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§ç§ï§â§ï§Ô§ä§ï§Û §Ó§ï?
2. §¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç§ï§Õ §ã§å§â§Ô§Ñ§ç ?§Ö §ê§Ñ§ä
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? §°§µ-§í§ß §é§Ú§Ô §ç§Ñ§ß§Õ§Ý§Ñ§Ô§Ñ, §ß§Ú§Û§Ô§Þ§Ú§Û§ß §ç§ï§â§ï§Ô§è§ï§ï: §¡§ß§Ô§Ú §ä§Ñ§ß§ç§Ú§Þ§Õ
§ã§å§â§Ô§Ñ§Ý§ä§í§ß §Ú§Õ§ï§Ó§ç§ä§ï§Û §Ñ§â§Ô§Ñ §Ù?§Û§Ô §ç§ï§â§ï§Ô§Ý§ï§ç, §Ò§Ñ§Ô§ê§Ý§Ñ§ç§å§Û,
§ã§å§â§Ñ§Ý§è§Ñ§ç§å§Û§ß §ç§å§Ó§î§ã§Ô§Ñ§Ý
? §³§å§â§Ñ§Ô§é§Õ§í§ß §ã§ï§ä§Ô§ï§ß §Ò§à§Õ§à§ç, §Ò?§ä§ï§ï§Ý§é, §ê??§ß §ä§å§ß§Ô§Ñ§Ñ§ç §ã§ï§ä§Ô§ï§Ý§Ô§ï§ï§Ô
§ç?§Ô§Ø??§Ý§Õ§ï§Ô.
? ??§â§Ú§Û§ß §å§Õ§Ú§â§Õ§Ý§Ñ§Ô§Ñ§ä§Ñ§Û §ã§å§â§Ñ§Ý§è§Ñ§ç§å§Û§Õ §ã§å§â§Ô§Ñ§ß§Ñ. (metecognitation)
? 21 §Õ?§Ô§ï§ï§â §Ù§å§å§ß§í §Ú§â§Ô§ï§ß§Ú§Û§Ô-§Ñ§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç §é§Ñ§Õ§Ó§Ñ§â§ä §ã§å§â§Ô§Ñ§ß§Ñ.
1. §¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç§ï§Õ §ã§å§â§Ñ§Ô§é§Ú§Õ §ñ§Ñ§Ô§Ñ§Ñ§Õ
§ã§å§â§Ñ§Ý§è§Ñ§ç §ç§ï§â§ï§Ô§ä§ï§Û §Ó§ï?
§¡§ã§å§å§Õ§á§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç §ã§å§â§Ô§Ñ§Ý§ä§í§ß §Ñ§â§Ô§Ñ
¡ô §®§ï§Õ§Ý§ï§Ô, §é§Ñ§Õ§Ó§Ñ§â, §Ñ§â§Ô§Ñ §ï§Ù§ï§Þ§ê§Ú§ç
¡ô §º??§Þ§Ø§Ý§ï§Ý§ä, §Ò?§ä§ï§ï§Ý§é §ã§ï§ä§Ô§ï§Ý§Ô§ï§ï§Ô §ç?§Ô§Ø??§Ý§ï§ç
¡ô §·?§ß §Ò§Ñ§Û§ç, §ç§Ñ§Þ§ä§â§Ñ§ß §ß§Ú§Û§Ô§ï§Þ§ê§Ú§Ø, §Ñ§Þ§î§Õ§â§Ñ§ç§Ñ§Õ §ã§å§â§Ñ§Ý§è§Ñ§ç
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§¢§Ñ§Ô§ê: ¡°§À§å §Ù§Ñ§Ñ§ç §Ó§ï?¡± ? ¡°§¿§ß§ï §Þ§ï§Õ§Ý§ï§Ô§Ú§Û§Ô §Ò?§ä§ï§ï§ç§ï§Õ §ñ§Þ§Ñ§â ?§Û§Ý §Ñ§Ø§Ú§Ý§Ý§Ñ§Ô§Ñ§Ñ,
§Ñ§ã§å§å§Õ§Ñ§Ý §ã§ï§Õ§ï§Ý §Ò§à§Õ§à§ç §Ò§à§Ý?¡±
¡°§Á§Þ§Ñ§â §ç§ï§â§ï§Ô§Ý§ï§Ô§Õ§ï§ç??§ß, §à§â§é§Ú§ß §Ò?§â§Õ??§Ý§ï§ç §Ó§ï?¡±
¡°§³§å§â§Ñ§Ô§é§Ú§Õ §ñ§Ñ§Ø §ã§ï§ä§Ô§ï§ß §Ò§à§Õ§à§Ø, §ñ§Þ§Ñ§â §ç§å§Ó§Ú§Ý§Ò§Ñ§â §Ô§Ñ§â§Ô§Ñ§ç §Ò§à§Ý?¡±
¡°§¢§å§â§å§å §à§Û§Ý§Ô§à§Ý§ä, §ä??§â?§Ô§Õ§Ý§Ú§Û§Ô §ç§ï§â§ç§ï§ß §Ù§Ñ§Ý§â§å§å§Ý§Ñ§ç §Ó§ï¡±
¡°§³§å§â§Ñ§Ô§é§Õ§í§ß §ç§ï§â§ç§ï§ß §ã§å§â§Ñ§Ý§è§Ñ§ç§å§Û§Õ §ã§å§â§Ô§Ñ§ç §Ó§ï?¡±
§³§å§â§Ñ§Ô§é: ¡°§¢§Ú §ð§å §ã§å§â§Ñ§ç §Ó§ï, §ñ§Ñ§Ø §ã§å§â§Ñ§ç §Ó§ï?¡±
¡° ?§Þ§ß?§ç §Þ§ï§Õ§Ý§ï§Ô§ï§ï §ç§ï§â§ç§ï§ß §ç§ï§â§ï§Ô§Ý§ï§ç §Ó§ï?¡±
¡°§¢§Ú §ð§å §ã§å§â§ã§Ñ§ß §Ò§ï?¡±
¡¾§·§Ú§é§ï§ï§Ý§Ú§Û§ß §ç§å§Ó§î§ã§Ô§Ñ§Ý §ç§Ú§Û§ç:¡¿
2. §¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç §ç§Ú§é§ï§ï§Ý
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§¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç- ¡°§¯§ï§ï§Ý§ä §ç§Ú§Û§ç¡±
§°§â§é§Ú§ß ?§Ö§Ú§Û§ß, §ã§å§â§Ñ§Ý§è§Ñ§Ô§é §ä?§Ó§ä ¡°§ã§Ñ§Û§ß §ç§Ú§é§ï§ï§Ý¡± §Ô§ï§Õ§ï§Ô §Ò§à§Ý §Ñ§ã§å§å§Õ§Ñ§Ý
§ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç ?§Û§Ý §ñ§Ó§è§Ñ§Ñ§â §Õ§Ñ§Þ§Ø§å§å§Ý§Ñ§ß §ã§å§â§Ñ§Ô§é§Ú§Õ §ç§ï§â§ç§ï§ß §ï§â§Ô§ï§è??§Ý§ï§ß
§Ò§à§Õ§à§Ø (?§Þ§ß?§ç §Þ§ï§Õ§Ý§ï§Ô, §ä§å§â§ê§Ý§Ñ§Ô§Ñ§Ñ §Ñ§ê§Ú§Ô§Ý§Ñ§Ø), §ç§Ñ§Þ§ä§â§Ñ§ß §ã§å§â§Ñ§Ý§è§Ñ§Ø,
§ß§ï§ï§Ý§ä §ç§Ú§Û§ç (§Þ§ï§Õ§Ý§ï§Ô §Ò?§ä§ï§ï§ç)-§Ú§Û§ß §Ñ§Þ§ä, §å§â§Þ§í§Ô §Þ§ï§Õ§ï§â§é §Ò§Ñ§Û§Ô§Ñ§Ñ§Ô§Ñ§Ñ§â
§ä§à§Õ§à§â§ç§à§Û§Ý§à§Ô§Õ§à§Ø §Ò§Ñ§Û§ß§Ñ. §³§å§â§Ñ§Ô§é§Õ§í§ß ??§â§ã§Õ?? §Ò?§ä§ï§ï§ã§ï§ß §Þ§ï§Õ§Ý§ï§Ô,
§ç§å§â§Ú§Þ§ä§Ý§å§å§Ý§Ø §Ò§å§Û §ä§å§â§ê§Ý§Ñ§Ô§Ñ §ß§î §Ú§Õ§ï§Ó§ç§ä§ï§Û§Ô§ï§ï§â §Ñ§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç,
§Ò?§ä§ï§ï§Ý§é §ã§ï§Õ§Ý§Ú§Û§Ô §ä?§â??§Ý§Ø §Ò§Ñ§Û§Õ§Ñ§Ô
Reference Twentieth century discovery
- Isaac Asimov (An American SF writer£© -
7
(1) §¡§ã§å§å§Õ§Ý§Ñ§Ñ §à§Û§Ý§Ô§à§ç
(2) §¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç §ä?§Ý?§Ó§Ý?§Ý§ä §ç§Ú§Û§ç
(3) §·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§Ó§ï§â §Ô§Ñ§â§Ô§Ñ§ç
(4) §º§Ú§Û§Õ§Ó§ï§â§ï§ï §ç§Ñ§â§î§è§å§å§Ý§Ñ§ç
(5) §¥?§Ô§ß§ï§Ý§ä(§³§å§â§Ñ§Ý§è§Ñ§ç§å§Û§Ô§Ñ§Ñ §ï§â§Ô§ï§ß §ç§Ñ§â§Ñ§ç)
3. §¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç §ç§Ú§é§ï§ï§Ý§Ú§Û§ß ?§Ö §ê§Ñ§ä
8
3. §¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç ?§Ö §ê§Ñ§ä
§¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç §ã§å§â§Ô§Ñ§Ý§ä§í§ß ?§Ö §ê§Ñ§ä: (§Ø§Ú§ê§ï§ï)
¢Ù §¡§ã§å§å§Õ§Ý§Ñ§Ñ §ä§à§Õ§à§â§ç§à§Û§Ý§à§ç, §à§Û§Ý§Ô§à§ç (§¡§ã§å§å§Õ§Ñ§Ý §Ò§à§Ý§à§ß
§ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç §Ñ§â§Ô§Ñ§Ñ §ä?§ã??§Ý?§ç, §ä?§Ý?§Ó§Ý?§ç)
¢Ú §¡§â§Ô§í§Ô §ç§ï§â§ï§Ô§Ø??§Ý§ï§ç, §Ô?§Û§è§ï§ä§Ô§ï§ç (§·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§Ó§ï§â
§Ô§Ñ§â§Ô§Ñ§ç)
¢Û §º§Ú§Û§Õ§Ó§ï§â§Ú§Û§Ô §ç§ñ§ß§Ñ§Ø, §ç§Ñ§â§î§è§å§å§Ý§Ñ§ç (§¢?§Ý§Ô§Ú§Û§ß
§ç§ï§Ý§ï§Ý§è??§Ý§ï§Ô §ç§Ú§Û§ç)
¢Ü ?§â §Õ?§ß§Ô §ß§ï§Ô§ä§Ô§ï§ß §Õ?§Ô§ß§ï§ç (§³§å§â§ã§Ñ§ß §Ù?§Û§Ý§ï§ï §ï§â§Ô§ï§ß §ç§Ñ§â§Ø,
§Õ?§Ô§ß§ï§Ý§ä §ç§Ú§Û§ç)
9
£¨1£©§¡§ã§å§å§Õ§Ý§Ñ§Ñ §ä§à§Õ§à§â§ç§à§Û§Ý§à§ç, §à§Û§Ý§Ô§à§ç
3. §¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§Ñ§ç ?§Ö §ê§Ñ§ä
1. §¡§ã§å§å§Õ§Ý§í§Ô (§Ñ§ã§å§å§Ý§ä§í§Ô) §à§Û§Ý§Ô§à§ç
2. §¡§ã§å§å§Õ§Ý§í§Ô §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç§ï§Õ §ê§Ñ§Ñ§â§Õ§Ý§Ñ§Ô§Ñ§ä§Ñ§Û
