{"id":29146,"date":"2021-12-03T15:02:43","date_gmt":"2021-12-03T12:02:43","guid":{"rendered":"https:\/\/www.difference.news\/edu\/%d9%84%d9%86%d8%aa%d8%b9%d8%b1%d9%81-%d8%b9%d9%84%d9%89-%d9%86%d9%85%d9%88%d8%b0%d8%ac-%d9%81%d8%a7%d9%86-%d9%87%d9%8a%d9%84-%d9%81%d9%8a-%d8%aa%d8%af%d8%b1%d9%8a%d8%b3-%d8%a7%d9%84%d9%87%d9%86%d8%af\/"},"modified":"2021-12-03T15:02:43","modified_gmt":"2021-12-03T12:02:43","slug":"%d9%84%d9%86%d8%aa%d8%b9%d8%b1%d9%81-%d8%b9%d9%84%d9%89-%d9%86%d9%85%d9%88%d8%b0%d8%ac-%d9%81%d8%a7%d9%86-%d9%87%d9%8a%d9%84-%d9%81%d9%8a-%d8%aa%d8%af%d8%b1%d9%8a%d8%b3-%d8%a7%d9%84%d9%87%d9%86%d8%af","status":"publish","type":"post","link":"https:\/\/www.difference.news\/edu\/%d9%84%d9%86%d8%aa%d8%b9%d8%b1%d9%81-%d8%b9%d9%84%d9%89-%d9%86%d9%85%d9%88%d8%b0%d8%ac-%d9%81%d8%a7%d9%86-%d9%87%d9%8a%d9%84-%d9%81%d9%8a-%d8%aa%d8%af%d8%b1%d9%8a%d8%b3-%d8%a7%d9%84%d9%87%d9%86%d8%af\/","title":{"rendered":"\u0644\u0646\u062a\u0639\u0631\u0641 \u0639\u0644\u0649 \u0646\u0645\u0648\u0630\u062c \u0641\u0627\u0646 \u0647\u064a\u0644 \u0641\u064a \u062a\u062f\u0631\u064a\u0633 \u0627\u0644\u0647\u0646\u062f\u0633\u0629\u00a0"},"content":{"rendered":"<p> <div class=\"e3lan e3lan-in-post1\"><center><br>\r\n<!-- f.336.280 -->\r\n<ins class=\"adsbygoogle\"\r\n    style=\"display:inline-block;width:336px;height:280px\"\r\n    data-ad-client=\"ca-pub-0007602327247913\"\r\n    data-ad-slot=\"8804957031\"\r\n    data-full-width-responsive=\"true\"><\/ins>\r\n<script>\r\n     (adsbygoogle = window.adsbygoogle || []).push({});\r\n<\/script>\r\n<br>\r\n<\/center><\/div>\n<br \/>\u0644\u0646\u062a\u0639\u0631\u0641 \u0639\u0644\u0649 \u0646\u0645\u0648\u0630\u062c \u0641\u0627\u0646 \u0647\u064a\u0644 \u0641\u064a \u062a\u062f\u0631\u064a\u0633 \u0627\u0644\u0647\u0646\u062f\u0633\u0629\u00a0<br \/>\n<br \/>\u062a\u0639\u0644\u064a\u0645 \u062c\u062f\u064a\u062f\u060c \u0623\u0641\u0643\u0627\u0631 \u062a\u0639\u0644\u064a\u0645\u064a\u0629 \u062c\u062f\u064a\u062f\u0629\u060c \u062a\u0639\u0644\u064a\u0645 \u0645\u062e\u062a\u0644\u0641: \u0644\u0646\u062a\u0639\u0631\u0641 \u0639\u0644\u0649 \u0646\u0645\u0648\u0630\u062c \u0641\u0627\u0646 \u0647\u064a\u0644 \u0641\u064a \u062a\u062f\u0631\u064a\u0633 \u0627\u0644\u0647\u0646\u062f\u0633\u0629\u00a0 \u0627\u0644\u062a\u0639\u0644\u064a\u0645 \u0641\u064a \u0648\u0632\u0627\u0631\u0629 \u0627\u0644\u062a\u0631\u0628\u064a\u0629 \u0648\u0627\u0644\u062a\u0639\u0644\u064a\u0645 \u0627\u0644\u0639\u0627\u0644\u064a<br \/>\n<br \/>#\u0644\u0646\u062a\u0639\u0631\u0641 #\u0639\u0644\u0649 #\u0646\u0645\u0648\u0630\u062c #\u0641\u0627\u0646 #\u0647\u064a\u0644 #\u0641\u064a #\u062a\u062f\u0631\u064a\u0633 #\u0627\u0644\u0647\u0646\u062f\u0633\u0629<br \/>\n<br \/><img decoding=\"async\" loading=\"lazy\" width=\"618\" height=\"309\" src=\"https:\/\/i0.wp.com\/www.difference.news\/edu\/wp-content\/uploads\/2021\/12\/\u0644\u0646\u062a\u0639\u0631\u0641-\u0639\u0644\u0649-\u0646\u0645\u0648\u0630\u062c-\u0641\u0627\u0646-\u0647\u064a\u0644-\u0641\u064a-\u062a\u062f\u0631\u064a\u0633-\u0627\u0644\u0647\u0646\u062f\u0633\u0629.jpg?resize=618%2C309&#038;ssl=1\" class=\"attachment-slider size-slider wp-post-image\" alt=\"\u0646\u0645\u0648\u0630\u062c \u0641\u0627\u0646 \u0647\u064a\u0644 \u0641\u064a \u062a\u062f\u0631\u064a\u0633 \u0627\u0644\u0647\u0646\u062f\u0633\u0629\u00a0\" data-recalc-dims=\"1\"><\/p><div id=\"ez-toc-container\" class=\"ez-toc-v2_0_57_1 counter-hierarchy ez-toc-counter-rtl ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title \" >\u0627\u0644\u0645\u062d\u062a\u0648\u064a\u0627\u062a<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\" role=\"button\"><label for=\"item-6a263758d3736\" ><span class=\"\"><span style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/label><input aria-label=\"Toggle\" aria-label=\"item-6a263758d3736\" style='display:none' type=\"checkbox\" id=\"item-6a263758d3736\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.difference.news\/edu\/%d9%84%d9%86%d8%aa%d8%b9%d8%b1%d9%81-%d8%b9%d9%84%d9%89-%d9%86%d9%85%d9%88%d8%b0%d8%ac-%d9%81%d8%a7%d9%86-%d9%87%d9%8a%d9%84-%d9%81%d9%8a-%d8%aa%d8%af%d8%b1%d9%8a%d8%b3-%d8%a7%d9%84%d9%87%d9%86%d8%af\/#%D8%A7%D9%84%D9%85%D8%B3%D8%AA%D9%88%D9%89_1_%D8%A7%D9%84%D9%85%D8%B3%D8%AA%D9%88%D9%89_%D8%A7%D9%84%D8%AA%D8%B5%D9%88%D8%B1%D9%8A_Visualization\" title=\"\u0627\u0644\u0645\u0633\u062a\u0648\u0649 (1): \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u062a\u0635\u0648\u0631\u064a Visualization\">\u0627\u0644\u0645\u0633\u062a\u0648\u0649 (1): \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u062a\u0635\u0648\u0631\u064a Visualization<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.difference.news\/edu\/%d9%84%d9%86%d8%aa%d8%b9%d8%b1%d9%81-%d8%b9%d9%84%d9%89-%d9%86%d9%85%d9%88%d8%b0%d8%ac-%d9%81%d8%a7%d9%86-%d9%87%d9%8a%d9%84-%d9%81%d9%8a-%d8%aa%d8%af%d8%b1%d9%8a%d8%b3-%d8%a7%d9%84%d9%87%d9%86%d8%af\/#%D8%A7%D9%84%D9%85%D8%B3%D8%AA%D9%88%D9%89_2_%D8%A7%D9%84%D9%85%D8%B3%D8%AA%D9%88%D9%89_%D8%A7%D9%84%D8%AA%D8%AD%D9%84%D9%8A%D9%84%D9%8A_Analysis\" title=\"\u0627\u0644\u0645\u0633\u062a\u0648\u0649 (2): \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a