ᥘᥣᥙᥳ ᥟᥢ ᥝᥣ ᥘᥭᥳ ᥙᥥᥢ ᥐᥣᥢ ᥘᥥᥙ ᥞᥥᥢᥰ ᥘᥩᥒ ᥖᥨᥝ ᥘᥙᥳ (ᥟᥤᥒᥰ ᥐᥣ ᥘᥥᥖ: numbers)၊ ᥘᥩᥒ ᥘᥙᥳ ᥔᥩᥢᥱ ᥖᥣᥒᥰ ᥘᥛᥴ ᥖᥣᥒᥰ ᥟᥥᥱ ᥔᥥᥴ ᥓᥫᥳ ᥔᥥᥴ ᥙᥫᥒ (quantity)၊ ᥘᥩᥒ ᥖᥣᥒᥰ ᥐᥣᥒᥲ ᥐᥦᥙ (space)၊ ᥘᥩᥒ ᥐᥩᥱ ᥞᥥᥖᥱ ᥙᥫᥒ ᥞᥣᥒ ᥙᥫᥒ ᥚᥣᥒᥴ (structure)၊ ᥘᥩᥒ ᥘᥦᥐ ᥘᥣᥭ (change) ᥓᥫᥰ ᥘᥢᥳ ᥕᥝᥳ။ ᥖᥨᥝ ᥘᥙᥳ ᥟᥢ ᥝᥣ ᥘᥢᥳ ᥛᥢᥰ ᥛᥤᥰ ᥘᥛᥳ ᥐᥖᥳ ᥞᥥᥖᥱ ᥘᥭᥲ ᥔᥒᥴ ᥘᥣᥭ ᥘᥣᥭ၊ ᥑᥝᥴ ᥘᥒᥱ ᥐᥢ ᥞᥥᥖᥱ ᥞᥪᥴ ᥐᥩᥒᥳ ᥐᥣᥭᥱ ᥐᥙᥴ ᥖᥣᥛᥰ ᥐᥢ၊ ᥑᥝᥴ ᥘᥒᥱ ᥐᥢ ᥞᥥᥖᥱ ᥞᥪᥴ ᥘᥨᥝᥰ ᥘᥥᥰ ᥐᥢ၊ ᥘᥩᥢᥳ ᥛᥩᥢᥰ ᥛᥢᥰ ᥛᥤᥰ ᥘᥒᥱ ᥞᥪᥴ၊ ᥐᥙᥴ ᥐᥣᥭᥱ ᥘᥨᥭ ᥘᥩᥒ ᥙᥣᥭᥰ ᥘᥙᥳ ᥘᥢᥳ ᥑᥝᥴ ᥑᥝᥲ ᥙᥣᥰ ᥘᥭᥲ ᥘᥒᥱ ᥞᥪᥴ၊ ᥙᥫᥒ ᥞᥣᥒ ᥑᥝᥴ ᥙᥥᥢ ᥘᥒᥱ ᥞᥪᥴ၊ ᥘᥣᥭᥰ ᥖᥦᥐ ᥛᥢᥰ ᥙᥥᥢ ᥞᥪᥴ၊ ᥘᥣᥭᥰ ᥘᥦᥐ ᥘᥣᥭ ᥛᥢᥰ ᥙᥥᥢ ᥞᥪᥴ၊ ᥖᥥᥴ ᥘᥭᥲ ᥞᥥᥖᥱ ᥞᥪᥴ ᥙᥩᥒᥱ ᥓᥬ ᥘᥙᥳ ᥔᥩᥢᥱ ᥘᥢᥳ ᥕᥝᥳ။ ᥙᥣᥭᥰ ᥘᥙᥳ ᥟᥢ ᥝᥣ ᥘᥭᥳ ᥙᥥᥢ ᥐᥣᥢ ᥘᥥᥙ ᥞᥥᥢᥰ ᥘᥩᥒ ᥘᥙᥳ၊ ᥘᥩᥒ ᥔᥩᥢᥱ၊ ᥘᥩᥒ ᥖᥦᥐ၊ ᥘᥩᥒ ᥑᥣᥭᥳ ᥕᥣᥢᥴ ᥘᥤᥴ ᥖᥣᥒᥰ ᥐᥭ ᥓᥛ ᥞᥬᥲ ᥞᥧᥳ ᥖᥦᥖ ᥘᥦᥖ၊ ᥞᥣᥒ ᥚᥣᥒᥴ ᥟᥢ ᥘᥣᥛᥰ ᥘᥭᥲ ᥕᥣᥙᥱ ᥘᥢᥳ ᥞᥬᥲ ᥙᥩᥰ ᥓᥣᥒ ᥘᥣᥛᥰ ᥘᥭᥲ ᥞᥧᥳ ᥘᥭᥲ ᥓᥫᥰ ᥘᥢᥳ ᥔᥥᥴ ᥝᥣᥭᥰ ᥘᥒᥴ ᥛᥣᥰ ᥓᥒᥱ ᥑᥩᥐᥱ ᥑᥦᥐᥱ ᥘᥫᥐ ᥟᥝ ᥘᥩᥐᥴ ᥘᥣᥭᥰ ᥟᥢ ᥙᥥᥢ ᥘᥭᥲ ᥛᥢᥰ ᥟᥢ ᥛᥤᥰ ᥘᥩᥢᥳ ᥛᥢᥰ ᥟᥢ ᥛᥤᥰ ᥙᥐᥴ ᥙᥫᥒ ᥛᥢᥰ ᥘᥢᥳ ᥔᥥᥴ ᥘᥦᥲ ᥑᥪᥢᥲ ᥕᥬᥱ ᥛᥣᥰ ᥓᥢᥳ ᥘᥪᥒ ᥘᥦᥳ ᥓᥢᥳ ᥘᥫᥒ ᥘᥢᥳ ᥕᥝᥳ။ ᥚᥧᥱ ᥛᥤᥰ ᥙᥦᥒᥱ ᥕᥣᥱ ᥑᥝᥴ ᥖᥥᥳ ᥘᥥᥙ ᥞᥥᥢᥰ ᥖᥨᥭᥰ ᥘᥩᥒ ᥘᥩᥢᥳ ᥛᥩᥢᥰ ᥙᥫᥒ ᥙᥥᥢ ᥛᥢᥰ ᥔᥥᥴ ᥓᥒᥱ ᥑᥨᥒ ᥟᥩᥐᥱ ᥛᥣᥰ ᥘᥩᥐᥴ ᥘᥣᥭᥰ ᥘᥙᥳ ᥔᥩᥢᥱ ᥛᥢᥰ ᥕᥝᥳ။ ᥙᥧᥢ ᥖᥣᥱ ᥙᥣᥭᥰ ᥔᥣᥭ၊ ᥙᥣᥭᥰ ᥑᥫᥒ ᥓᥣᥐ၊ ᥙᥣᥭᥰ ᥛᥨᥝᥴ ᥕᥣ၊ ᥙᥣᥭᥰ ᥔᥣᥭ ᥙᥣᥭᥰ ᥛᥫᥒᥰ ᥑᥝᥴ ᥓᥫᥰ ᥘᥢᥳ ᥙᥣᥭᥰ ᥘᥙᥳ ᥘᥭᥳ ᥟᥛᥱ ᥛᥤᥰ ᥖᥪᥢᥰ ᥟᥛᥱ ᥙᥥᥢ ᥘᥦᥰ ᥙᥣᥭᥰ ᥘᥙᥳ ᥘᥭᥳ ᥘᥭᥲ ᥝᥣ ᥛᥢᥰ ᥙᥥᥢ ᥑᥫᥒ ᥕᥤᥙᥱ ᥘᥨᥒᥴ ᥘᥬᥰ ᥐᥛᥱ ᥚᥣᥱ ᥟᥢ ᥘᥫᥒ ᥕᥧᥱ။[1]
ᥖᥛ ᥖᥤ ᥖᥨᥝ ᥘᥙᥳ ᥘᥢᥳᥘᥦᥳ ᥔᥒᥴ၊ ᥘᥛᥳ ᥐᥖᥳ ᥐᥣ ᥑᥢᥴ ᥟᥢ ᥑᥝᥴ ᥛᥤᥰ ᥝᥭᥳ ᥔᥥᥴ ᥙᥩᥒ ᥙᥥᥢ ᥘᥭᥲ ᥘᥢᥳ ᥘᥦᥰ ᥔᥒᥴ၊ ᥘᥩᥒ ᥑᥝᥴ ᥘᥒᥱ ᥐᥢ ᥐᥙᥴ ᥔᥪᥙᥱ ᥐᥩᥒᥳ ᥐᥣᥭᥱ ᥐᥢ ᥘᥢᥳᥘᥦᥳ ᥔᥒᥴ၊ ᥘᥩᥒ ᥑᥝᥴ ᥑᥨᥢᥰ ᥘᥨᥝᥰ ᥐᥢ ᥘᥢᥳ ᥘᥦᥳ ᥘᥩᥢᥳ ᥛᥩᥢᥰ ᥑᥝᥴ ᥔᥥᥴ ᥟᥛᥱ ᥐᥣᥰ ᥖᥨᥝ ᥘᥙᥳ ᥓᥫᥰ ᥘᥢᥳ ᥑᥝᥴ ᥞᥥᥖᥱ ᥞᥪᥴ ᥛᥤᥰ ᥘᥛᥳ ᥐᥖᥳ ᥓᥧᥐᥴ ᥕᥣᥢᥴ ᥖᥒ ᥖᥨᥝ ᥘᥭᥰ ᥓᥩᥛᥰ ᥞᥤᥛᥰ ᥞᥩᥛᥰ ᥑᥝᥴ၊ ᥑᥝᥴ ᥞᥥᥖᥱ ᥞᥪᥴ ᥘᥦᥐ ᥘᥣᥭ ᥙᥥᥢ ᥐᥣᥱ ᥘᥭᥲ ᥘᥒᥱ ᥞᥪᥴ ᥘᥭᥴ ᥔᥥᥴ ᥙᥥᥢ ᥘᥩᥒ ᥘᥥᥙ ᥞᥥᥢᥰ ᥓᥫᥰ ᥘᥭᥳ ᥕᥝᥳ။ ᥐᥩᥭᥰ ᥐᥣ ᥐᥣᥙ ᥙᥣᥢ ᥕᥣᥛᥰ ᥘᥥᥝ ᥙᥣᥭᥰ ᥘᥙᥳ ᥘᥭᥳ ᥘᥪᥐ ᥘᥛᥱ ᥐᥛᥱ ᥚᥤᥱ ᥛᥣᥰ ᥖᥥᥳ ᥖᥥᥳ ᥔᥥᥴ ᥘᥧᥐ ᥖᥤ ᥟᥝ ᥓᥬ ᥘᥙᥳ ᥔᥩᥢᥱ ᥘᥢᥳ ᥔᥥᥴ ᥔᥩᥢᥱ ᥘᥙᥳ ᥙᥣᥰ ᥘᥨᥭ ᥘᥩᥒ ᥞᥣᥒ ᥚᥣᥒᥴ ᥘᥥᥐᥳ ᥕᥬᥱ ᥐᥭ ᥓᥛ ᥐᥣᥒᥲ ᥐᥦᥙ ᥘᥬᥰ ᥘᥩᥰ ᥐᥣ ᥘᥨᥒᥴ ᥘᥭᥳ ᥕᥧᥱ။
ᥙᥣᥭᥰ ᥘᥙᥳ ᥟᥢ ᥝᥣ ᥘᥢᥳ ᥛᥢᥰ ᥙᥩᥒᥱ ᥔᥒᥴ ᥖᥥᥳ ᥖᥥᥳ ᥘᥭᥴ ᥞᥬᥲ ᥐᥨᥢᥰ ᥖᥒᥰ ᥘᥛᥴ ᥙᥩᥰ ᥚᥩᥛᥳ ᥐᥢ ᥔᥥᥴ ᥘᥣᥖ ᥟᥩᥐᥱ ᥘᥭᥲ ᥖᥤ ᥙᥩᥒᥱ ᥛᥢᥰ ᥘᥢᥳ ᥕᥒᥰ ᥙᥭᥱ ᥛᥤᥰ ᥐᥩᥢᥱ။ ᥐᥨᥢᥰ ᥓᥫᥰ ᥟᥢ ᥘᥙᥳ ᥔᥩᥢᥱ ᥞᥥᥖᥱ ᥐᥣᥢ ᥛᥢᥰ ᥕᥧᥱ ᥓᥫᥰ ᥘᥢᥳ ᥐᥩᥲ ᥑᥝᥴ ᥖᥩ ᥟᥛᥱ ᥑᥝᥲ ᥓᥬ ᥘᥫᥴ ᥑᥨᥝᥲ ᥗᥣᥛᥴ ᥟᥢ ᥘᥭᥳ။ ᥐᥩᥭᥰ ᥐᥣ ᥚᥧᥱ ᥘᥨᥒᥳ ᥘᥦᥢᥱ ᥑᥝᥴ ᥓᥫᥒᥳ ᥘᥒᥱ ᥐᥥᥱ ᥘᥤᥱ ᥘᥤᥱ ᥕᥨᥝᥱ (1564-1642) ᥖᥥᥳ ᥘᥣᥖ ᥝᥣ “ᥔᥣᥱ ᥚᥣᥱ ᥝᥣᥳ ᥖᥣᥰ ᥘᥣᥰ ᥘᥢᥳ ᥔᥒᥴ ᥝᥣ ᥟᥝ ᥖᥦᥛᥲ ᥙᥥᥢ ᥚᥪᥢᥴ ᥗᥛᥰ ᥝᥭᥳ ᥓᥪᥒ ᥘᥤᥐ ᥟᥢ ᥖᥦᥛᥲ ᥛᥢᥰ ᥘᥢᥳ ᥖᥥᥴ ᥙᥥᥢ ᥘᥤᥐ ᥙᥣᥭᥰ ᥘᥙᥳ ᥐᥩᥭᥰ” ᥘᥭᥴ ᥕᥝᥳ။ ᥚᥧᥱ ᥘᥨᥒᥳ ᥘᥦᥢᥱ ᥙᥣᥭᥰ ᥘᥙᥳ ᥐᥣᥰ ᥘᥣ ᥜᥤᥰ ᥖᥤᥖᥳ ᥐᥩᥖᥳ (1777-1855) ᥘᥣᥖ ᥝᥣ “ᥙᥣᥭᥰ ᥘᥙᥳ ᥘᥭᥳ ᥙᥥᥢ ᥘᥣᥒᥰ ᥞᥨᥝᥴ ᥑᥛᥰ ᥘᥨᥒᥴ ᥙᥣᥭᥰ ᥔᥣᥭ” ᥘᥭᥴ ᥕᥝᥳ။ ᥚᥧᥱ ᥘᥨᥒᥳ ᥘᥦᥢᥱ ᥙᥣᥭᥰ ᥘᥙᥳ ᥙᥤᥢᥱ ᥓᥣᥱ ᥛᥤᥢᥱ ᥙᥤᥱ (1809-1880) ᥘᥣᥖᥝᥣ “ᥙᥣᥭᥰ ᥘᥙᥳ ᥘᥭᥳ ᥙᥥᥢ ᥙᥣᥭᥰ ᥔᥣᥭ ᥟᥢ ᥖᥦᥛᥲ ᥛᥣᥭᥴ ᥖᥛᥰ ᥝᥣᥒᥰ ᥘᥭᥲ ᥚᥩᥢᥰ ᥘᥤ ᥟᥢ ᥖᥦᥖ ᥘᥦᥖ ᥛᥢᥰ” ᥘᥭᥴ ᥕᥝᥳ။
ᥘᥬᥰ ᥐᥛᥱ ᥚᥣᥱ ᥘᥭᥳ ᥙᥣᥭᥰ ᥘᥙᥳ ᥘᥢᥳ ᥑᥝᥲ ᥙᥥᥢ ᥘᥩᥒ ᥐᥣᥢ ᥙᥨᥒ ᥔᥩᥢᥴ ᥟᥢ ᥘᥫᥒ ᥟᥢ ᥟᥛᥱ ᥛᥤᥰ ᥟᥛᥱ ᥙᥥᥢ ᥔᥥᥴ ᥟᥛᥱ ᥐᥣᥰ ᥖᥛ ᥖᥤ ᥙᥣᥭᥰ ᥔᥣᥭ ᥔᥣᥱ ᥚᥣᥱ ᥝᥣᥳ၊ ᥙᥣᥭᥰ ᥓᥣᥒ ᥟᥤᥢᥱ ᥓᥤᥢᥱ ᥢᥤᥱ ᥕᥣᥱ၊ ᥙᥣᥭᥰ ᥛᥨᥝᥴ ᥕᥣ ᥘᥦᥳ ᥙᥣᥭᥰ ᥔᥣᥭ ᥖᥨᥒᥱ ᥝᥨᥒᥰ ᥐᥨᥢᥰ ᥓᥫᥰ ᥘᥢᥳ ᥙᥣᥭᥰ ᥘᥙᥳ ᥢᥭᥳ ᥙᥥᥢ ᥑᥫᥒ ᥕᥤᥙᥴ ᥘᥤ ᥘᥨᥒᥴ ᥙᥧᥢ ᥖᥣᥱ ᥖᥒᥰ ᥐᥛᥱ ᥚᥣᥱ ᥕᥝᥳ။
ᥙᥫᥒ ᥟᥤᥒ
- ↑ Mura, Roberta (December 1993). "Images of Mathematics Held by University Teachers of Mathematical Sciences". Educational Studies in Mathematics. 25 (4): 375–85.