§Þ§ï§Õ§Ý§ï§Ô, §Þ§ï§Õ§ï§ï§Ý§ï§Ý §è§å§Ô§Ý§å§å§Ý§Ñ§ç (?§Þ§ß?§ç §Þ§ï§Õ§Ý§ï§Ô,
§ä§å§â§ê§Ý§Ñ§Ô§Ñ§Ñ§ã§Ñ§Ñ §ï§ß§ï§ç?? §Ñ§ã§å§å§Õ§Ý§í§Ô
§ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç§ï§Õ §ç§ï§â§ï§Ô§ä§ï§Û §Ò§Ñ§Û§Ô§Ñ§Ñ§Ô §ñ§Ý§Ô§Ñ§ß §ä§Ñ§ß§î§Ø,
§à§Ý§à§ç)
3. "§¡§ã§å§å§Õ§Ý§í§Ô §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç §Ñ§â§Ô§Ñ"-§Ñ§Ñ §ä?§Ý?§Ó§Ý?§ç,
"?§â §Õ?§ß"-§Ô §ä?§ã??§Ý?§ç, §ä§Ñ§Ñ§Þ§Ñ§Ô§Ý§Ñ§ç
¢Ú §¡§â§Ô§í§Ô §ç§ï§â§ï§Ô§Ø??§Ý§ï§ç, §Ô?§Û§è§ï§ä§Ô§ï§ç (§·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§Ó§ï§â
§Ô§Ñ§â§Ô§Ñ§ç) ?§Ö §ê§Ñ§ä§Ñ§ß§Õ:
1.§·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§Ý§ï§ï §ç§ï§â§ï§Ô§Ø??§Ý§ï§ç ?§Û§Ý §ñ§Ó§è, §ä??§ß§Ú§Û ?§â §Õ?§ß§Ô
§Ú§Ý§ï§â§ç§Ú§Û§Ý§ï§ç (§·?§ã§ß§ï§Ô§ä, §Õ§Ú§Ñ§Ô§â§Ñ§Þ, §ä§à§Þ§î§×§à/§Ý§à§Ô§Ú§Ü
§Ú§Ý§ï§â§ç§Ú§Û§Ý§ï§Ý, §Ù§à§ç§Ú§à§Þ§Ø, §Ù§å§â§Ñ§Ô§Ý§Ñ§Ý, §ã§ç§Ö§Þ.... )
2.§·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§ï§Ý, §ê§Ú§Û§Õ§Ó§ï§â§ï§ï §ß§ñ§Ô§ä§Ý§Ñ§ç, §ã§Ñ§Û§Ø§â§å§å§Ý§Ñ§ç
(§Ú§Õ§ï§Ó§ç§ä§ï§Û §ã§å§â§Ñ§Ý§è§Ñ§ç)
3."§·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§ï§Ý, §ê§Ú§Û§Õ§Ó§ï§â"-§ï§ï §ä§Ñ§ß§Ú§Ý§è§å§å§Ý§Ñ§ç§Ñ§Õ §Ò§ï§Ý§ä§Ô§ï§ç
11
£¨2£©Execution of and Considering about
¡°Individual Solutions¡±
3. Problem-Solving Coaching Processes
§·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§ï§Ý, §ê§Ú§Û§Õ§Ó§ï§â§ï§ï §ß§ñ§Ô§ä§Ý§Ñ§ç,
§ã§Ñ§Û§Ø§â§å§å§Ý§Ñ§ç (§Ú§Õ§ï§Ó§ç§ä§ï§Û §ã§å§â§Ñ§Ý§è§Ñ§ç§å§Û)
? §·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§Ý§ï§ï §ç§ï§â§ï§Ô§Ø??§Ý§ï§ç ?§Û§Ý §ñ§Ó§è,
§ä??§ß§Ú§Û ?§â §Õ?§ß§Ô §Ú§Ý§ï§â§ç§Ú§Û§Ý§ï§ç
(§·?§ã§ß§ï§Ô§ä, §Õ§Ú§Ñ§Ô§â§Ñ§Þ, §ä§à§Þ§î§×§à/§Ý§à§Ô§Ú§Ü §Ú§Ý§ï§â§ç§Ú§Û§Ý§ï§Ý, §Ù§à§ç§Ú§à§Þ§Ø,
§Ù§å§â§Ñ§Ô§Ý§Ñ§Ý, §ã§ç§Ö§Þ....
? "§·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§ï§Ý, §ê§Ú§Û§Õ§Ó§ï§â"-§ï§ï §ä§Ñ§ß§Ú§Ý§è§å§å§Ý§Ñ§ç§Ñ§Õ
§Ò§ï§Ý§ä§Ô§ï§ç
12
?§â §Õ?§ß§Ô §ç§Ñ§â§î§è§å§å§Ý§Ñ§ç
£¨3£© §¢?§Ý§Ô§Ú§Û§ß §ç§ï§Ý§ï§Ý§è??§Ý§ï§Ô §ç§Ú§Û§ç
3. Problem-Solving Coaching Processes
§¢?§Ý§Ô§Ú§Û§ß §ç§ï§Ý§ï§Ý§è??§Ý§ï§Ô §ç§Ú§Û§ç
§º§Ú§Û§Õ§ï§Ý §Ò?§â§Ú§Û§ß §à§ß§è§Ý§à§Ô, §Ù§à§ç§Ú§ã§ä§à§Û §Ò§Ñ§Û§Õ§Ñ§Ý, §Ý§à§Ô§Ú§Ü
?§ß§Õ§ï§ã§Ý§ï§Ý§Ú§Û§ß §ä§Ñ§Ý§Ñ§Ñ§â §ã§Ñ§ß§Ñ§Ý §Ò§à§Õ§Ý§à§à §ã§à§Ý§Ú§Ý§è§à§ç
?§â §Õ?§ß§ä§ï§Û, §à§ß§à§Ó§é§ä§à§Û §ê§Ú§Û§Õ§Ý??§Õ§Ú§Û§Ô §Ñ§ß§ç§Ñ§Ñ§â§é ?§Ù§ï§ç,
§ç§Ñ§â§î§è§å§å§Ý§Ñ§ç (§·§ñ§Ý§Ò§Ñ§â, §à§ß§à§Ó§é§ä§à§Û §ï§ã§ï§ç, §Ò§å§ã§Ñ§Õ §Ò§Ñ§Û§Ø §Ò§à§Ý§à§ç
§ç§å§Ó§Ú§Ý§Ò§Ñ§â§å§å§Õ, §ä§å§ç§Ñ§Û§ß §Ò§à§Ý§à§ß §Ö§â?§ß§ç§Ú§Û §ä§à§ç§Ú§à§Ý§Õ§Ý§í§Ô
§ï§â§Ô§ï§è??§Ý§ï§ç)
13
3. Problem-Solving Coaching Processes
(4) ?§â §Õ?§ß§Ô §ß§ï§Ô§ä§Ô§ï§ß §Õ?§Ô§ß§ï§ç (§³§å§â§ã§Ñ§ß §Ù?§Û§Ý§ï§ï
§ï§â§Ô§ï§ß §ç§Ñ§â§Ø, §Õ?§Ô§ß§ï§Ý§ä §ç§Ú§Û§ç) ?§Ö §ê§Ñ§ä§Ñ§ß§Õ:
?§¡§ã§å§å§Õ§Ý§í§Ô §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ã§ï§ß ?§Û§Ý §ñ§Ó§è§Ñ§Ñ §ï§â§Ô§ï§ß
§ç§Ñ§â§Ø, §ç§ñ§ß§Ñ§ß ?§Ù§ï§ç
??§ß??§Õ§â§Ú§Û§ß §ç§Ú§é§ï§ï§Ý§Ú§Û§ß §Ñ§Ô§å§å§Ý§Ô§Ñ, §à§Ý§Ø §Ñ§Ó§ã§Ñ§ß
§Þ§ï§Õ§Ý§ï§Ô§ï§ï §Ò§Ñ§ä§Ñ§Ý§Ô§Ñ§Ñ§Ø§å§å§Ý§Ñ§ß §Õ?§Ô§ß§ï§ç
?§º§Ú§ß§ï §Ñ§ã§å§å§Õ§Ñ§Ý §Õ§ï§Ó§ê??§Ý§ï§ç §Ù§ï§â§ï§Ô
14
§¡§ã§å§å§Õ§Ñ§Ý
§ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç§ï§Õ
§ã§å§â§Ñ§Ô§é§Õ§í§Ô §ã§å§â§Ô§Ñ§ç
?§Ö §ê§Ñ§ä
£¨3£©§¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç§ï§Õ §ã§å§â§Ô§Ñ§ç §ß§î
?§Þ§ß?§ç §Þ§ï§Õ§Ý§ï§Ô, §ä§å§â§ê§Ñ§Ô§í§Ô §ê§Ú§ß§ï §Þ§ï§Õ§Ý§ï§Ô
§Ò?§ä§ï§ï§ç§ï§Õ §Ñ§ê§Ú§Ô§Ý§Ñ§ç , §ç§å§Ó§Ú§â§Ô§Ñ§ß §ç§ï§â§ï§Ô§Ý§ï§Ø §ã§å§â§Ô§Ñ§ç
§¥§ï§Ó§ê??§Ý§ã§ï§ß §Ñ§ã§å§å§Õ§Ý§í§Ô §å§Õ§Ú§â§Õ§Ñ§Þ§Ø§Ú§Û§ß §Õ§Ñ§Ô§å§å
§ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§Ô§é§ï§ï§ã §Ñ§ã§å§å§Õ§Ý§í§Ô §Ú§Õ§ï§Ó§ç§ä§ï§Û
§ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§Ô§é §Ò§à§Ý§Ô§à§Ø §ç§å§Ó§Ú§â§Ô§Ñ§ç
§¡§ã§å§å§Õ§Ý§í§Ô ?§â§Ô?§ä§Ô?§ß, §Ö§â?§ß§ç§Ú§Û§Ý?§ç §é§Ñ§Õ§Ó§Ñ§â§ä
§ã§å§â§Ô§Ñ§ç
? §³§å§â§Ñ§Ô§é§Ú§Õ §ç§ï§â§ç§ï§ß §ï§â§Ô§ï§è??§Ý§ï§ß §Ò§à§Õ§à§Ø, ?§ß§Õ§ï§ã§Ý§ï§Ý§ä§ï§Û,
§Ý§à§Ô§Ú§Ü§ä§à§Û §ç§Ñ§ß§Õ§Ñ§Ø §Ò§Ñ§Û§Ô§Ñ§Ñ§Ô §Ñ§ß§ç§Ñ§Ñ§â§Ñ§ç
? §³§å§â§Ñ§Ô§é§Õ§Ñ§Ñ§ã §Ô§Ñ§â§é §Ò§å§Û §ã§Ñ§ß§Ñ§Ñ§ß§å§å§Õ§í§Ô ?§ß§ï§Ý§ï§ç
? §·??§ç§ï§Õ §ß§ï§Ô §Ò?§â§Ú§Û§ß §à§ß§è§Ý§à§Ô§Ú§Û§Ô §Þ§ï§Õ§â§ï§ç
? §Á§Ó§è§í§ß ?§ß§ï§Ý§Ô§ï§ï §ß§î §Õ?§ß §ä§Ñ§Ó§Ú§ç§Ñ§Õ §Ò§Ú§ê §ã§å§â§Ñ§Ô§é§Ú§Õ §ç§ï§â§ç§ï§ß
§Ò§à§Õ§à§Ø, §ã§å§â§Ñ§Ý§è§Ñ§Ø §Ò§Ñ§Û§Ô§Ñ§Ñ§Ô §Ú§Ý§â??§Ý§ï§ç§ï§Õ §é§Ú§Ô§Ý§ï§ß§ï §Ô§ï§Õ§Ô§Ú§Û§Ô
§Ñ§ß§ç§Ñ§Ñ§â§ß§Ñ §å§å
15
§·??§ç§ï§Õ §ß§ï§Ô §Ò?§â§Ú§Û§ß
§Ñ§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç ?§Û§Ý
§ñ§Ó§è§í§Ô §Ñ§Ø§Ú§Ô§Ý§Ñ§ç
4. §¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç §Ñ§â§Ô§Ñ §Ò§Ñ §ñ§Ó§è§í§ß ?§ß§ï§Ý§Ô§ï§ï
16
§®§ï§Õ§Ý§ï§Ô §é§Ñ§Õ§Ó§Ñ§â
§ï§Ù§ï§Þ§ê§Ú§Ø §Ò§Ñ§Û§Ô§Ñ§Ñ
§Ò§Ñ§Û§Õ§Ñ§Ý
§³§å§å§â§î §Þ§ï§Õ§Ý§ï§Ô, §é§Ñ§Õ§Ó§Ñ§â
§³§å§â§ã§ß§Ñ§Ñ §ç§ï§â§ï§Ô§Ý§ï§ç
§é§Ñ§Õ§Ó§Ñ§â
§³§ï§ä§Ô§ï§ß §Ò§à§Õ§à§ç, §ê§Ú§Û§Õ§Ó§ï§â
§Ô§Ñ§â§Ô§Ñ§ç, ??§â§Ú§Û§Ô??
