¡°Ê¤¤±o¨ì­«²Õ¡A¹ïÀ³©ó§Ú­Ì©Ò¿×¼Æ²zÅ޿誺©â¶H§Î¦¡¼h­±¡C§Ú ­Ì¤]¥²¶·ºò°O¡A«Ä¤l¦³¯à¤O°µªº»P¤Î¦b¬¡°Ê¤¤ªº²z¸Ñ¡A»·¤ñ¥L­Ì¯à¥Î »y¨¥ªí¹Fªº¬°¦h¡CPiaget¦b¥t¤@½g¤å³¹´¿³o¼Ë¶}©v©ú¸q¦a´£¿ôÃöª`¨à µ£¾Ç²ß¼Æ¾Çªº¤H¡G ¡u¦p»{¬°«Ä¤l¹ï¼Æ¦rªºÆ[©À©Î¨ä¥L¼Æ¾Çªº·§©Àªº²ß±o¬O¯Âºé³z¹L ±Ð±Â¦Ó±o¨Óªº¡A³o«K¤j¿ù¯S¿ù¡C¬Û¤Ï¦a¡A³o¦b«Ü¤jµ{«×¤W¬O¾a¨à µ£¥»¨­ªº¦Û§Úµo®i¡B¿W¥ß¦Ó¦Ûµoªº¾Ç²ß¦Ó±o¨Óªº¡C§Y¨Ï¦¨¤H¥ø¹Ï ¦b¥L­Ì¤ß´¼©|¥¼¦³¨¬°÷ªº¦¨¼ô«×®É¡A¥HÄé¿éªº§Î¦¡±Ð±Â¼Æ¾Çªºª¾ ÃÑ¡A¨àµ£¾Ç¨ìªº¤]¥u¬O¥Î»y¤Wªº¼Ò¥é¡AµM¦Ó¯u¥¿ªº¾Ç²ß¡B²z¸Ñ«o ¥²¶·¨Ó¦Û¨àµ£¥»¨­ªº´¼¤O¦¨ªø¡C¡v(Piaget, 1953, p. 74)¡C ¦¹¥~¡A¥L©Ò±j½Õªº«Ä¤l¦b¤ß´¼¤W¤£¦Pªºµo®i¶¥¬q¤Î¦¨¼ô«×¡A¦p²z¸Ñ¦u «í(conservation)¡B¥i°f©Ê (reversibility) µ¥µo®i¯S¼x¡A»P¾Ç²ß¦¨®ÄªºÃö «Y¡A¦­¤w¬O¼Æ¾Ç±Ð®v­Ì¦Õ¼ô¯à¸Ôªº²z½×¡C ¤Þ­z¤W­zªº¨£¸Ñ¡A«D¥u¦]Piaget¬O³o¤è­±ªºª¾¦W¾ÇªÌ¡A¦Ó¬O³o¨Ç Æ[ÂI½T¹ê¥i¥H±aµ¹±q¨Æ¼Æ¾Ç±Ð¨|ªº¤u§@ªÌ«Ü¤jªº±Òµo¡A¦]¬°±q¤¤¥O¤H ©ú¥Õ¨ì­Y©¿µø¤F¾Ç²ßªÌ¤ß´¼µo®iªº¦ÛµM¾úµ{©Î­Ó§Oªº®t²§¡A¤S©Î¦¨¤H ¹ï¤§¨S¦³¥R¨¬ªºÁA¸Ñ¡A¥u·|¥X²{¦pÆxÄM¾Ç¸Üªº¾Ç²ß¼Ò¦¡¡A¦Ó§óÄY­« ªº¡A¬O·|²¿Ãª©ÎÂZ¶Ã¾Ç²ßªÌ¥»¨­ªº¾Ç²ß¨B¥ï¤Î¼Ò¦¡¡A¾É­P¾Ç²ß§xÃøªº ²£¥Í¡C ±Ð¨ã¹B¥Î¤§¤@ÂI¦A«ä ­±¹ïªì¤p¶¥¬qªº¾Ç¥Í¡A¥Ñ©ó¥L­Ì¤´³B©óPiaget©Ò¹º¤À¤§¨ãÅé¹B«ä ´Á (concrete operation stage)¡A°ò¥»¤W¯à¥H¨ãÅ骺¸gÅç¤Î³q¹L¨ãÅ鍯ª« ©ÒÀò±oªº¤ß²zªí¶H¡A¶i¦æ¦X¥GÅ޿誺«ä¦Ò¡C¦]¦¹¡A«Ü¦h¤H³£·|ª½Ä±¦a »{¬°³o¤@¶¥¬qªº¼Æ¾Ç¾Ç²ß§¡»Ý§Q¥Î¥i¾Þ§Ë¤§±Ð¨ã (manipulatives) §@ »²§U¡A¥H«K¨àµ£¯à³q¹L¹êª«´£¨Ñªº¨ãÅé¸gÅç¡A«Ø¥ß¦³Ãöªº¼Æ¾Ç·§©À¡C ³oÃþ±Ð¨ã«Ü´¶¹M¡A¨Ò¦p¼Æ²É¡B¤Q¶i¦ì¿n¤ì¡Bºâ¬W©Î¨ä¥L¹CÀ¸¥Îªº§÷®Æ µ¥¡A¬Û«H«Ü¦h¼Æ¾Ç±Ð®v¹ï©ó³o¨Ç±Ð¨ã¤Î¦³Ãöªº¨Ï¥Î¤èªk³£«Ü¼ô±x¡C ¦ý¦b¦¹±ý´£¥Xªº°ÝÃD¡A«o¬O¨àµ£ªº¨ãÅé¸gÅç»P«Ø¥ß¼Æ¾Ç·§©À¤§¶¡ ¨s³º¦³µÛ¬Æ»òÃö«Y©O¡H¤@¨Ç¾ÇªÌ´£¿ô§Ú­Ì (¨Ò¦p Baroody, 1989; Clements & McMillen, 1996)¡A±qPiagetªº²z½×¤¤¡A¨Ã¤£¯àª½±µ¤Þ¥Ó¥X ¨àµ£¥²¶·¾Þ§Ë¨ãÅ骫¥ó¡A¤Î³q¹L¤Ï«ä³o¨Ç¨ãÅ鬡°Ê (·Pª¾¬¡°Ê) ¨Ó«Ø ºc¼Æ¾Ç·§©À¡A­È±o§Ú­Ìª`·Nªº¤Ï¦Ó¬O³o¨Ç³Q¾Þ§ËªºªF¦è¡A¬O§_¤@¨Ç«Ä µ£©Ò¼ô±xªº¡F©Ò±a¨Óªº¸gÅç¬O§_¤@¨Ç¹ï«Äµ£¦³·N¸q¡A¨Ã¥B¯à¥O¥L­Ì¥D °Ê¦a¥[¥H«ä¦Òªº¤º®e¡C¦¹¥~¡AÁa¨Ï¬Y¨Ç¤º®e©Î³\¤w«Dª«²z·Pª¾·N¸q¤U ªº¨ãÅé¸gÅç¡A¦ý­Y¬O¤@¨Ç¥L­Ì¸g¤w¼ô±xªº·§©À¬¡°Ê[4]¡A¬Ò¦³¾÷·|¦¨¬° «Äµ£¾Ç²ß¬¡°Ê¤¤«ä¦Ò¡B¸g¾úªº¹ï¶H¡C¤@©wµ{«×¤W¡A¥ô¦ó¯à°÷¦¨¬°»{ª¾ ¥DÅ骺¤Ï«ä¹ï¶H¡A¥²¥ý¥H¬YºØ¤ß²zªí¶H¤è¦¡¥X²{¡A¤~¯à¦¨¬°¨ä¸gÅç¥@ ¬Éªº¤º®e¡C ¨Æ¹ê¤W¡A¨ãÅé»P©â¶Hªº¹º¤À¡A¨Ã«Dª½Ä±¥H¬°¨º¯ë²³æ¡C¦b³o°ÝÃD ¤W¡AQuine (1960) ªº­õ¾Ç°Q½×¨ä¹ê¬Æ¦³·N«ä¡G§Ú­Ì²´¤¤¥@¬É¤£¦Pª«¥ó ªºÂkÃþ¡B¹º¤À¡A»P¥DÅ骺¬ÛÃöªº¸gÅç¥@¬É±K¤£¥i¤À¡F´«¨¥¤§¡A¥@¬É¤¤ ªº¤£¦P¨Æª«¡A¦s¦bµÛ«Ü¦h¤Àªù§OÃþªº¥i¯à©Ê¡AºÝµø¨º¨Ç©Ê½è¡B¤ÀÃþ¹ï »{ª¾¥DÅ馳¦óºØ·N¸q¡C¥Ñ¦¹¡AWilensky (1991) ©ú½T¦a«ü¥X©Ò¿×¡u¨ã Åé¨Ã«D¬Y­Ó«ÈÅé [¥»¦³] ªº©Ê½è¡A¦Ó¬O¤H»P³o­Ó«ÈÅ餧¶¡Ãö«Yªº¤@­Ó ©Ê½è¡v(p. 198¡A­ì¤å±×Åé)¡A¤]´N¬O»¡»{ª¾¥DÅé«ç¼Ë²z¸Ñ¦³Ãöªº¨Æª«¡A ¥L­Ì¤§¶¡¦s¦bµÛ¬Æ»ò¤¬°ÊªºÃö«Y©Î¥i¯à©Ê¡A¦b­Ó§Oªº±¡¹Ò¤U¤~¯à¨M©w ¨Æª«ªº¨ãÅé©Ê¦³¦h±j¡C§Y¦p¹ï¤@­Ó¼ôª¾ 100 ¥H¤º¦U¼Æªº¦]¦¡¤À¸Ñªº ¼Æ¾Ç±Ð®v¨Ó»¡¡A¨C­Ó¦X¦¨¼Æªº¤£¦P²Õ¦¨¤è¦¡³£¥i¯à¦³¬ÛÀ³ªºªø¤è§Î¼Ò «¬ªí¶H¡A¦]¼Æªº·§©À¥i¥HÅܱo«Ü¨ãÅé¡A¦ý¹ïªì¾Çªº«Ä¤l­Ì¡A¦]¼Æªº·§ ©À´N«Ü©â¶H¤F¡C ¦Ó¥H°T®§³B²z¼Ò¦¡ (information-processing model) ¶i¦æªº¬ã¨s¡A ´N¹B¥Î±Ð¨ãªº°ÝÃD´£¥X¤F¤@­Ó­È±oª`·Nªºµ²ªG¡A´N¬O¥u¦³·í¨àµ£¼ô±x ¦³Ãöªº¨ãÅé±Ð¨ã¡A¤~¯à©ú½T¦a¬Ý¨ì³o¨Ç¨ãÅ骫¥ó»P©Ò­n¶Ç»¼¤§±Ð¾Ç·§ ©À¶¡¤§¹ïÀ³Ãö«Y¡A³o­Ó±Ð¨ãªº¹B¥Î¤~ºâ±o¤W¦¨¥\ (Boulton-Lewis, 1991; Halford & Boulton-Lewis, 1992)¡C¦]¬°¨àµ£¦b¾Þ§Ë³o¨Ç±Ð¨ã®É¡A­n´x´¤ ¦³Ãöªºª«Åé»P·§©À¶¡¤§¹ïÀ³¡A·|¼W¥[°T®§³B²zªº­t²ü¡F­Y«DÄÝ©ó¼ô±x ¸gÅç½d³òªº¨Æª«¡A´N·|§«Ãª¤F©Ò±ý¹F¨ì¤§³Ì¨Î¾Ç²ß®ÄªG¡C ºî¦X¨Ó»¡¡A·í±Ð®v­n¬°¾Ç²ß¦³§xÃøªº¨àµ£³]­p»²§U±Ð¾Çªº±Ð¨ã©M ¹CÀ¸®É¡A¥²¶·¥H¾Çµ£¬°¤¤¤ß¥Xµo¡A¦Ó«D¯Âºé±qª«Å骺©Ê½è¡A¦Ò¼{¦³Ãö ¤§±Ð¨ã©Î¹CÀ¸¤è¦¡¬O§_¨ãÅé¡A­«­nªº¬O­n¦ô­p«Äµ£¹ï¸Ó¨Æª«ªº¼ô±xµ{ «×¡A¥H¤Î¨ä¤¤Ä­§tªº¼Æ¾ÇÃö«Y¡B·§©À¡B·N¸qµ¥¯à§_¬°¨àµ£»´©ö¹îı±o ¨ì¡A¨Ó¿Å¶q§@¬°±Ð¨ãªº¾A¤Á©Ê¡C ­Ó®×±´°Q ¥H¤U§Ú­Ì¸Õ¥H¤@­Ó¯u¹ê­Ó®×¡A±´°Q¦p¦ó«ö·Ó¥H¤Wªº²z½×°ò¦¡A¶i ¦æ±Ð¾Ç»²§Uªº³]­p¤u§@¡A¬J»¡©ú²z½×­ì«hªºÀ³¥Î·N¸q¡A¦P®É¥ç¯à¥[²` §Ú­Ì¹ï¦³Ãö½×ÂI¤§»{ÃÑ¡C 1. ­I´º¸ê®Æ ¬O¦¸­Ó®×ªº¹ï¶H¤D´NŪ©ó¤p¾Ç¤@¦~¯Åªº¤p²» (°²¦W)¡A¦~ÄÖ¤»·³ ¥b¡C³æ±q¥Lªº¾Ç·~¦¨ÁZ¤À¼Æ¨Ó¬Ý¡A´¶¹Mªº¦¨ÁZ¤]¤£«U¡A¤@¯ë³£¦³¤K¤Q ¤À¥H¤W¡A°ß¿W¬O¼Æ¾Ç¬ìªº¦¨ÁZ«o°¾§C¡A¨C¦¸´úÅ窺¥­§¡¤À³£¤£¶W¹L¤T ¤Q¤À¡C¦¹¥~¡A±qµ§ªÌ»P¥Lªº¥æ½Í¤¤¡Aµo²{¥Lªº¤f»yªí¹F¯à¤O»á¨Î¡A¦p ­z»¡¥Lªº®a®xª¬ªp¡B¹L©¹ªº¦¨ÁZµ¥³£¬Æ¬°²M´·©M¦³±ø²z¡C¥i¥H¬Û«H¡A ¤p²»¨Ã¤£ÄÝ©ó»y¨¥¾Ç²ß§xÃøªº¤@Ãþ¡A¦]¦¹³o­Ó®×¤]¤£¤Ó½ÆÂø¡C µ§ªÌ¶}©l¯d·N¥Lªº­ì¦]¡A¬O¦b¹ê²ß´Á¶¡±Ð±Â¡u¨â¦ì¼Æ¥[ªk (¶i¦ì)¡v ¦¹½ÒÃD®É¡Aµo²{¥L¸g±`¥X¿ù¡A¦ý¿ù³B«o«D¤@¯ë¤@¦~¯Å¾Ç¥Í©Ò±`¥Çªº¿ù »~¡A¦p¦C¦¡®É¹ï¿ù¦ì¡B¶i¦ì®É§Ñ°O¤F¦b¤Q¦ì¥[¦^¶i¤F¦ìªº¡u1¡vµ¥¡A ¦Ó¬O¦b­Ó¦ìªº¹Bºâ¤W¤w¥X¿ù¡C¬°¤FÁA¸Ñ¥Lªº½T¹ê°ÝÃD©Ò¦b¡Aµ§ªÌ«K©ó ¤p®§®É½Ð¤p²»·í­±­pºâ¤@¨Çºâ¦¡¡C¨ä¤@ªºµo²{¬O¥L©¹©¹¥u¬O±æµÛºâ¦¡ ¦b¡u·Q¡v«ç­p¡A·í¥L«ç¼Ë¤]­p¤£¨ìµª®×®É¡Aµ§ªÌ«K°Ý¥L°£¤F¤ßºâªº¤è ªk¥~¡A¥iÁÙ¦³¬Æ»ò¤èªk¥iÀ°§U¥L­pºâ®É¡A¥L¦^µª»¡¡G¡u¼Æ¤â«ü¡v¡A¦ý ¤SÀH§Yªí¥Ü¥À¿Ë¤£­ã¥L¥Î¼Æ¤â«ü³oÄø¤èªk¡A¦Ñ®v¤]»¡³o¬O¥®¸X¶é¥Í¤~ ¥Îªº¤èªk¡C«á¨Ó¦bµ§ªÌ´X¸g¹ªÀy¤U¡A¥L²×©óªÖ¥Î¼Æ¤â«üªº¤èªk¡C³o®É «Kµo²{¤F²Ä¤G­Ó°ÝÃD©Ò¦b¡A­ì¨Ó¥L¦b¼Æ¤â«üªº¹Lµ{¤¤¡A¤]¦³§xÃø©M¸g ±`¥X¿ù¡A«Ýµ§ªÌ¤Þ¾É¥LºCºC¦a¤@°¦¤@°¦¤â«ü¦ù¥X¡A¨Ã¦P®É°á¥X¸Ó¼Æ ®É¡A¥L¤~¯à¸û·Ç½T¦a¼Æ¥X»Ý¬Û¥[ªº¼Æ¡A¥H¤Î­p¥X¥¿½Tªºµª®×¡C 2. °ÝÃD§Î¦¨ªº­ì¦] ¨s³º§Ú­ÌÀ³¸Ó¦p¦ó»²§U³o¦b¼Æ¾Ç­pºâ¤W¦³¾Ç²ß§xÃøªº«Ä¤l©O¡H ³o°ÝÃD­n±o¨ì¸Ñµª¡A«K¥²¶·¥ý¥Ñ°ÝÃDªº§Î¦¨­ì¦]¶}©l¤J¤â¡A¥H¨ÏÀH«á ªº³]­p¯à°w¹ï¦³Ãöªº­ì¦]¨Ó³]©w¡CµM¦Ó­º¥ý­n²M´·ªº¡A¬O¦ó¥H§Ú­Ì·| §â³o­Ó®×©w¬°¾Ç²ß§xÃøªº¨Ò¤l¡C³o¬O¦]¬°¤p²»ªº¾Ç²ß±¡ªp¥¿¦n²Å¦X¤W ¤å¦³Ãö¾Ç²ß§xÃøªº©w¸q¡A´N¬O¥Lªº´¼¤O¥¿±` (³o¥i±q¥Lªº¨ä¥L¾Ç¬ìªí ²{¤Î»P¤H·¾³qªº§Þ¯à¤W±oª¾)¡A¦ý¬O¦b¼Æ¾Çªº­pºâ¤W¡A«o¦³»P´¼¤O¤£²Å ªºªí²{¡A§Y¬°¡uÅãµÛªº±Ð¨|®t¶Z¡v(¸Ô¨£¤W¤å)¡C ¦Ü©ó¤p²»¾Ç²ß§xÃøªº§Î¦¨­ì¦]¡A±q»P¥L±µÄ²ªº¹Lµ{¤¤¡Aµ§ªÌµo²{ ¥L¹ï¼Æ¦rªºÅª©M¼g³£¨S¦³°ÝÃD¡F¦b§Q¥Î¤â«ü¼Æ¼Æ®É¡A¥u­n¯à¹ï¥L¥[¥H ¦w¼¾©Î´£¥Ü¡A¤]¨S¦³¤Ó¤jªº°ÝÃD¥X²{¡C¬G©úÅã¦a¥L¦b¾÷¯à¤Wªº¹B§@¬Ò ¨S¦³¯S®í°ÝÃD©Î¯Ê³´¡A©ó¬O§Ú­Ì«K´`µÛ¡u­pºâ¯à¤O¥¢±`¡vªº§Î¦¨­ì¦] ªº²Ä¤G¶µ ¢w¢w ¼Æ¾Ç¾Ç²ßªº¯S½è¤Î¯S¦³¹Lµ{¢w¢w§@¥X­åªR¡C ©úÅã¦a¡A¤p²»¦b¼Æ¼Æ¤Î¹Bºâ¤W¥X²{ªº§xÃø¡A¨ä­ì¦]¤D¦b©ó¥L¥¼¯à ¨Ì¾Ú¦Û¤vªº¾Ç²ß¼Ò¦¡¨Ó¶i¦æ¾Ç²ß¡A³Ì©ú½Tªº¨Ò¤l¬O¥L¤£À´­pºâ®É¡A¥L ª¾¹D¼Æ¤â«ü¦¹¤èªk¯àÀ°§U¥L¡C¦ý¥Ñ©ó¨­Ã䪺¦¨¦~¤H¤£Â_½á¤©¦¹¤èªk­t ­±ªº§Î¶H¡A¦p»{¬°³o¬OÄø©Î¥®¸Xªº¤èªk¡A³oÆ[©À¥²©w¨Ï¤p²»µLªk¦Û¦p ¦a¹B¥Î³o¥»¨Ó¦³§U¥L¾Ç²ßªº¤èªk¡A¬Æ¦Ü¦]¬°À£¤O¤Î¥]µö¤Ó¤j¡A¦Ó¾É­P ¥L¦b¼Æ¼Æ®É¤]¸g±`¥X²{¿ù¶Ã¡C ¦¹¥~¡A¦]¬°¤p²»ªº»{ª¾µo®i¦bPiagetªº¥|­Ó»{ª¾µo®i´Á (·Pı°Ê §@´Á¡A0-2·³¡F«e¹B«ä´Á¡A2-7·³¡F¨ãÅé¹B«ä´Á¡A7-11·³¡F§Î¦¡¹B«ä ´Á¡A11·³¥H¤W) ¤¤¡A¦ô­pÄÝ«e¹B«ä´Á¡A¥Lªº«äºû¤è¦¡¤j·§¤´¥¼¯à¦¨¼ô ¦a¥H²Å¦XÅÞ¿è³W«ßªº¤è¦¡¡A¨Ó³B²z¨Æª«¶¡ªºÃö«Y©MÅܤơC³o¬O¥Ñ©ó³o ®É´Áªº«Ä¤l¤´¬O¦³ª¾Ä±¶°¤¤ªº¶É¦V¡A§Y¥u¯à¾Ìª¾Ä±©Ò¤Îªº¨Æª«©Î°ÝÃD §@¥X«ä¦Ò¡A¦Ó³o¤S¬O°ò©ó¹ï·§©Àªº¦u«í¤Î¥i°f©Êªº¯à¤O¥¼¨c©T¡C«eªÌ ¨Ï¥L­Ì¹ï¦P¤@·§©Àªº¥»½èªº²z¸Ñ¤£¯à­ç°£«D¥»½è¤Wªº§ïÅÜ¡A¦ÓÄ~Äòºû «ù¤£ÅÜ¡F«áªÌ§Y«ü¹ï¤@­Ó°ÝÃD¤£¯à±q¥¿¤Ï¨â­±¥h¬Ý¡A¦p9+6=15§Y 15-9=6¡C¥Ñ¦¹¥iª¾¤p²»ªº»{ª¾µo®i¤´¥¼¥i¥H§¹¥þ©âÂ÷¹êª«¥@¬É¡A¾ÌªÅ ¶i¦æ«ä¦Ò¡A¦p¤ßºâ¤@Ãþªº§Î¦¡¨Ã«D¤p²»©Ò¯à»´©ö§â´¤ªº¡A«j±j¬°¤§¡A ¥u·|¼W¥[¥L¦b¾Ç²ß¤Wªº§xÃø¡C 3. ±Ð¾Ç»²¾É³]­p §Ú­Ì¦bÁA¸Ñ¤p²»ªº°ÝÃD§Î¦¨ªº­I´º¤Î¥Lªº»{ª¾µo®i±¡ªp«á¡A¹E°w ¹ï¦¹©w¤U¦³Ãöªº»²¾É°ò¥»­ì«h¡G¤@¬°±q¨ãÅé¨ì©â¶H¡A¥HÀ°§U¤p²»§â¼Æ ¦r¡B¦ì­Èµ¥©â¶Hªº¼Æ¾ÇÆ[©À¨ãÅ餯¡AÂÇ¥H¨Ï³o¨Ç¼Æ¾ÇÆ[©À¯à§ó§Î¶H¦a «Ø¥ß¦b¥Lªº¤ß¤¤¡A¦Ó«D¥u¬O¾ÌªÅ¦a¼Æ¼Æ¤Î­pºâ¡A²æÂ÷¤F¥Lªº»{ª¾µo®i ¶¥¬q¡F¤G¬°±q¸û´I½ì¨ýªº¬¡°Ê¤¤¡A¤Þµo¤p²»¦Û§Úµo²{ªº¾Ç²ß¯à¤O¡A¥H À°§U¥L¯à¨Ì¾Ú¦Û¤vªº¾Ç²ß¨B¥ï¾Ç²ß¡A¨Ã¥i³z¹L»´ÃPªº¬¡°Ê¤è¦¡À°§U¥L ®ø°£¤@¨Ç¦b¼Æ¾Ç¾Ç²ß¹Lµ{¤¤¤£¥²­nªºµJ¼{©Î­t¾á¡C ¦b³]­pªº¾ãÅé¾É¦V¤W¡A¥i¥H±Ä¥Î¦æ¬°¥D¸qªº¼Ò¦¡ (behavioural approach)¡A§Y¦p§Q¥Î½Ò·~¤ÀªRªº¤èªk (task analysis)¡A½s¼g¾Ç²ß¦æ¬°¥Ø ¼Ðªº¼h§Ç¡C¤£¤Ö¾ÇªÌ³£»{¬°³o¼Ò¦¡¯à¦³§U¶i¦æ¾Ç²ß§xÃø»²¾Éªº¤H¡A§ó ¦³¥Øªº¡B¦³±ø²z¦a³]­p´`§Çº¥¶iªº­p¹º¹F¨ì¦³Ãöªº¾Ç²ß¥Ø¼Ð (³\¤Ñ «Â¡A1986)¡C¦¹¼Ò¦¡¤@¯ë¨Ì¾Ú¥H¤Uªºµ{§Ç¶i¦æ±Ð¾Ç¥Ø¼ÐªºÀÀ©w (³\¤Ñ «Â¡A1986¡App. 53 - 54)¡G ¡u(1) ­n¥Î«ÈÆ[ªº¡B¨ãÅ骺¡B¥iÆ[¹îªº¦æ¬°¨Ó³¯­z [±Ð¾Ç¥Ø¼Ð]¡C (2) ­n«öÃø©öµ{«×¦w±Æ¾A·í¶¶§Ç¡C (3) ­n¦b¾Ç²ßªÌ¯à¤ÏÀ³ªº½d³ò¤º¡C (4) ­n¹º¤À¦¨¥i¾r¶¿ªº³æ¦ì¡A¨Ï¾Ç¥Í©ö©ó°µ¥¿½Tªº¤ÏÀ³¡C¡v ¦Ó¦b¦¹¼Ò¦¡ªº³]­p¤¤¡A¹ï¤º®e§@¥X½Ò·~¤ÀªR¬O·í¤¤ªº°ò¥»¨BÆJ¤§ ¤@¡A¤]¬O­«­nªº¤@Àô¡A¦]¬°³o¯àÀ°§U³]­pªÌ§ó²M´·©M¥J²Ó¦a´x´¤¾Ç²ß ¥Ø¼Ðªº¦U¦³Ãö­«ÂI¡A¦³®Ä¦a´À¦Û¤vªº»²¾É¤Î¾Ç²ßªÌªº¾Ç²ß¡A©w¤U²Ó¤À ©M´`§Çº¥¶iªº¥Ø¼Ð¡C¦Ó³o¤S¥¿¦n¬O¦b¼Æ¾Ç³o¬ÆÁ¿¨s¤º®eªº¬ÛÃö¼h¦¸©M ¨t²Î©Êªº±Ð¾Ç¤¤¡A¬Æ³Q¼sªxÀ³¥Îªº¤èªk¡A¯÷¥H¦¹Â²²¤¤ÀªR¨â­Ó­Ó¦ì¼Æ ¥[ªk (¥i¶i¦ì) ¤§¾Ç²ß¦p¤U¡G ¨â­Ó­Ó¦ì¼Æ¥[ªk(¥i¶i¦ì) ¡ô ¥[ªkªº·§©À ¡ô ¦ì­Èªº·§©À (­Ó¦ì¤Î¤Q¦ì) ¡ô 1-99¤ºªº¼Æªº»{ÃѤδx´¤ ¡ô ¼Æ¼Æªº§Þ¯à ¡ô ¹ï¼Æ¦r·§©Àªº´x´¤ Ų©ó¤p²»ªº±¡ªp¸û¯S®í¡A¬°·ÓÅU¥Lªº¯à¤O®t²§¡A¬G§Ú­Ì¦b³]©wµu ´Á¤º³Ì²×ªº±Ð¾Ç¥Ø¼Ð®É¡A¨S¦³­n¨D¥L¤@©w­n°µ¨ì¸ò¾Ç®Õªº¶i«×¤@¼Ë¡A ¯à­pºâ¨â¦ì¼Æ¥[ªk (¶i¦ì) ªº¼Æ¡C©Ò¥H¦b¬O¦¸­p¹º¤¤¡A¥u¬O§Æ±æ¥L¯à ¥ý´x´¤¤ÎÀ³¥Î¨â­Ó­Ó¦ì¼Æ¥[ªk (¥i¶i¦ì) ªº¤èªk¡A¦Ó¨ä¥Lªº¦¸¯Å¾Ç²ß ¥Ø¼Ð¥ç¨Ì·Ó¥H¤Wªº½Ò·~¤ÀªR¡A§@´`§Çº¥¶iªº³]©w¡A¯÷²¤¤À­z¦p¤U[5]¡G ±ý¹F¦¨ªº¥Ø¼Ð µ{§Ç 1. ¹ï¼Æ¦r·§©Àªº´x ´¤ §@¬°·Å²ß¡C§Q¥Î¾A·í¼Æ¶qªº¿n¤ì©Î¥ô¦ó¥i¨£ ªº¡B¥iIJªºª«¥ó¡A¦A­«·s¤¶²Ð1-10¥H¤ºªº¼Æªº ·§©À¡C 2. ¾d©T¼Æ¼Æªº§Þ¥© «Ý¾Ç¥Í¹ï¦³Ãö¼Æ¦rªº·§©À¦³¤F´x´¤«á¡A¥i¨Ì¦¸ §Ç¶i¦æ¥H¤Uµ{§Ç¡G 1. ¦P¼Ë§Q¥Î¤@¨Ç¥i¨£¥iIJªº¹êª«¡A¦p¿n¤ì¡A¹ª Ày¾Ç¥Í¥Î¦Û¤vªº¤èªk¡A¦pÕiÂIµÛ¨Ó¼Æ¡B¥XÁn ¼Æµ¥¡A¼Æ¥X¨ä¼Æ¶q¡C 1.1 ¥ý­n¨D¥L¼Æ¥X¥Î¥¿³Wªº±Æ¦C¤èªkªº¹êª« ¼Æ¶q¡A¦p ©Î ¡C 1.2 ¦b¥L´x´¤¤F¥H«á¡A«h¥Î¤£³W«hªº¤è¦¡Â\ ©ñ¡A¦p ¡C³o¼Ë¯à¦³§U¥L«Ø¥ß¦u«íªº Æ[©À¡A¹ï¨ä¼Æ¼Æ¤Î¶i¤@¨Bªº·§©À¾Ç²ß³£¦³ À°§U¡C 2. ¡u¼Æ¼Æ¤â«ü´X¦h°¦¡v¹CÀ¸¡G ¬°¼W¥[½ì¬N©Ê¡A¥i¦A¥Î¦¹¤èªk¶i¦æ¡C§Q¥Î±Ð ®v©Î¹ï¶Hªº¤â ¡A¦A©ñ¤W¿n¤ì¡A ¦p ¡A¹ªÀy¾Ç¥Í¼Æ¥X¨äÁ`¼Æ¡C³o°£¤F ¯à¦A¤@¦¸¥[²`¨ä¼Æ¼ÆªºÆ[©À¤Î§Þ¥©¥~¡A¥ç¥i ÂǦ¹À°§U¹ï¶H¦b¨ä¼Æ¼Æªº¨t²Î¤¤«Ø¥ß¡u¤â¡v ³o¤@¼Æ¼Æ³æ¦ì©M¤u¨ã¡A³o¹ï¥LÀH«áªº¾Ç²ß¬O ­«­n©M¦³À°§Uªº¡C 3. ¦P¼Ë§Q¥Î¥H¤Wªº¤èªk¡A¦ý³oùØ¥i¼Æ¦h¹L¤Qªº ¼Æ¡C 3. ¤Þ¤J¼Æ¦rªº²Å¸¹ «Ý¾Ç¥Íªì¨Bí©T¦a´x´¤¤F¼Æ¼Æªº²z©À©M¤èªk «á¡A«K§Q¥Î¼Æ¦rµP¤Þ¤J¼Æ¦rªº²Å¸¹¡G 1. µÛ¾Ç¥Í±q¼Æ¦r¥d (¥]¬A1¦Ü10) ¤¤©â¥X¤@ ±i¡A½Ð¾Ç¥ÍŪ¥X¼Æ¦r¡A¥çµÛ¾Ç¥Í¥H¤â«üªí¥Ü ³o­Ó¼Æ¥Ø¡A¦A±q¤@°ï¿n¤ì¤¤¼Æ¥X³o­Ó¼Æ¶qªº ¿n¤ì¡C 2. ¥Î¨âÅ|¼Æ¦r¥d¡A²Ä¤@Å|¥Ñ1¦Ü9¡A²Ä¤GÅ|¥Ñ0 ¦Ü9¡CµÛ¾Ç¥Í±q²Ä¤@Å|¥d©â¥X¤@±i¡A¨Ò¦p¡G 3 ¡A©ñ¦bÂi¤W¤wµe¦³ ªº¥ª­±¡A¦A¥Ñ²Ä ¤GÅ|©â¥X¤@±i¡A¨Ò¦p¡G 8 ¡A©ñ¦b²Ä¤@±iªº ¥k­±¡A«K¦¨ 3 8 ¡FµM«á½Ð¾Ç¥ÍŪ¥X¥d¤W ªº¼Æ¦r¬O¦h¤Ö¡C­Y³o­Ó¼Æ¦r¤Ö©ó30¡A¥i¦AµÛ ¾Ç¥Í±q¿n¤ì°ï¤¤¼Æ¥X³o­Ó¼Æ¥Øªº¿n¤ì¡C 4. «Ø¥ß¦ì­Èªº·§©À ¥ý´²©ñ¿n¤ì µÛ¾Ç¥Í¼Æ¥X¨ä¼Æ¶q¡AµM«á½Ð ¥L¨C¤Q­Ó¤@±Æ±Æ¦n¡A¦p¡G ¡A¨Ã¥Î ¼Æ¦r²Å¸¹ªí¥Ü¨ä¼Æ¶q¡A±q¦Ó¤Þ¾É¾Ç¥Í§ä¥X¤Q¦ì »P­Ó¦ìªºÃö«Y©M·N¸q¡C 5. §â¨â­Ó­Ó¦ìªº¼Æ ¬Û¥[ 1. §Q¥ÎÂY»ë¥J±a¤p°Êª«¦^®aªº¹CÀ¸[6]¡A¥ý¥Î¤@ ²É»ë¥J¨Óª±¡A«Ý¼ô²ß«á¦A¥Î¨â²É¡A¦]¦Ó§â¨â ¼Æ¬Û¥[ªº­ì²zº¯¤J·í¤¤¡A±q¦ÓÅý¾Ç¥Í¯àªì¨B ¼ô²ß¨Ã´x´¤¨â¼Æ¬Û¥[ªº·§©À¡C¦Ó¦b»ë¥Jªº¹B ¥Î¤W¡A¥i¥ý¥Î¹ï¶HºD±`ª±ªº»ë¥J¼Ë¦¡¡G ¡A µM«á¦A¥Î¼g¤W¼Æ¦rªº»ë¥J ¡A¥H§U¥L§â¹CÀ¸ »P¼Æ¦r²Å¸¹³sô°_¨Ó¡A«Ø¥ß¦³Ãöªº©â¶H·§ ©À¡C´Ñ½L¨£¤U¹Ï¡G 2. ¦P¼Ë¬°¤F¥H¤Wªº¥Øªº¡A¥i¦A¥H¥t¤@ºØ¤è¦¡¶i ¦æ¡C §Q¥Î²q®±ªº¤è¦¡¡A¥i¥Ñ¹ï¶H¾Ç¥Í»P¥t¤@¾Ç¥Í ¹ïª±¡A©Î¥Ñ±Ð®v»P¹ï¶H¾Ç¥Íª±¡C¤èªk¬O¨C¤H ®³¥X¥ª¤â²q®±¡A³W©w¨C¤H¨C¦¸¥²¶·¥X¥Ü1¦Ü5 °¦¤â«ü¡AµM«á½ü¬y§â²q®±®É©Ò¥X¥Üªº¤â«ü¼Æ ¥Ø¬Û¥[¡A¥iÅý°Ñ»PªÌ¥Î¥k¤â¼Æ¼Æ¡Aª½¦Ü´x´¤ ¹B¥Î¥[ªkªº­ì²z¡C (µù¡G³o¨â­Ó¹CÀ¸ªº¹Lµ{§¡¤£¯A¤Î¥[¸¹ªº¹B ¥Î¡Aªì´Á¥u¬O¨ãÅé¦a°Ý¹ï¶H¡G³oùئX¦@¦³¦h ¤Ö¡A«á´Á¤~¤fÀY±a¥X¡u¥[¡v³o¦WºÙ¡C) 6. »{ÃÑ¡u+¡v¤Î¡u=¡v ³o¨â­Ó²Å¸¹ ªu¥Î¥H¤Wªº¹CÀ¸¤èªk¡A¦ý¤µ¦¸«o¥H¼Æ¦rµP§@Å㠥ܡA¨Ã»²¥H¡u+¡v³o²Å¸¹¡A¦p¹ï¶H©â¨ì5©M4¡A ±Ð®v´N¥H¼Æ¦rµP¦AÅã¥Ü¡G 5 4 ¡A¤¤¶¡¦A©ñ ¤J + ³o²Å¸¹¡C·í¾Ç¥Íºâ¥Xµª®×«á¡A¥i¥H¥Î = ¨Óªí¥Üµ²ªG¡C¨Ã±q¥t¤@Å|¥Ñ2¦Ü18ªº¼Æ¦r¥d¤¤ ¿ï¥Xµª®×¡A©ñ¦b³o­Óºâ¦¡¤W¨Ó§¹¦¨¡C ¹Lµ{¤¤¥i¥H¹êª«»²§U¼Æ¼Æ¡A¤Î­«´£­è¤~ª±¹CÀ¸ ¤è¦¡©M±¡ªp§@¬°»²§U¡C 7. §Q¥Îºâ¦¡­pºâ a + b = ? (1 ?a¡Ab ?9) ·í¾Ç¥Í¹ï¥H¤Wªºµ{§Ç§¡¯à´x´¤«á¡A«K¥i¹Á¸Õµ¹ ¤@¨Ç¸û²Lªººâ¦¡ÃD¥Øµ¹¾Ç¥Í°µ¡C(¦p¦³»Ý­n¡A¤´ ¥i±Ä¥Î¹êª«¦p¿n¤ì¡Bºâ¯]µ¥§@»²§U) ¥H¤Wªº»²¾É³]­p¡A¥i¥H¹ï¶H­Ó¤H©ÎÁܽФ@¨Ç»P¹ï¶Hªºµ{«×¨S¦³¤Ó ¤j¶ZÂ÷ªº¾Ç¥Í¤@°_°Ñ¥[¡A¥H¤p²Õªº§Î¦¡¶i¦æ¡A³o¼Ë¬J¥i´î»´¹ï¶H±µ¨ü »²¾Éªº§xµ~¡A¤S¥i¦P®ÉÀ°§U¨ä¥L¹ï¦³Ãö·§©À¥¼§¹¥þ¨c©T¦a´x´¤ªº¾Ç ¥Í¡C¦Ó¾ã­Ó­p¹ºªº¶i¦æ¡A§¡¥H¾Ç²ßªÌªº¶i«×¬°¨ÌÂk¡Aµ´¤£¥i¾Þ¤§¹L«æ¡C ¦¹¥~¡A¦b¶i¦æ®É¤]À³µ¹¤©¦h¨Ç¹ªÀy¡A¨Ï¹ï¶H¯à§ó¦³«H¤ß©M´r§Ö¦a¾Ç ²ß¡C µ²»y ¥Ñ©ó¬O¦¸ªº±Ð¾Ç³]­p¥u¬O°ò©ó¹ï­Ó®×ªºªì¨B±´°Q¦Ó³]©w¡A¥¼¦³À³ ¥Î©ó¹ê»Úªº±¡¹Ò¤¤¡A¬G¨ä¦³®Ä©Ê¥¼¯à³Q§¹¥þªÖ©w¡A§ó½Í¤£¤WµûŲ¨ä¾Ç ²ßªG®Ä¡CµM¦Ó¡A¦³¤@ÂI¥i¥HªÖ©wªº¡A¬O·í­n¬°­Ó§O¾Ç¥Íªº¾Ç²ß§xÃø´£ ¨Ñ»²§U®É¡A¥²¶·­n¹ï¥H¤W¦³Ãöªº²z½×©M¬ã¨sµ²ªG¦³¤@©wªº²z¸Ñ¡AµM«á ¦A§Ë²M­Ó§O¾Ç²ßªÌªº¾Ç²ß¶¥¬q¤Î¼Ò¦¡¡B®t²§©Ò¦b¡B¦³Ãö§xÃøªº§Î¦¨­I ´º¡B­ì¦]µ¥¡A¤~¯à§@¥X¾A·íªº°w¹ï©Ê»²§U¡A¦Ó³o¥ç¥¿¬O¬O¦¸ªº±Ð¾Ç»² ¾É³]­p©Ò¨Ì´`ªº­ì«h¡C­n¬°¨àµ£ ¢w¢w ¯S§O¬O¦³¾Ç²ß§xÃøªº¨àµ£ ¢w ¢w ´£¨Ñ¾A·í¦Ó¦³®Äªº±Ð¾Ç¡A¥²¶·±q»{²M­Ó§O®t²§¡B¥¿µø¤Î´L­«­Ó§O ®t²§¶}©l¡A¦³¤F¦¹°ò¥»¦Ó¥²¶·ªº·NÃÑ«á¡A¦AºÉ¤O¦a¦]À³­Ó§Oªº®t²§¨Ó ¬I±Ð¡C¦Ó¬O¦¸ªº¸gÅ祿¦nµ¹§Ú­Ì¸g¾ú¤F¤@¦¸¦p¦¹Ä_¶Qªº±Ð¾Ç³]­p¹L µ{¡A¤]§Æ±æ±q¨Æ¦³Ãö¤u§@ªº±Ð¨|¤u§@ªÌ¥ç¦p§Ú­Ì¤@¼Ë¡A¯à¦b·í¤¤Åé·| ¨ì¤@ÂI¦³»ù­Èªº«H®§¡A¨Ã¦@¦P¬°¨C¤@­Ó«Ä¤l¼½¤U´¼¼z»P·RªººØ¤l¦ÓÄ~ Äò§V¤O¡C µùÄÀ [1] ®Ú¾Ú³\¤Ñ«Â (1986¡App. 279 - 281) ©Ò¦Cªº¦U¶µºî¦X¾ã²z¦Ó¦¨¡C [2] ¦Pµù [1]¡C [3] ¦³Ãö³o­Ó¡u¤Ï·Ó¦¡¡vªº©â¶H¤Æ¹Lµ{¡A¸Ô¨£von Glasersfeld (1991) ªº °Q½×¡C¨ä¤¤§@ªÌ«ü¥X¥Ñ©óPiaget­ì¤åªk¤åªº¤T­«¤£¦P·N¸q¡A¦b­^ ͮɥ¼³Q·Ç½Tªí¹F¡A¤Þ°_»~¸Ñ¡Cvon Glasersfeld (1991) ¥J²Ó¦a°Ï ¤À¤F³o¤TºØ¤£¦Pªº¡u¤Ï·Ó¦¡¡vªº©â¶H¤Æ¹Lµ{¡C [4] ¨Ò¦pªì¤p¨àµ£§¡¤w¹ï¤@¯ëª«Åé§Îª¬¦b¹B°Ê¤¤¤£·|§ïÅܳo¨Æ¹ê¦³©Ò ´x´¤¡A¥L­Ì¦³¯à¤O·Q¹³¤@­Ó¥¿¤è§Î©Î¨ä¥L§Îª¬¦b±ÛÂà¨ì¥ô¦ó¦ì¸m ¤W§¡«O«ùµÛ³o­Ó§Îª¬¡A³o¥çºâ±o¤W¹ï¼ôª¾ªº¸gÅç¶i¤@¨B¦b·§©À¼h ­±ªº¾Þ±±¡C [5] ¥Ñ©ó½g´TÃö«Y,¥H¤U¦U¶µ»P³]­p¦³Ãöªº²z½×­ì²z±q²¤¡C¦ý¬Û«H¹ïÀ³ «e¤å¤§°Q½×¡AÀ³¤£Ãø²z¸Ñ¡C [6] ·N©À¨ú¦ÛHughes (1986)¡App. 135 - 136¡C °Ñ¦Ò®Ñ¥Ø ¤ý§J¥ý (1987)¡C¡m¾Ç²ß¤ß²z¾Ç¡n¡C¥x¥_¥«¡G®Û«a¹Ï®Ñ¤½¥q¡C ¤ò³s¶ó (1991)¡C¡m¾Ç²ß»Ùê¨àµ£ªº¦¨ªø»P±Ð¨|¡n¡C¥x¥_¥«¡G¤ß²z¥Xª© ªÀ¡C ³\¤Ñ«Â (1986)¡C¡m¾Ç²ß»ÙêªÌ¤§±Ð¨|¡n¡C¥x¥_¥«¡G¤­«n¹Ï®Ñ¥Xª©¤½¥q¡C Baroody, A.J. (1989). Manipulatives don't come with guarantees. Arithmetic Teacher, 37(2), 4-5. Boulton-Lewis, G.M. (1991). The values and limitations of using concrete representations to teach mathematics to young children. In Proceedings of ICMI-China Regional Conference on Mathematical Education, Volume 