§Ú§Ý§ï§â§ç§Ú§Û§Ý§ï§ç §é§Ñ§Õ§Ó§Ñ§â
§®§ï§Õ§Ý§ï§Ô, §é§Ñ§Õ§Ó§Ñ§â§í§Ô ?§ß§ï§Ý§ï§ç?
§³§å§â§ã§ß§Ñ§Ñ §ç§ï§â§ï§Ô§Ý§ï§ç §é§Ñ§Õ§Ó§Ñ§â§í§Ô ?§ß§ï§Ý§ï§ç
?§ß§ï§Ý§Ô§ï§ï§ß§Ú§Û 3 §Ô§à§Ý §é§Ú§Ô§Ý§ï§Ý
§³§å§â§Ñ§ç §ç?§ã§ï§Ý,
§ï§â§Þ§ï§Ý§Ù§Ý§ï§Ý
§³§å§â§Ñ§Ô§é§Õ§í§ß §ç§Ñ§ß§Õ§Ý§Ñ§Ô§Ñ,
§Ñ§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç§ï§Õ
??§â§Ú§Û§ß §ç?§ã§Ý§ï§ï§â,
§Ò?§ä§ï§ï§Ý§é§ï§ï§â §à§â§à§Ý§è§à§Ø
§Ò§Ñ§Û§Ô§Ñ§Ñ §ï§ã§ï§ç
¡°+¡±, ¡°-¡±, ¡°¡Á¡±, ¡°¡Â¡± §ä§ï§Þ§Õ§ï§Ô §Ñ§ê§Ú§Ô§Ý§Ñ§ß ?§ß§ï§ß §ä§ï§ß§è§ï§ä§Ô§ï§Ý ??§ã§Ô§ï§ß§ï
??. (§·§Ñ§Ñ§Ý§ä §Ñ§ê§Ú§Ô§Ý§Ñ§Ø §Ò§à§Ý§ß§à.)
£´¡õ£´¡õ£´¡õ£´£½£°
£´¡õ£´¡õ£´¡õ£´£½£·
£´¡õ£´¡õ£´¡õ£´£½£¸
£´¡õ£´¡õ£´¡õ£´£½£¹
£´¡õ£´¡õ£´¡õ£´£½£±¡­
(Break time)
18
¡ô §·§Ú§é§ï§ï§Ý §Ò§à§Ý §ã§å§â§Ñ§Ý§è§Ñ§Ô§ã§Õ§Ñ§Õ §Þ§ï§Õ§Ý§ï§Ô, §Þ§ï§Õ§ï§ï§Ý§ï§Ý
§Õ§Ñ§Þ§Ø§å§å§Ý§Ñ§ç §Ô§Ñ§Ù§Ñ§â §Ò§Ú§ê.
¡ô §·§Ú§é§ï§ï§Ý§Ú§Û§ß §ä§å§â§ê§Ú§Õ §ã§å§â§Ñ§Ý§è§Ñ§Ô§ã§Ñ§Õ §Ò§à§Õ§à§Ø, §ã§ï§ä§Ô§ï§ç
§à§â§é§Ú§ß §Ò?§â§Õ??§Ý§ï§ç
¡ô §¢§Ñ§Ô§ê§Ú§Û§ß ??§â§ï§Ô §Ò§à§Ý §ã§å§â§Ñ§Ô§é§Õ§í§ß §ã§ï§ä§Ô§ï§ß §Ò§à§Õ§à§ç
§é§Ñ§Õ§Ó§Ñ§â§í§Ô §ß§ï§Þ§ï§Ô§Õ??§Ý§ï§ç §ñ§Ó§Õ§Ñ§Ý §ð§Þ.
§·§Ú§é§ï§ï§Ý §Ò§à§Ý ??§â§Ú§Û§Ô§ï§ï §ç?§Ô§Ø??§Ý§ï§ç
§ä§Ñ§Ý§Ò§Ñ§â §ð§Þ.
§³§å§â§Ñ§Ô§é§Õ§í§ß §ç§Ñ§â§Ñ§ç ?§ß§è§Ô??§ã
§ç§Ñ§â§Ø, §ã§ï§ä§Ô§ï§ß §Ò§à§Õ§à§ç
2. Problem-solving type lessons
§¡§ã§å§å§Õ§Ñ§Ý §Õ§ï§Ó§ê??§Ý§ï§ç §Ñ§â§Ô§Ñ:
¢Ù §³§à§ß§Ú§â§ç§à§Ý§ä§à§Û §Ù§å§â§Ñ§Ô
¢Ú ?§Õ?§â §ä§å§ä§Þ§í§ß §Ñ§Þ§î§Õ§Ñ§Ý§ä§Ñ§Û §ç§à§Ý§Ò§à§ç l
¢Û §³§à§ß§Ú§â§ç§à§Ý§ä§à§Û §Ñ§ã§å§å§Ý§ä, §ç§Ñ§é§Ú§ß §Ø§Ú§Ô§ä§ï§Û
§ä§à§ç§Ú§à§Ý§Õ§à§Ý
¢Ü §º§Ú§Û§Õ§Ó§ï§â §Ô§Ñ§â§Ô§Ñ§ç §ç§ï§â§ï§Ô§è§ï§ï §Ò§Ú§Û
§Ò§à§Ý§Ô§à§ç
(1) §¡§ã§å§å§Õ§Ý§Ñ§Ñ §à§Û§Ý§Ô§à§ç, §ä§à§Þ§î§×§à§Ý§à§ç
?§Û§Ý §Ñ§Ø§Ú§Ý§Ý§Ñ§Ô§Ñ§Ñ
§¿§ç§Ý§ï§Ý
§¡§ã§å§å§Õ§Ñ§Ý
§Õ§ï§Ó§ê??§Ý§ï§ç:
?§â§ß?§Ý
Individual
solutions
Consideration
for solution
§¥?§Ô§ß§ï§Ý§ä
Summary
Review
?§Ù??§Ý§ï§ç §Ñ§â§Ô§Ñ §ç§ï§Ý§Ò§ï§â:
¢Ù §³§Ñ§Þ§Ò§Ñ§â
¢Ú §¸§Ñ§Ñ§ã
¢Û §Á§â§Ú§ç
¢Ü §¬§Ú§ß§à, §Õ?§â§ã §Ò§Ú§é§Ý§ï§Ô
3. §¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç §ç§Ú§é§ï§ï§Ý§Ú§Û§ß ?§Ö §ê§Ñ§ä
?§Û§Ý §Ñ§Ø§Ú§Ý§Ý§Ñ§Ô§Ñ§Ñ
§¿§ç§Ý§ï§Ý
§¡§ã§å§å§Õ§Ý§Ñ§Ñ §à§Û§Ý§Ô§à§ç:
§¡§ã§å§å§Õ§Ñ§Ý
§ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç
§ä?§Ý?§Ó§Ý?§Ô??
§Ô§Ñ§â§Ô§Ñ§ç
?§â§ß?§Ý
Individual
solutions
Consideration for
solution
§¥?§Ô§ß§ï§Ý§ä
Summary
Review
?§Þ§ß? §ã§å§â§ã§Ñ§ß §Ù?§Û§Ý§ï§ï §ã§ï§â§Ô§ï§ï§ß §ã§Ñ§ß§Ñ§ç
¢Ù §¡§ã§å§å§Õ§Ý§í§Ô §å§ß§ê§Ú§Ø §à§Û§Ý§Ô§à§ç
¢Ú §¡§ã§å§å§Õ§Ñ§Ý §Õ§ï§Ó§ê??§Ý§ã§ï§ß ?§Ô??§Ý§Ò§ï§â§Ú§Û§Ô
§Ò§Ú§é§Ú§ç
¢Û §¡§ã§å§å§Õ§Ý§í§Ô §Ù§å§â§Ñ§Ô§Ý§Ñ§Ø, §ä?§ã??§Ý?§ç
¢Ü§¡§ã§å§å§Õ§Ý§í§Ô §ã§ç§Ö§Þ, §Õ§Ú§Ñ§Ô§â§Ñ§Þ§Ñ§Ñ§â
§Ú§ï§Ý§â§ï§ç§Ú§Û§Ý§ï§ç
§·??§ç§ï§Õ §Ò?§â§Ú§Û§ß ?§Þ§ß?§ç,
§Þ§ï§Õ§Ý§ï§Ô, §ä§å§â§ê§Ý§Ñ§Ô§Ñ §ç§Ñ§â§Ú§Ý§è§Ñ§ß
§Ñ§Õ§Ú§Ý§Ô?§Û §Ô§ï§Õ§Ô§Ú§Û§Ô §Ñ§ß§ç§Ñ§Ñ§â§Ñ§ç
(2) §¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç ?§Û§Ý §Ñ§Ø§Ú§Ý§Ý§Ñ§Ô§Ñ§Ñ
3. §¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç §ç§Ú§é§ï§ï§Ý§Ú§Û§ß ?§Ö §ê§Ñ§ä
?§Û§Ý §Ñ§Ø§Ú§Ý§Ý§Ñ§Ô§Ñ§Ñ
§¿§ç§Ý§ï§Ý
Understanding the
Problem
Prospects for
problem-solving
?§â§ß?§Ý
§·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§Ó§ï§â
§Ô§Ñ§â§Ô§Ñ§ç
Consideration for
solution
§Õ?§Ô§ß§ï§Ý§ä
Summary
Review
<§¢§Ñ§Ô§ê§Ú§Û§ß §Õ§ï§Þ§Ø§Ý§ï§Ô>
¢Ù §³§å§â§Ñ§Ý§è§Ñ§ç §Ñ§â§Ô§Ñ §ä?§Ý?§Ó§ê??§Ô?§Û §ã§å§â§Ñ§Ô§é§Ú§Õ
¢Ú §¡§ã§å§å§Õ§Ý§í§Ô §ç§ï§â§ç§ï§ß §ê§Ú§Û§Õ§ï§ç§ï§ï §Þ§ï§Õ§ï§ç§Ô?§Û
§Ò§Ñ§Û§Ô§Ñ§Ñ §ã§å§â§Ñ§Ô§é§Ú§Õ
¢Û §¡§ã§å§å§Õ§Ý§í§Ô §ê§å§å§Õ §ê§Ú§Û§Õ§ï§Ø §é§Ñ§Õ§Ñ§ç §ã§å§â§Ñ§Ô§é§Ú§Õ
¢Ü §·§Ú§é§ï§ï§Ý§Ú§Û§Ô §ç§ï§â§ç§ï§ß §ã§Ñ§Û§Ø§â§å§å§Ý§Ñ§ç §Ó§ï?
<§³§å§â§Ñ§Ô§é§Õ§í§ß ?§Û§Ý §Ñ§Ø§Ú§Ý§Ý§Ñ§Ô§Ñ§Ñ>
? §³§å§â§Ñ§Ô§é §Ò?§â ??§â§Ú§Û§ß§ç??§â?? §Ñ§ã§å§å§Õ§Ý§í§ß
§ê§Ú§Û§Õ§Ý§Ú§Û§Ô §ï§â§Ø §à§Ý§à§ç
? §¥§Ñ§Ñ§Ý§Ô§Ñ§Ó§Ñ§â §Ô?§Û§è§ï§ä§Ô§ï§ç...
<§¡§ß§ç§Ñ§Ñ§â§Ñ§ç §Ù?§Û§Ý>
? §³§å§â§Ñ§Ô§é§Õ§Ñ§Õ §ç§ï§ä §Ú§ç §Ù?§Ó§Ý?§Ô?? ?§Ô?§ç §ß§î
§ä??§ß§Ú§Û §Ò§à§Õ§à§Ø §ã§ï§ä§Ô§ï§ç§ï§Õ §ã§Ñ§Ñ§Õ §Ò§à§Ý§Õ§à§Ô.
(3) §·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§Ó§ï§â §Ô§Ñ§â§Ô§Ñ§ç
3. §¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç §ç§Ú§é§ï§ï§Ý§Ú§Û§ß ?§Ö §ê§Ñ§ä
?§Û§Ý §Ñ§Ø§Ú§Ý§Ý§Ñ§Ô§Ñ§Ñ
§¿§ç§Ý§ï§Ý
Understanding the
Problem
Prospects for problem-
solving
?§â§ß?§Ý
Individual solutions
§·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§Ý??§Õ§ï§ï
§ç§Ñ§â§î§è§å§å§Ý§Ñ§ç
§¥?§Ô§ß§ï§Ý§ä
Summary
Review
<§·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§Ó§ï§â, ?§â §Õ?§ß§Ô§ï§ï
§ç§å§Ó§Ñ§Ñ§Ý§è§Ñ§ç, §ç§Ñ§â§î§è§å§å§Ý§Ñ§ç>
¢Ù §¿§ß§ï §ç§Ñ§â§Ú§å§Ý§ä §Ù?§Ó ???
¢Ú §¡§ã§å§Õ§Ý§í§Ô §ê§Ú§Û§Õ§ã§ï§ß §Ñ§â§Ô§Ñ §ß§î §ï§ß§Ô§Ú§Û§ß,
§ç§ñ§Ý§Ò§Ñ§â §Ò§Ñ§Û§ß§Ñ §å§å?
<?§â §Õ?§ß§Ô §Ò§Ñ§ä§Ñ§Ý§Ô§Ñ§Ñ§Ø§å§å§Ý§Ñ§ç, §ê§Ñ§Ý§Ô§Ñ§ç>
¢Ù ??§ß§ï§ï§ã §Ú§Ý?? §ç§ñ§Ò§Ñ§â §Ñ§â§Ô§Ñ §Ò§Ñ§Û§Ô§Ñ§Ñ
§Ò§à§Ý§à§Ó §å§å?
¢Ú ??§â §ç§Û§Ó§Ú§Ý§Ò§Ñ§â, §ã§Ñ§ß§Ñ§Ñ §Ò§Ñ§Û§ß§Ñ §å§å?
* §´?§â??§Ý§Ø §Ô§Ñ§â§Ñ§Ñ ?§â§Ô?§ã?§ß §ã§å§â§Ñ§Ô§é§Õ§í§Ô
§ï§ç§ï§Ý§Ø §Ñ§ã§å§å§Ô§Ñ§Ñ§Õ §Ò§Ñ§Û§ç §ß§î §ä§Ú§Û§Þ §é §ã§Ñ§Û§ß
§Ñ§â§Ô§Ñ §Ò§Ú§ê §ð§Þ.
§¢?§Ý§Ô§Ú§Û§ß
§ç§ï§Ý§ï§Ý§è??§Ý§ï§Ô
§¡§ß§Ô§Ú §ß§Ú§Û§ä§ï§ï§â
§ç§ï§Ý§ï§Ý§è§ï§ç
(4) §º§Ú§Û§Õ§Ó§ï§â??§Õ§ï§ï §ç§Ñ§â§î§è§å§å§Ý§Ñ§ç
?§Û§Ý §Ñ§Ø§Ú§Ý§Ý§Ñ§Ô§Ñ§Ñ
§ï§ç§Ý§ï§Ý
Understanding the
Problem
Prospects for
problem-solving
?§â§ß?§Ý
Individual
solutions
Consideration for
solution
§¥?§Ô§ß§ï§Ý§ä §¥?§Ô§ß§ï§Ý§ä
<§³§å§â§Ñ§Ý§è§Ñ§ç§å§Û§Ô §ï§â§Ô§ï§ß §Õ?§Ô§ß§ï§ç>
1. §¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç§Õ§ï§ï §ã§å§â§Ñ§Ô§é§Ú§Õ
§ç§ï§â§ç§ï§ß §ñ§Þ§Ñ§â ?§Û§Ý §Ñ§Ø§Ú§Ý§Ý§Ñ§Ô§Ñ§Ñ §ç§Ú§Û§Ó?
2. §¿§ß§ï §Ñ§â§Ô§Ñ§Ñ§â ??§â §ñ§Þ§Ñ§â §Ñ§ã§å§å§Õ§Ý§å§å§Õ§í§Ô
§ê§Ú§Û§Õ§ï§Ø §Ò§à§Ý§à§ç §Ò§à§Ý?
<§¥?§Ô§ß§ï§Ý§ä §ç§Ú§Û§ç>
¡°?§ß??§Õ§â§Ú§Û§ß §ç§Ú§é§ï§ï§Ý§ï§ï§â §Ò§Ú§Õ §ð§å §ã§å§â§Ñ§Ó?¡±
¡°??§â§Ú§Û§ß §ß§ï§ï§Ý§ä??§Õ§ï§ï §Ò§Ú§é§ï§ï§â§ï§Û¡±
¡ý
§·§Ú§é§ï§ï§Ý§Ú§Û§ß §Ù§à§â§Ú§Ý§Ô§à§Õ §é§Ú§Ô§Ý??§Ý§ï§ß §Õ?§Ô§ß§ï§Ý§ä§Ú§Û§Ô
§ä§Ý§Þ§î§×§à§Ý§à§ç
§³§å§â§Ñ§Ô§é§Õ§í§ß §Þ§ï§Õ§ã§ï§ß, §ã§å§â§ã§Ñ§ß §Ù?§Û§Ý,
§ç§Ñ§ß§Õ§Ý§Ñ§Ô§Ñ §Ù§ï§â§Ô§Ú§Û§Ô ?§ß§ï§Ý§Ø, §Õ?§Ô§ß§ï§Ø §Ò§à§Ý§ß§à.
(5) §¥?§Ô§ß§ï§Ý§ä (§ã§å§â§ã§ß§Ñ§Ñ §ï§â§Ô§ï§ß §ç§Ñ§â§Ñ§ç)
3. §¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç §ç§Ú§é§ï§ï§Ý§Ú§Û§ß ?§Ö §ê§Ñ§ä
24
Let us divide the figures
into two groups.
(Elementary school
2nd graders)
From classification, guide
students to definitions of figures.
Practical example
Points of teaching about ¡°concept of sets¡±
(classification)
25
Proportion of vertical
length to horizontal
length
£±:£²
Laying out figures
Grade 3 & 4
Materials & teaching aids
Cardboard, Scissors, Ruler
£¨Ex.£©10¡Á20
Development of home-made
teaching materials -1-
26
Let¡¯s make some shape with the six pieces
§´§Ñ§Ñ§Þ§Ñ§Ô§Ý§Ñ§Ý§´§å§â§ê§Ú§Ý§ä§¡§ã§å§å§Õ§Ñ§Ý
§¡§Ô§Ñ§Ñ§â§í§Ô §ç§Ñ§Ý§Ñ§Ñ§ç §Ò§Ñ
§ç?§â§Ô?§ç?§Õ §ï§Ù§Ý§ï§ç??§ß §ß§î
§ç§ï§â§ç§ï§ß ??§â§é§Ý?§Ô§Õ?§ç §Ò§à§Ý?
§·§Ñ§Ý§Ñ§Ñ§ç
§¿§Ù§Ý§ï§ç??§ß ??§â§é§Ý?§Ô§Õ?§ç§Ô?§Û
§¿§Ù§Ý§ï§ç??§ß §Ú§ç§ï§ã§ß§ï.
§¿§Ù§Ý§ï§ç??§ß §Ò§Ñ§Ô§Ñ§ã§ß§Ñ.
§·?§â§Ô?§ç
§¿§Ù§Ý§ï§ç??§ß ??§â§é§Ý?§Ô§Õ?§ç§Ô?§Û
§¿§Ù§Ý§ï§ç??§ß §Ò§Ñ§Ô§Ñ§ã§ß§Ñ.
§¿§Ù§Ý§ï§ç??§ß §Ú§ç§ï§ã§ß§ï.
§¿§ß§ï §Ñ§ã§å§å§Õ§Ý§í§ß §ç?§â§ï§ï§ß§Õ §Õ§Ñ§â§Ñ§Ñ§ç §ä§å§â§ê§Ú§Ý§ä§å§å§Õ §ç§Ú§Û§Ø §Ò§à§Ý§ß§à.
§¯§ï§Ô§Õ?§Ô§ï§ï§â §ä§å§â§ê§Ú§Ý§ä: §¸§ï§Ó§ï§â §å§ã§ß§í §ç§à§à§ã§à§ß §ç§å§Ó§Ñ§ß§è§Ñ§â §ã§Ñ§Ó§í§Ô §Ò?§Ô§Ý??§Õ §Þ?§ã§ä§ï§Û §ç?§Û§ä§ï§ß §å§ã§Ñ§ß§Õ §Õ?§â§ß§ï. §®§ï§Õ§ï§ï§Ø §Ú§ß§Ô§ï§ç§ï§Õ §ã§Ñ§Ó ?§â§é§Ú§Û§Ø, §ç§ï§Ý§Ò§ï§â§ï§ï
§Ñ§Ý§Õ§Ñ§ß §ï§Ù§Ý§ï§ç??§ß §ß§î §Ò§Ñ§Ô§Ñ§ã§ã§Ñ§ß §ß§î §Ñ§Ø§Ú§Ô§Ý§Ñ§Ô§Õ§Ñ§ß§Ñ. §¥§Ñ§â§Ñ§Ñ §ß§î §ç§Ñ§Ý§å§å§ß §å§ã§Ñ§ß§Õ §Õ?§â§ï§ç§ï§Õ §ã§Ñ§Ó §ï§â§Ô§ï§ï§Õ §ä§ï§ß§Ú§Û§Ø, §ï§Ù§Ý§ï§ç??§ß §Ú§ç§ï§ã§ã§ï§ß. §³§Ñ§Ó §ñ§Ñ§Ô§Ñ§Ñ§Õ ?§â§é§Ú§Û§Ø,
§ï§ã§Ó§ï§Ý §ä§ï§ß§Ú§Û§Ø §Ò§Ñ§Û§Ô§Ñ§Ñ §ä§Ñ§Ý§Ñ§Ñ§â §ã§å§â§Ñ§Ô§é§Ú§Õ §ä§Ñ§Ñ§Þ§Ñ§Ô§Ý§Ñ§Ø §ç§ï§Ý§ï§Ý§è??§Ý§ï§Ô §ç§Ú§Û§ß§ï.
2 §Õ§å§Ô§Ñ§Ñ§â §ä§å§â§ê§Ú§Ý§ä: §ç§à§à§ã§à§ß (§Õ§à§ä§à§â §ß§î §Ñ§Ô§Ñ§Ñ§â §Ò§Ñ§Û§Ô§Ñ§Ñ) §ç§à§à§ã§à§ß §Ò§Ñ§Ý§Ý§à§ß §Ò§å§ð§å §è§ï§Ó§ï§â §å§ã§ß§í §ã§Ñ§Ó§ß§í §Ñ§Þ§ã§â§í§Ô §Ñ§Ô§Ñ§Ñ§â§í§ß §Ò?§Þ§Ò?§Ý?§Ô§ß§Ú§Û §Ñ§Þ§ã§Ñ§â§ä§Ñ§Û
§ç§à§Ý§Ò§à§à§Õ §ç§Ñ§Ý§å§å§ß §å§ã§Ñ§ß§Õ §Õ?§â§Ø "§Õ§å§Ý§Ñ§Ñ§è§å§å§Ý§Ñ§ç¡± §Ò§Ñ §Þ?§ã§ä§ï§Û §ç§ï§Û§ä§ï§ß §å§ã§Ñ§Õ §Õ?§â§Ø ¡°§Õ§Ñ§Ñ§â§å§å§Ý§ß§Ñ¡±. §·§Ñ§Ý§Ñ§Ñ§ç§Ñ§Õ §Ñ§Ô§Ñ§Ñ§â§í§ß §Ò?§Þ§Ò?§Ý?§Ô §â?? §Ñ§Ô§Ñ§Ñ§â ?§â§ï§Ô§Õ§ï§ß
§à§â§Ø §ä§ï§Ý§ï§ç §Ò§Ñ §ç?§â§Ô?§ç?§Õ §Ñ§Ô§Ñ§Ñ§â§í§ß §Ò?§Þ§Ò?§Ý?§Ô§ä §à§â§Ø §Ú§â§ã§ï§ß §Ñ§Ô§Ñ§Ñ§â §Ò§å§è§Ñ§Ñ§Õ §Ý§à§ß§ç §â§å§å §ã§à§â§à§Ô§Õ§à§ß §à§â§à§ç §Ò§Ñ §Ò??§â §Ñ§Ô§Ñ§Ñ§â§í§ß §Ò?§Þ§Ò?§Ý§Ô§Ú§Û§Ô §é ??§â§Ú§Û§Ô §ß§î
§Õ§à§ä§à§Ô§ê §ã§à§â§à§ß §Ñ§Ó§é §Þ§Ñ§Ô§Ñ§Õ§Ô?§Û. §¿§Õ§Ô§ï§ï§â §ä§å§â§ê§Ú§Ý§ä§å§å§Õ§í§ß ?§â §Õ?§ß§Ô §ç§ï§Ý§ï§Ý§è§ã§ï§ß§ï§ï§â §Ñ§Ô§Ñ§Ñ§â§í§ß §ï§Ù§Ý§ï§ç??§ß §ä§Ö§Þ§á§Ö§â§Ñ§ä§å§â§Ñ§Ñ§ã §ç§ï§â§ç§ï§ß §ç§Ñ§Þ§Ñ§Ñ§â§é §Ò§Ñ§Û§Ô§Ñ§Ñ§Ô
§ç??§ç§Õ??§Õ §Ñ§Þ§Ñ§â§ç§Ñ§ß §à§Û§Ý§Ô§à§Ø, §Õ?§Ô§ß§ï§Ý§ä§ï§ï §Ô§Ñ§â§Ô§Ñ§ß§Ñ.
§¥?§Ô§ß§ï§Ý§ä: §¡§Ô§Ñ§Ñ§â§í§Ô §ç§Ñ§Ý§Ñ§Ñ§ç§Ñ§Õ §ï§Ù§Ý§ï§ç??§ß §ß§î §Ú§ç§ã§ï§ç §Ò§Ñ §ç?§â§Ô?§ç?§Õ §ï§Ù§Ý§ï§ç??§ß §ß§î §Ò§Ñ§Ô§Ñ§ã§é §Ò§Ñ§Û§ß§Ñ.
297
Which has the bigger mouth?
A B
(1) Size of Angles
30
a
c
b
Angle
(2) Rotation Angle
20 §Õ§Ñ§ç§î §Ô§å§â§Ó§Ñ§Ý§Ø§Ú§ß §ç§ï§Õ§ï§ß §Õ§å§Ô§å§Û§Ô§Ñ§Ñ§ã §Ò?§â§Õ§ï§ç §Ó§ï?
§¿§ß§ï §Ñ§ã§å§å§Õ§Ý§í§Ô §ç§ï§Õ§Õ?§Ô§ï§ï§â §Ñ§ß§Ô§Ú§Û§ß §ñ§Þ§Ñ§â §ç§Ú§é§ï§ï§Ý
§Õ§ï§ï§â §Õ§ï§Ó§ê??§Ý§Ø §Ò§à§Ý§à§ç §Ó§ï?
§¡§ã§å§å§Õ§Ý§í§Ô §ç§ï§â§ç§ï§ß §Ö§â?§ß§ç§Ú§Û§Ý§Ø §Ò§à§Ý§à§ç §Ó§ï?
120 §Õ§å§Ô§å§Û§Ô§Ñ§Ñ§ã §Ò?§ä§ï§ç §Ô§å§â§Ó§Ñ§Ý§Ø§Ú§ß §ç§ï§Õ§Õ?§Ô§ï§ï§â§ä §Ò§Ñ§Û§ç §Ó§ï?
N §Õ?§Ô§ï§ï§â§ç §Ô§å§â§Ó§Ñ§Ý§Ø§ß§í §Õ§å§Ô§å§Û§ß §ä§à§à§Ô §à§Ý§à§ç §ä§à§Þ§î§×§à §Ù§à§ç§Ú§à§Ô§à§à§â§à§Û.
§¿§ß§ï §ä§à§Þ§î§×§à§Ô ??§â §ð§å§ß§Õ §ç§ï§â§ï§Ô§Ý§ï§Ø §Ò§à§Ý§à§ç §Ó§ï?
33
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and the horizontal rows??? Each answer is 18.
3 5 8 91 4 76 102
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¡ô Line 1~9 cards, and add up the vertical row,
the horizontal row, and diagonal rows???
Each answer is 15.
35
(1) Patterns Made by Origami Paper
36
The Rule of
discover
37
BackFront
¡ñ¡ñ
Le temps
(Table) 1 2 3 4
Le temps
(Le dos) 12 11
(2) Mysterious Clock
38
See the changes in the slide-show
Change in time
Change in water volume (depth)
Proportional
relationship
Materials & teaching
aids
PowerPoint ºÝºÝߣs
Understanding corresponding
changes in numbers and volume
Development of home-made
teaching materials -5-
39
A rectangular water tank is filled with water.
The chart shows the depth after every 5 minute.
Time (1 min.) 5 10 15 20 25 30
Water depth
(cm) 2 4 6 8 10 12
40
2 ©M
1
minutes
41
2 ©M
2
minutes
42
2 ©M
3
minutes
43
2 ©M
4
minutes
44
5
minutes
2 ©M
45
I¡¯m going to guess
your birthday!
Break Mathematics is mysterious
I¡¯m a magician!
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  • 10. ¢Ú §¡§â§Ô§í§Ô §ç§ï§â§ï§Ô§Ø??§Ý§ï§ç, §Ô?§Û§è§ï§ä§Ô§ï§ç (§·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§Ó§ï§â §Ô§Ñ§â§Ô§Ñ§ç) ?§Ö §ê§Ñ§ä§Ñ§ß§Õ: 1.§·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§Ý§ï§ï §ç§ï§â§ï§Ô§Ø??§Ý§ï§ç ?§Û§Ý §ñ§Ó§è, §ä??§ß§Ú§Û ?§â §Õ?§ß§Ô §Ú§Ý§ï§â§ç§Ú§Û§Ý§ï§ç (§·?§ã§ß§ï§Ô§ä, §Õ§Ú§Ñ§Ô§â§Ñ§Þ, §ä§à§Þ§î§×§à/§Ý§à§Ô§Ú§Ü §Ú§Ý§ï§â§ç§Ú§Û§Ý§ï§Ý, §Ù§à§ç§Ú§à§Þ§Ø, §Ù§å§â§Ñ§Ô§Ý§Ñ§Ý, §ã§ç§Ö§Þ.... ) 2.§·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§ï§Ý, §ê§Ú§Û§Õ§Ó§ï§â§ï§ï §ß§ñ§Ô§ä§Ý§Ñ§ç, §ã§Ñ§Û§Ø§â§å§å§Ý§Ñ§ç (§Ú§Õ§ï§Ó§ç§ä§ï§Û §ã§å§â§Ñ§Ý§è§Ñ§ç) 3."§·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§ï§Ý, §ê§Ú§Û§Õ§Ó§ï§â"-§ï§ï §ä§Ñ§ß§Ú§Ý§è§å§å§Ý§Ñ§ç§Ñ§Õ §Ò§ï§Ý§ä§Ô§ï§ç
  • 11. 11 £¨2£©Execution of and Considering about ¡°Individual Solutions¡± 3. Problem-Solving Coaching Processes §·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§ï§Ý, §ê§Ú§Û§Õ§Ó§ï§â§ï§ï §ß§ñ§Ô§ä§Ý§Ñ§ç, §ã§Ñ§Û§Ø§â§å§å§Ý§Ñ§ç (§Ú§Õ§ï§Ó§ç§ä§ï§Û §ã§å§â§Ñ§Ý§è§Ñ§ç§å§Û) ? §·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§Ý§ï§ï §ç§ï§â§ï§Ô§Ø??§Ý§ï§ç ?§Û§Ý §ñ§Ó§è, §ä??§ß§Ú§Û ?§â §Õ?§ß§Ô §Ú§Ý§ï§â§ç§Ú§Û§Ý§ï§ç (§·?§ã§ß§ï§Ô§ä, §Õ§Ú§Ñ§Ô§â§Ñ§Þ, §ä§à§Þ§î§×§à/§Ý§à§Ô§Ú§Ü §Ú§Ý§ï§â§ç§Ú§Û§Ý§ï§Ý, §Ù§à§ç§Ú§à§Þ§Ø, §Ù§å§â§Ñ§Ô§Ý§Ñ§Ý, §ã§ç§Ö§Þ.... ? "§·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§ï§Ý, §ê§Ú§Û§Õ§Ó§ï§â"-§ï§ï §ä§Ñ§ß§Ú§Ý§è§å§å§Ý§Ñ§ç§Ñ§Õ §Ò§ï§Ý§ä§Ô§ï§ç
  • 12. 12 ?§â §Õ?§ß§Ô §ç§Ñ§â§î§è§å§å§Ý§Ñ§ç £¨3£© §¢?§Ý§Ô§Ú§Û§ß §ç§ï§Ý§ï§Ý§è??§Ý§ï§Ô §ç§Ú§Û§ç 3. Problem-Solving Coaching Processes §¢?§Ý§Ô§Ú§Û§ß §ç§ï§Ý§ï§Ý§è??§Ý§ï§Ô §ç§Ú§Û§ç §º§Ú§Û§Õ§ï§Ý §Ò?§â§Ú§Û§ß §à§ß§è§Ý§à§Ô, §Ù§à§ç§Ú§ã§ä§à§Û §Ò§Ñ§Û§Õ§Ñ§Ý, §Ý§à§Ô§Ú§Ü ?§ß§Õ§ï§ã§Ý§ï§Ý§Ú§Û§ß §ä§Ñ§Ý§Ñ§Ñ§â §ã§Ñ§ß§Ñ§Ý §Ò§à§Õ§Ý§à§à §ã§à§Ý§Ú§Ý§è§à§ç ?§â §Õ?§ß§ä§ï§Û, §à§ß§à§Ó§é§ä§à§Û §ê§Ú§Û§Õ§Ý??§Õ§Ú§Û§Ô §Ñ§ß§ç§Ñ§Ñ§â§é ?§Ù§ï§ç, §ç§Ñ§â§î§è§å§å§Ý§Ñ§ç (§·§ñ§Ý§Ò§Ñ§â, §à§ß§à§Ó§é§ä§à§Û §ï§ã§ï§ç, §Ò§å§ã§Ñ§Õ §Ò§Ñ§Û§Ø §Ò§à§Ý§à§ç §ç§å§Ó§Ú§Ý§Ò§Ñ§â§å§å§Õ, §ä§å§ç§Ñ§Û§ß §Ò§à§Ý§à§ß §Ö§â?§ß§ç§Ú§Û §ä§à§ç§Ú§à§Ý§Õ§Ý§í§Ô §ï§â§Ô§ï§è??§Ý§ï§ç)
  • 13. 13 3. Problem-Solving Coaching Processes (4) ?§â §Õ?§ß§Ô §ß§ï§Ô§ä§Ô§ï§ß §Õ?§Ô§ß§ï§ç (§³§å§â§ã§Ñ§ß §Ù?§Û§Ý§ï§ï §ï§â§Ô§ï§ß §ç§Ñ§â§Ø, §Õ?§Ô§ß§ï§Ý§ä §ç§Ú§Û§ç) ?§Ö §ê§Ñ§ä§Ñ§ß§Õ: ?§¡§ã§å§å§Õ§Ý§í§Ô §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ã§ï§ß ?§Û§Ý §ñ§Ó§è§Ñ§Ñ §ï§â§Ô§ï§ß §ç§Ñ§â§Ø, §ç§ñ§ß§Ñ§ß ?§Ù§ï§ç ??§ß??§Õ§â§Ú§Û§ß §ç§Ú§é§ï§ï§Ý§Ú§Û§ß §Ñ§Ô§å§å§Ý§Ô§Ñ, §à§Ý§Ø §Ñ§Ó§ã§Ñ§ß §Þ§ï§Õ§Ý§ï§Ô§ï§ï §Ò§Ñ§ä§Ñ§Ý§Ô§Ñ§Ñ§Ø§å§å§Ý§Ñ§ß §Õ?§Ô§ß§ï§ç ?§º§Ú§ß§ï §Ñ§ã§å§å§Õ§Ñ§Ý §Õ§ï§Ó§ê??§Ý§ï§ç §Ù§ï§â§ï§Ô
  • 14. 14 §¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç§ï§Õ §ã§å§â§Ñ§Ô§é§Õ§í§Ô §ã§å§â§Ô§Ñ§ç ?§Ö §ê§Ñ§ä £¨3£©§¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç§ï§Õ §ã§å§â§Ô§Ñ§ç §ß§î ?§Þ§ß?§ç §Þ§ï§Õ§Ý§ï§Ô, §ä§å§â§ê§Ñ§Ô§í§Ô §ê§Ú§ß§ï §Þ§ï§Õ§Ý§ï§Ô §Ò?§ä§ï§ï§ç§ï§Õ §Ñ§ê§Ú§Ô§Ý§Ñ§ç , §ç§å§Ó§Ú§â§Ô§Ñ§ß §ç§ï§â§ï§Ô§Ý§ï§Ø §ã§å§â§Ô§Ñ§ç §¥§ï§Ó§ê??§Ý§ã§ï§ß §Ñ§ã§å§å§Õ§Ý§í§Ô §å§Õ§Ú§â§Õ§Ñ§Þ§Ø§Ú§Û§ß §Õ§Ñ§Ô§å§å §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§Ô§é§ï§ï§ã §Ñ§ã§å§å§Õ§Ý§í§Ô §Ú§Õ§ï§Ó§ç§ä§ï§Û §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§Ô§é §Ò§à§Ý§Ô§à§Ø §ç§å§Ó§Ú§â§Ô§Ñ§ç §¡§ã§å§å§Õ§Ý§í§Ô ?§â§Ô?§ä§Ô?§ß, §Ö§â?§ß§ç§Ú§Û§Ý?§ç §é§Ñ§Õ§Ó§Ñ§â§ä §ã§å§â§Ô§Ñ§ç
  • 15. ? §³§å§â§Ñ§Ô§é§Ú§Õ §ç§ï§â§ç§ï§ß §ï§â§Ô§ï§è??§Ý§ï§ß §Ò§à§Õ§à§Ø, ?§ß§Õ§ï§ã§Ý§ï§Ý§ä§ï§Û, §Ý§à§Ô§Ú§Ü§ä§à§Û §ç§Ñ§ß§Õ§Ñ§Ø §Ò§Ñ§Û§Ô§Ñ§Ñ§Ô §Ñ§ß§ç§Ñ§Ñ§â§Ñ§ç ? §³§å§â§Ñ§Ô§é§Õ§Ñ§Ñ§ã §Ô§Ñ§â§é §Ò§å§Û §ã§Ñ§ß§Ñ§Ñ§ß§å§å§Õ§í§Ô ?§ß§ï§Ý§ï§ç ? §·??§ç§ï§Õ §ß§ï§Ô §Ò?§â§Ú§Û§ß §à§ß§è§Ý§à§Ô§Ú§Û§Ô §Þ§ï§Õ§â§ï§ç ? §Á§Ó§è§í§ß ?§ß§ï§Ý§Ô§ï§ï §ß§î §Õ?§ß §ä§Ñ§Ó§Ú§ç§Ñ§Õ §Ò§Ú§ê §ã§å§â§Ñ§Ô§é§Ú§Õ §ç§ï§â§ç§ï§ß §Ò§à§Õ§à§Ø, §ã§å§â§Ñ§Ý§è§Ñ§Ø §Ò§Ñ§Û§Ô§Ñ§Ñ§Ô §Ú§Ý§â??§Ý§ï§ç§ï§Õ §é§Ú§Ô§Ý§ï§ß§ï §Ô§ï§Õ§Ô§Ú§Û§Ô §Ñ§ß§ç§Ñ§Ñ§â§ß§Ñ §å§å 15 §·??§ç§ï§Õ §ß§ï§Ô §Ò?§â§Ú§Û§ß §Ñ§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç ?§Û§Ý §ñ§Ó§è§í§Ô §Ñ§Ø§Ú§Ô§Ý§Ñ§ç 4. §¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç §Ñ§â§Ô§Ñ §Ò§Ñ §ñ§Ó§è§í§ß ?§ß§ï§Ý§Ô§ï§ï
  • 16. 16 §®§ï§Õ§Ý§ï§Ô §é§Ñ§Õ§Ó§Ñ§â §ï§Ù§ï§Þ§ê§Ú§Ø §Ò§Ñ§Û§Ô§Ñ§Ñ §Ò§Ñ§Û§Õ§Ñ§Ý §³§å§å§â§î §Þ§ï§Õ§Ý§ï§Ô, §é§Ñ§Õ§Ó§Ñ§â §³§å§â§ã§ß§Ñ§Ñ §ç§ï§â§ï§Ô§Ý§ï§ç §é§Ñ§Õ§Ó§Ñ§â §³§ï§ä§Ô§ï§ß §Ò§à§Õ§à§ç, §ê§Ú§Û§Õ§Ó§ï§â §Ô§Ñ§â§Ô§Ñ§ç, ??§â§Ú§Û§Ô?? §Ú§Ý§ï§â§ç§Ú§Û§Ý§ï§ç §é§Ñ§Õ§Ó§Ñ§â §®§ï§Õ§Ý§ï§Ô, §é§Ñ§Õ§Ó§Ñ§â§í§Ô ?§ß§ï§Ý§ï§ç? §³§å§â§ã§ß§Ñ§Ñ §ç§ï§â§ï§Ô§Ý§ï§ç §é§Ñ§Õ§Ó§Ñ§â§í§Ô ?§ß§ï§Ý§ï§ç ?§ß§ï§Ý§Ô§ï§ï§ß§Ú§Û 3 §Ô§à§Ý §é§Ú§Ô§Ý§ï§Ý §³§å§â§Ñ§ç §ç?§ã§ï§Ý, §ï§â§Þ§ï§Ý§Ù§Ý§ï§Ý §³§å§â§Ñ§Ô§é§Õ§í§ß §ç§Ñ§ß§Õ§Ý§Ñ§Ô§Ñ, §Ñ§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç§ï§Õ ??§â§Ú§Û§ß §ç?§ã§Ý§ï§ï§â, §Ò?§ä§ï§ï§Ý§é§ï§ï§â §à§â§à§Ý§è§à§Ø §Ò§Ñ§Û§Ô§Ñ§Ñ §ï§ã§ï§ç
  • 17. ¡°+¡±, ¡°-¡±, ¡°¡Á¡±, ¡°¡Â¡± §ä§ï§Þ§Õ§ï§Ô §Ñ§ê§Ú§Ô§Ý§Ñ§ß ?§ß§ï§ß §ä§ï§ß§è§ï§ä§Ô§ï§Ý ??§ã§Ô§ï§ß§ï ??. (§·§Ñ§Ñ§Ý§ä §Ñ§ê§Ú§Ô§Ý§Ñ§Ø §Ò§à§Ý§ß§à.) £´¡õ£´¡õ£´¡õ£´£½£° £´¡õ£´¡õ£´¡õ£´£½£· £´¡õ£´¡õ£´¡õ£´£½£¸ £´¡õ£´¡õ£´¡õ£´£½£¹ £´¡õ£´¡õ£´¡õ£´£½£±¡­ (Break time)
  • 18. 18 ¡ô §·§Ú§é§ï§ï§Ý §Ò§à§Ý §ã§å§â§Ñ§Ý§è§Ñ§Ô§ã§Õ§Ñ§Õ §Þ§ï§Õ§Ý§ï§Ô, §Þ§ï§Õ§ï§ï§Ý§ï§Ý §Õ§Ñ§Þ§Ø§å§å§Ý§Ñ§ç §Ô§Ñ§Ù§Ñ§â §Ò§Ú§ê. ¡ô §·§Ú§é§ï§ï§Ý§Ú§Û§ß §ä§å§â§ê§Ú§Õ §ã§å§â§Ñ§Ý§è§Ñ§Ô§ã§Ñ§Õ §Ò§à§Õ§à§Ø, §ã§ï§ä§Ô§ï§ç §à§â§é§Ú§ß §Ò?§â§Õ??§Ý§ï§ç ¡ô §¢§Ñ§Ô§ê§Ú§Û§ß ??§â§ï§Ô §Ò§à§Ý §ã§å§â§Ñ§Ô§é§Õ§í§ß §ã§ï§ä§Ô§ï§ß §Ò§à§Õ§à§ç §é§Ñ§Õ§Ó§Ñ§â§í§Ô §ß§ï§Þ§ï§Ô§Õ??§Ý§ï§ç §ñ§Ó§Õ§Ñ§Ý §ð§Þ. §·§Ú§é§ï§ï§Ý §Ò§à§Ý ??§â§Ú§Û§Ô§ï§ï §ç?§Ô§Ø??§Ý§ï§ç §ä§Ñ§Ý§Ò§Ñ§â §ð§Þ. §³§å§â§Ñ§Ô§é§Õ§í§ß §ç§Ñ§â§Ñ§ç ?§ß§è§Ô??§ã §ç§Ñ§â§Ø, §ã§ï§ä§Ô§ï§ß §Ò§à§Õ§à§ç 2. Problem-solving type lessons
  • 19. §¡§ã§å§å§Õ§Ñ§Ý §Õ§ï§Ó§ê??§Ý§ï§ç §Ñ§â§Ô§Ñ: ¢Ù §³§à§ß§Ú§â§ç§à§Ý§ä§à§Û §Ù§å§â§Ñ§Ô ¢Ú ?§Õ?§â §ä§å§ä§Þ§í§ß §Ñ§Þ§î§Õ§Ñ§Ý§ä§Ñ§Û §ç§à§Ý§Ò§à§ç l ¢Û §³§à§ß§Ú§â§ç§à§Ý§ä§à§Û §Ñ§ã§å§å§Ý§ä, §ç§Ñ§é§Ú§ß §Ø§Ú§Ô§ä§ï§Û §ä§à§ç§Ú§à§Ý§Õ§à§Ý ¢Ü §º§Ú§Û§Õ§Ó§ï§â §Ô§Ñ§â§Ô§Ñ§ç §ç§ï§â§ï§Ô§è§ï§ï §Ò§Ú§Û §Ò§à§Ý§Ô§à§ç (1) §¡§ã§å§å§Õ§Ý§Ñ§Ñ §à§Û§Ý§Ô§à§ç, §ä§à§Þ§î§×§à§Ý§à§ç ?§Û§Ý §Ñ§Ø§Ú§Ý§Ý§Ñ§Ô§Ñ§Ñ §¿§ç§Ý§ï§Ý §¡§ã§å§å§Õ§Ñ§Ý §Õ§ï§Ó§ê??§Ý§ï§ç: ?§â§ß?§Ý Individual solutions Consideration for solution §¥?§Ô§ß§ï§Ý§ä Summary Review ?§Ù??§Ý§ï§ç §Ñ§â§Ô§Ñ §ç§ï§Ý§Ò§ï§â: ¢Ù §³§Ñ§Þ§Ò§Ñ§â ¢Ú §¸§Ñ§Ñ§ã ¢Û §Á§â§Ú§ç ¢Ü §¬§Ú§ß§à, §Õ?§â§ã §Ò§Ú§é§Ý§ï§Ô 3. §¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç §ç§Ú§é§ï§ï§Ý§Ú§Û§ß ?§Ö §ê§Ñ§ä