1 (pp. 3.82-3.86), Beijing/China, August 5-8. Bruner, J.S. (1960). The process of education. Cambridge, MA: Harvard University Press. Chinn, S.J., & Ashcroft, J.R. (1993). Mathematics for dyslexics: A teaching handbook. London: Whurr Publishers Ltd. Clements, D.H., & McMillen, S. (1996). Rethinking "concrete" manipulatives. Teaching Children Mathematics, 2, 270-279. Geary, D.C. (1994). Children's mathematical development: Research and practical applications. Washington, DC: American Psychological Association. Halford, G.S., & Boulton-Lewis, G.M. (1992). Value and limitations of analogues in teaching mathematics. In A. Demetriou, M. Shayer, & A. Efklides (Eds.), Neo-Piagetian theories of cognitive development: Implications and applications for education (pp. 183-209). London: Routledge. Hughes, M. (1986). Children and number: Difficulties in learning mathematics. Oxford: Basil Blackwell. Piaget, J. (1953). How children form mathematical concepts. Scientific American, 189(5), 74-79. Piaget, J. (1973). Comments on mathematical education. In A.G. Howson (Ed.), Developments in mathematical education: Proceedings of the Second International Congress on Mathematical Education (pp. 79-87). Cambridge: Cambridge University Press. Quine, W.V.O. (1960). Word and object. Cambridge, MA: The MIT Press. von Glasersfeld, E. (1991). Abstraction, re-presentation, and reflection: An interpretation of experience and Piaget's approach. In L.P. Steffe (Ed.), Epistemological foundations of mathematical experience (pp. 45-67). New York: Springer-Verlag. Wilensky, U. (1991). Abstract meditations on the concrete and concrete implications for mathematics education. In I. Harel, & S. Papert (Eds.), Constructionism (pp. 193-203). Norwood, NJ: Ablex Publishing Corporation. ¼Æ¾Ç±Ð¨| ²Ä¥|´Á Edumath 4 ( 6/97) 72 71