  • 20. ?§Û§Ý §Ñ§Ø§Ú§Ý§Ý§Ñ§Ô§Ñ§Ñ §¿§ç§Ý§ï§Ý §¡§ã§å§å§Õ§Ý§Ñ§Ñ §à§Û§Ý§Ô§à§ç: §¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç §ä?§Ý?§Ó§Ý?§Ô?? §Ô§Ñ§â§Ô§Ñ§ç ?§â§ß?§Ý Individual solutions Consideration for solution §¥?§Ô§ß§ï§Ý§ä Summary Review ?§Þ§ß? §ã§å§â§ã§Ñ§ß §Ù?§Û§Ý§ï§ï §ã§ï§â§Ô§ï§ï§ß §ã§Ñ§ß§Ñ§ç ¢Ù §¡§ã§å§å§Õ§Ý§í§Ô §å§ß§ê§Ú§Ø §à§Û§Ý§Ô§à§ç ¢Ú §¡§ã§å§å§Õ§Ñ§Ý §Õ§ï§Ó§ê??§Ý§ã§ï§ß ?§Ô??§Ý§Ò§ï§â§Ú§Û§Ô §Ò§Ú§é§Ú§ç ¢Û §¡§ã§å§å§Õ§Ý§í§Ô §Ù§å§â§Ñ§Ô§Ý§Ñ§Ø, §ä?§ã??§Ý?§ç ¢Ü§¡§ã§å§å§Õ§Ý§í§Ô §ã§ç§Ö§Þ, §Õ§Ú§Ñ§Ô§â§Ñ§Þ§Ñ§Ñ§â §Ú§ï§Ý§â§ï§ç§Ú§Û§Ý§ï§ç §·??§ç§ï§Õ §Ò?§â§Ú§Û§ß ?§Þ§ß?§ç, §Þ§ï§Õ§Ý§ï§Ô, §ä§å§â§ê§Ý§Ñ§Ô§Ñ §ç§Ñ§â§Ú§Ý§è§Ñ§ß §Ñ§Õ§Ú§Ý§Ô?§Û §Ô§ï§Õ§Ô§Ú§Û§Ô §Ñ§ß§ç§Ñ§Ñ§â§Ñ§ç (2) §¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç ?§Û§Ý §Ñ§Ø§Ú§Ý§Ý§Ñ§Ô§Ñ§Ñ 3. §¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç §ç§Ú§é§ï§ï§Ý§Ú§Û§ß ?§Ö §ê§Ñ§ä
  • 21. ?§Û§Ý §Ñ§Ø§Ú§Ý§Ý§Ñ§Ô§Ñ§Ñ §¿§ç§Ý§ï§Ý Understanding the Problem Prospects for problem-solving ?§â§ß?§Ý §·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§Ó§ï§â §Ô§Ñ§â§Ô§Ñ§ç Consideration for solution §Õ?§Ô§ß§ï§Ý§ä Summary Review <§¢§Ñ§Ô§ê§Ú§Û§ß §Õ§ï§Þ§Ø§Ý§ï§Ô> ¢Ù §³§å§â§Ñ§Ý§è§Ñ§ç §Ñ§â§Ô§Ñ §ä?§Ý?§Ó§ê??§Ô?§Û §ã§å§â§Ñ§Ô§é§Ú§Õ ¢Ú §¡§ã§å§å§Õ§Ý§í§Ô §ç§ï§â§ç§ï§ß §ê§Ú§Û§Õ§ï§ç§ï§ï §Þ§ï§Õ§ï§ç§Ô?§Û §Ò§Ñ§Û§Ô§Ñ§Ñ §ã§å§â§Ñ§Ô§é§Ú§Õ ¢Û §¡§ã§å§å§Õ§Ý§í§Ô §ê§å§å§Õ §ê§Ú§Û§Õ§ï§Ø §é§Ñ§Õ§Ñ§ç §ã§å§â§Ñ§Ô§é§Ú§Õ ¢Ü §·§Ú§é§ï§ï§Ý§Ú§Û§Ô §ç§ï§â§ç§ï§ß §ã§Ñ§Û§Ø§â§å§å§Ý§Ñ§ç §Ó§ï? <§³§å§â§Ñ§Ô§é§Õ§í§ß ?§Û§Ý §Ñ§Ø§Ú§Ý§Ý§Ñ§Ô§Ñ§Ñ> ? §³§å§â§Ñ§Ô§é §Ò?§â ??§â§Ú§Û§ß§ç??§â?? §Ñ§ã§å§å§Õ§Ý§í§ß §ê§Ú§Û§Õ§Ý§Ú§Û§Ô §ï§â§Ø §à§Ý§à§ç ? §¥§Ñ§Ñ§Ý§Ô§Ñ§Ó§Ñ§â §Ô?§Û§è§ï§ä§Ô§ï§ç... <§¡§ß§ç§Ñ§Ñ§â§Ñ§ç §Ù?§Û§Ý> ? §³§å§â§Ñ§Ô§é§Õ§Ñ§Õ §ç§ï§ä §Ú§ç §Ù?§Ó§Ý?§Ô?? ?§Ô?§ç §ß§î §ä??§ß§Ú§Û §Ò§à§Õ§à§Ø §ã§ï§ä§Ô§ï§ç§ï§Õ §ã§Ñ§Ñ§Õ §Ò§à§Ý§Õ§à§Ô. (3) §·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§Ó§ï§â §Ô§Ñ§â§Ô§Ñ§ç 3. §¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç §ç§Ú§é§ï§ï§Ý§Ú§Û§ß ?§Ö §ê§Ñ§ä
  • 22. ?§Û§Ý §Ñ§Ø§Ú§Ý§Ý§Ñ§Ô§Ñ§Ñ §¿§ç§Ý§ï§Ý Understanding the Problem Prospects for problem- solving ?§â§ß?§Ý Individual solutions §·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§Ý??§Õ§ï§ï §ç§Ñ§â§î§è§å§å§Ý§Ñ§ç §¥?§Ô§ß§ï§Ý§ä Summary Review <§·§å§Ó§Ú§Û§ß §ê§Ú§Û§Õ§Ó§ï§â, ?§â §Õ?§ß§Ô§ï§ï §ç§å§Ó§Ñ§Ñ§Ý§è§Ñ§ç, §ç§Ñ§â§î§è§å§å§Ý§Ñ§ç> ¢Ù §¿§ß§ï §ç§Ñ§â§Ú§å§Ý§ä §Ù?§Ó ??? ¢Ú §¡§ã§å§Õ§Ý§í§Ô §ê§Ú§Û§Õ§ã§ï§ß §Ñ§â§Ô§Ñ §ß§î §ï§ß§Ô§Ú§Û§ß, §ç§ñ§Ý§Ò§Ñ§â §Ò§Ñ§Û§ß§Ñ §å§å? <?§â §Õ?§ß§Ô §Ò§Ñ§ä§Ñ§Ý§Ô§Ñ§Ñ§Ø§å§å§Ý§Ñ§ç, §ê§Ñ§Ý§Ô§Ñ§ç> ¢Ù ??§ß§ï§ï§ã §Ú§Ý?? §ç§ñ§Ò§Ñ§â §Ñ§â§Ô§Ñ §Ò§Ñ§Û§Ô§Ñ§Ñ §Ò§à§Ý§à§Ó §å§å? ¢Ú ??§â §ç§Û§Ó§Ú§Ý§Ò§Ñ§â, §ã§Ñ§ß§Ñ§Ñ §Ò§Ñ§Û§ß§Ñ §å§å? * §´?§â??§Ý§Ø §Ô§Ñ§â§Ñ§Ñ ?§â§Ô?§ã?§ß §ã§å§â§Ñ§Ô§é§Õ§í§Ô §ï§ç§ï§Ý§Ø §Ñ§ã§å§å§Ô§Ñ§Ñ§Õ §Ò§Ñ§Û§ç §ß§î §ä§Ú§Û§Þ §é §ã§Ñ§Û§ß §Ñ§â§Ô§Ñ §Ò§Ú§ê §ð§Þ. §¢?§Ý§Ô§Ú§Û§ß §ç§ï§Ý§ï§Ý§è??§Ý§ï§Ô §¡§ß§Ô§Ú §ß§Ú§Û§ä§ï§ï§â §ç§ï§Ý§ï§Ý§è§ï§ç (4) §º§Ú§Û§Õ§Ó§ï§â??§Õ§ï§ï §ç§Ñ§â§î§è§å§å§Ý§Ñ§ç
  • 23. ?§Û§Ý §Ñ§Ø§Ú§Ý§Ý§Ñ§Ô§Ñ§Ñ §ï§ç§Ý§ï§Ý Understanding the Problem Prospects for problem-solving ?§â§ß?§Ý Individual solutions Consideration for solution §¥?§Ô§ß§ï§Ý§ä §¥?§Ô§ß§ï§Ý§ä <§³§å§â§Ñ§Ý§è§Ñ§ç§å§Û§Ô §ï§â§Ô§ï§ß §Õ?§Ô§ß§ï§ç> 1. §¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç§Õ§ï§ï §ã§å§â§Ñ§Ô§é§Ú§Õ §ç§ï§â§ç§ï§ß §ñ§Þ§Ñ§â ?§Û§Ý §Ñ§Ø§Ú§Ý§Ý§Ñ§Ô§Ñ§Ñ §ç§Ú§Û§Ó? 2. §¿§ß§ï §Ñ§â§Ô§Ñ§Ñ§â ??§â §ñ§Þ§Ñ§â §Ñ§ã§å§å§Õ§Ý§å§å§Õ§í§Ô §ê§Ú§Û§Õ§ï§Ø §Ò§à§Ý§à§ç §Ò§à§Ý? <§¥?§Ô§ß§ï§Ý§ä §ç§Ú§Û§ç> ¡°?§ß??§Õ§â§Ú§Û§ß §ç§Ú§é§ï§ï§Ý§ï§ï§â §Ò§Ú§Õ §ð§å §ã§å§â§Ñ§Ó?¡± ¡°??§â§Ú§Û§ß §ß§ï§ï§Ý§ä??§Õ§ï§ï §Ò§Ú§é§ï§ï§â§ï§Û¡± ¡ý §·§Ú§é§ï§ï§Ý§Ú§Û§ß §Ù§à§â§Ú§Ý§Ô§à§Õ §é§Ú§Ô§Ý??§Ý§ï§ß §Õ?§Ô§ß§ï§Ý§ä§Ú§Û§Ô §ä§Ý§Þ§î§×§à§Ý§à§ç §³§å§â§Ñ§Ô§é§Õ§í§ß §Þ§ï§Õ§ã§ï§ß, §ã§å§â§ã§Ñ§ß §Ù?§Û§Ý, §ç§Ñ§ß§Õ§Ý§Ñ§Ô§Ñ §Ù§ï§â§Ô§Ú§Û§Ô ?§ß§ï§Ý§Ø, §Õ?§Ô§ß§ï§Ø §Ò§à§Ý§ß§à. (5) §¥?§Ô§ß§ï§Ý§ä (§ã§å§â§ã§ß§Ñ§Ñ §ï§â§Ô§ï§ß §ç§Ñ§â§Ñ§ç) 3. §¡§ã§å§å§Õ§Ñ§Ý §ê§Ú§Û§Õ§Ó§ï§â§Ý§ï§ç §ç§Ú§é§ï§ï§Ý§Ú§Û§ß ?§Ö §ê§Ñ§ä
  • 24. 24 Let us divide the figures into two groups. (Elementary school 2nd graders) From classification, guide students to definitions of figures. Practical example Points of teaching about ¡°concept of sets¡± (classification)
  • 25. 25 Proportion of vertical length to horizontal length £±:£² Laying out figures Grade 3 & 4 Materials & teaching aids Cardboard, Scissors, Ruler £¨Ex.£©10¡Á20 Development of home-made teaching materials -1-
  • 26. 26 Let¡¯s make some shape with the six pieces
  • 27. §´§Ñ§Ñ§Þ§Ñ§Ô§Ý§Ñ§Ý§´§å§â§ê§Ú§Ý§ä§¡§ã§å§å§Õ§Ñ§Ý §¡§Ô§Ñ§Ñ§â§í§Ô §ç§Ñ§Ý§Ñ§Ñ§ç §Ò§Ñ §ç?§â§Ô?§ç?§Õ §ï§Ù§Ý§ï§ç??§ß §ß§î §ç§ï§â§ç§ï§ß ??§â§é§Ý?§Ô§Õ?§ç §Ò§à§Ý? §·§Ñ§Ý§Ñ§Ñ§ç §¿§Ù§Ý§ï§ç??§ß ??§â§é§Ý?§Ô§Õ?§ç§Ô?§Û §¿§Ù§Ý§ï§ç??§ß §Ú§ç§ï§ã§ß§ï. §¿§Ù§Ý§ï§ç??§ß §Ò§Ñ§Ô§Ñ§ã§ß§Ñ. §·?§â§Ô?§ç §¿§Ù§Ý§ï§ç??§ß ??§â§é§Ý?§Ô§Õ?§ç§Ô?§Û §¿§Ù§Ý§ï§ç??§ß §Ò§Ñ§Ô§Ñ§ã§ß§Ñ. §¿§Ù§Ý§ï§ç??§ß §Ú§ç§ï§ã§ß§ï.
  • 28. §¿§ß§ï §Ñ§ã§å§å§Õ§Ý§í§ß §ç?§â§ï§ï§ß§Õ §Õ§Ñ§â§Ñ§Ñ§ç §ä§å§â§ê§Ú§Ý§ä§å§å§Õ §ç§Ú§Û§Ø §Ò§à§Ý§ß§à. §¯§ï§Ô§Õ?§Ô§ï§ï§â §ä§å§â§ê§Ú§Ý§ä: §¸§ï§Ó§ï§â §å§ã§ß§í §ç§à§à§ã§à§ß §ç§å§Ó§Ñ§ß§è§Ñ§â §ã§Ñ§Ó§í§Ô §Ò?§Ô§Ý??§Õ §Þ?§ã§ä§ï§Û §ç?§Û§ä§ï§ß §å§ã§Ñ§ß§Õ §Õ?§â§ß§ï. §®§ï§Õ§ï§ï§Ø §Ú§ß§Ô§ï§ç§ï§Õ §ã§Ñ§Ó ?§â§é§Ú§Û§Ø, §ç§ï§Ý§Ò§ï§â§ï§ï §Ñ§Ý§Õ§Ñ§ß §ï§Ù§Ý§ï§ç??§ß §ß§î §Ò§Ñ§Ô§Ñ§ã§ã§Ñ§ß §ß§î §Ñ§Ø§Ú§Ô§Ý§Ñ§Ô§Õ§Ñ§ß§Ñ. §¥§Ñ§â§Ñ§Ñ §ß§î §ç§Ñ§Ý§å§å§ß §å§ã§Ñ§ß§Õ §Õ?§â§ï§ç§ï§Õ §ã§Ñ§Ó §ï§â§Ô§ï§ï§Õ §ä§ï§ß§Ú§Û§Ø, §ï§Ù§Ý§ï§ç??§ß §Ú§ç§ï§ã§ã§ï§ß. §³§Ñ§Ó §ñ§Ñ§Ô§Ñ§Ñ§Õ ?§â§é§Ú§Û§Ø, §ï§ã§Ó§ï§Ý §ä§ï§ß§Ú§Û§Ø §Ò§Ñ§Û§Ô§Ñ§Ñ §ä§Ñ§Ý§Ñ§Ñ§â §ã§å§â§Ñ§Ô§é§Ú§Õ §ä§Ñ§Ñ§Þ§Ñ§Ô§Ý§Ñ§Ø §ç§ï§Ý§ï§Ý§è??§Ý§ï§Ô §ç§Ú§Û§ß§ï. 2 §Õ§å§Ô§Ñ§Ñ§â §ä§å§â§ê§Ú§Ý§ä: §ç§à§à§ã§à§ß (§Õ§à§ä§à§â §ß§î §Ñ§Ô§Ñ§Ñ§â §Ò§Ñ§Û§Ô§Ñ§Ñ) §ç§à§à§ã§à§ß §Ò§Ñ§Ý§Ý§à§ß §Ò§å§ð§å §è§ï§Ó§ï§â §å§ã§ß§í §ã§Ñ§Ó§ß§í §Ñ§Þ§ã§â§í§Ô §Ñ§Ô§Ñ§Ñ§â§í§ß §Ò?§Þ§Ò?§Ý?§Ô§ß§Ú§Û §Ñ§Þ§ã§Ñ§â§ä§Ñ§Û §ç§à§Ý§Ò§à§à§Õ §ç§Ñ§Ý§å§å§ß §å§ã§Ñ§ß§Õ §Õ?§â§Ø "§Õ§å§Ý§Ñ§Ñ§è§å§å§Ý§Ñ§ç¡± §Ò§Ñ §Þ?§ã§ä§ï§Û §ç§ï§Û§ä§ï§ß §å§ã§Ñ§Õ §Õ?§â§Ø ¡°§Õ§Ñ§Ñ§â§å§å§Ý§ß§Ñ¡±. §·§Ñ§Ý§Ñ§Ñ§ç§Ñ§Õ §Ñ§Ô§Ñ§Ñ§â§í§ß §Ò?§Þ§Ò?§Ý?§Ô §â?? §Ñ§Ô§Ñ§Ñ§â ?§â§ï§Ô§Õ§ï§ß §à§â§Ø §ä§ï§Ý§ï§ç §Ò§Ñ §ç?§â§Ô?§ç?§Õ §Ñ§Ô§Ñ§Ñ§â§í§ß §Ò?§Þ§Ò?§Ý?§Ô§ä §à§â§Ø §Ú§â§ã§ï§ß §Ñ§Ô§Ñ§Ñ§â §Ò§å§è§Ñ§Ñ§Õ §Ý§à§ß§ç §â§å§å §ã§à§â§à§Ô§Õ§à§ß §à§â§à§ç §Ò§Ñ §Ò??§â §Ñ§Ô§Ñ§Ñ§â§í§ß §Ò?§Þ§Ò?§Ý§Ô§Ú§Û§Ô §é ??§â§Ú§Û§Ô §ß§î §Õ§à§ä§à§Ô§ê §ã§à§â§à§ß §Ñ§Ó§é §Þ§Ñ§Ô§Ñ§Õ§Ô?§Û. §¿§Õ§Ô§ï§ï§â §ä§å§â§ê§Ú§Ý§ä§å§å§Õ§í§ß ?§â §Õ?§ß§Ô §ç§ï§Ý§ï§Ý§è§ã§ï§ß§ï§ï§â §Ñ§Ô§Ñ§Ñ§â§í§ß §ï§Ù§Ý§ï§ç??§ß §ä§Ö§Þ§á§Ö§â§Ñ§ä§å§â§Ñ§Ñ§ã §ç§ï§â§ç§ï§ß §ç§Ñ§Þ§Ñ§Ñ§â§é §Ò§Ñ§Û§Ô§Ñ§Ñ§Ô §ç??§ç§Õ??§Õ §Ñ§Þ§Ñ§â§ç§Ñ§ß §à§Û§Ý§Ô§à§Ø, §Õ?§Ô§ß§ï§Ý§ä§ï§ï §Ô§Ñ§â§Ô§Ñ§ß§Ñ. §¥?§Ô§ß§ï§Ý§ä: §¡§Ô§Ñ§Ñ§â§í§Ô §ç§Ñ§Ý§Ñ§Ñ§ç§Ñ§Õ §ï§Ù§Ý§ï§ç??§ß §ß§î §Ú§ç§ã§ï§ç §Ò§Ñ §ç?§â§Ô?§ç?§Õ §ï§Ù§Ý§ï§ç??§ß §ß§î §Ò§Ñ§Ô§Ñ§ã§é §Ò§Ñ§Û§ß§Ñ.
  • 29. 297 Which has the bigger mouth? A B (1) Size of Angles
  • 31. 20 §Õ§Ñ§ç§î §Ô§å§â§Ó§Ñ§Ý§Ø§Ú§ß §ç§ï§Õ§ï§ß §Õ§å§Ô§å§Û§Ô§Ñ§Ñ§ã §Ò?§â§Õ§ï§ç §Ó§ï? §¿§ß§ï §Ñ§ã§å§å§Õ§Ý§í§Ô §ç§ï§Õ§Õ?§Ô§ï§ï§â §Ñ§ß§Ô§Ú§Û§ß §ñ§Þ§Ñ§â §ç§Ú§é§ï§ï§Ý §Õ§ï§ï§â §Õ§ï§Ó§ê??§Ý§Ø §Ò§à§Ý§à§ç §Ó§ï? §¡§ã§å§å§Õ§Ý§í§Ô §ç§ï§â§ç§ï§ß §Ö§â?§ß§ç§Ú§Û§Ý§Ø §Ò§à§Ý§à§ç §Ó§ï? 120 §Õ§å§Ô§å§Û§Ô§Ñ§Ñ§ã §Ò?§ä§ï§ç §Ô§å§â§Ó§Ñ§Ý§Ø§Ú§ß §ç§ï§Õ§Õ?§Ô§ï§ï§â§ä §Ò§Ñ§Û§ç §Ó§ï?
  • 32. N §Õ?§Ô§ï§ï§â§ç §Ô§å§â§Ó§Ñ§Ý§Ø§ß§í §Õ§å§Ô§å§Û§ß §ä§à§à§Ô §à§Ý§à§ç §ä§à§Þ§î§×§à §Ù§à§ç§Ú§à§Ô§à§à§â§à§Û. §¿§ß§ï §ä§à§Þ§î§×§à§Ô ??§â §ð§å§ß§Õ §ç§ï§â§ï§Ô§Ý§ï§Ø §Ò§à§Ý§à§ç §Ó§ï?
  • 33. 33 £±£¸ ¡ô Line 1~10 cards, and add up the vertical rows and the horizontal rows??? Each answer is 18. 3 5 8 91 4 76 102 £±£¸ £±£¸ £±£¸ £± £²£³ £´ £µ £¶£· £¸ £¹
  • 34. 34 £¸ £¸ £¸ £¸ £¸ £¸ £¸ £¸ £¸ ¡ô Line 1~9 cards, and add up the vertical row, the horizontal row, and diagonal rows??? Each answer is 15.
  • 35. 35 (1) Patterns Made by Origami Paper
  • 37. 37 BackFront ¡ñ¡ñ Le temps (Table) 1 2 3 4 Le temps (Le dos) 12 11 (2) Mysterious Clock
  • 38. 38 See the changes in the slide-show Change in time Change in water volume (depth) Proportional relationship Materials & teaching aids PowerPoint ºÝºÝߣs Understanding corresponding changes in numbers and volume Development of home-made teaching materials -5-
  • 39. 39 A rectangular water tank is filled with water. The chart shows the depth after every 5 minute. Time (1 min.) 5 10 15 20 25 30 Water depth (cm) 2 4 6 8 10 12
  • 45. 45 I¡¯m going to guess your birthday! Break Mathematics is mysterious I¡¯m a magician! M ¡Á£² £«£µ ¡Á£µ£° £«D

Editor's Notes

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