Analysis\">\u0627\u0644\u0645\u0633\u062a\u0648\u0649 (2): \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a Analysis<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.difference.news\/edu\/%d9%84%d9%86%d8%aa%d8%b9%d8%b1%d9%81-%d8%b9%d9%84%d9%89-%d9%86%d9%85%d9%88%d8%b0%d8%ac-%d9%81%d8%a7%d9%86-%d9%87%d9%8a%d9%84-%d9%81%d9%8a-%d8%aa%d8%af%d8%b1%d9%8a%d8%b3-%d8%a7%d9%84%d9%87%d9%86%d8%af\/#%D8%A7%D9%84%D9%85%D8%B3%D8%AA%D9%88%D9%89_3_%D9%85%D8%B3%D8%AA%D9%88%D9%89_%D8%A7%D9%84%D8%A7%D8%B3%D8%AA%D9%86%D8%AA%D8%A7%D8%AC_%D8%BA%D9%8A%D8%B1_%D8%A7%D9%84%D8%B4%D9%83%D9%84%D9%8A_Informal_deduction\" title=\"\u0627\u0644\u0645\u0633\u062a\u0648\u0649 (3): \u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c \u063a\u064a\u0631 \u0627\u0644\u0634\u0643\u0644\u064a Informal deduction\">\u0627\u0644\u0645\u0633\u062a\u0648\u0649 (3): \u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c \u063a\u064a\u0631 \u0627\u0644\u0634\u0643\u0644\u064a Informal deduction<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.difference.news\/edu\/%d9%84%d9%86%d8%aa%d8%b9%d8%b1%d9%81-%d8%b9%d9%84%d9%89-%d9%86%d9%85%d9%88%d8%b0%d8%ac-%d9%81%d8%a7%d9%86-%d9%87%d9%8a%d9%84-%d9%81%d9%8a-%d8%aa%d8%af%d8%b1%d9%8a%d8%b3-%d8%a7%d9%84%d9%87%d9%86%d8%af\/#%D8%A7%D9%84%D9%85%D8%B3%D8%AA%D9%88%D9%89_4_%D9%85%D8%B3%D8%AA%D9%88%D9%89_%D8%A7%D9%84%D8%A7%D8%B3%D8%AA%D9%86%D8%AA%D8%A7%D8%AC_%D8%A7%D9%84%D8%B4%D9%83%D9%84%D9%8A_Formal_deduction\" title=\"\u0627\u0644\u0645\u0633\u062a\u0648\u0649 (4): \u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0627\u0644\u0634\u0643\u0644\u064a Formal deduction\">\u0627\u0644\u0645\u0633\u062a\u0648\u0649 (4): \u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0627\u0644\u0634\u0643\u0644\u064a Formal deduction<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.difference.news\/edu\/%d9%84%d9%86%d8%aa%d8%b9%d8%b1%d9%81-%d8%b9%d9%84%d9%89-%d9%86%d9%85%d9%88%d8%b0%d8%ac-%d9%81%d8%a7%d9%86-%d9%87%d9%8a%d9%84-%d9%81%d9%8a-%d8%aa%d8%af%d8%b1%d9%8a%d8%b3-%d8%a7%d9%84%d9%87%d9%86%d8%af\/#%D8%A7%D9%84%D9%85%D8%B3%D8%AA%D9%88%D9%89_5_%D9%85%D8%B3%D8%AA%D9%88%D9%89_%D8%A7%D9%84%D8%AF%D9%82%D8%A9_%D9%88%D8%A7%D9%84%D8%B5%D8%B1%D8%A7%D9%85%D8%A9_Precision_and_Rigor\" title=\"\u0627\u0644\u0645\u0633\u062a\u0648\u0649 (5): \u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u062f\u0642\u0629 \u0648\u0627\u0644\u0635\u0631\u0627\u0645\u0629 Precision and Rigor\">\u0627\u0644\u0645\u0633\u062a\u0648\u0649 (5): \u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u062f\u0642\u0629 \u0648\u0627\u0644\u0635\u0631\u0627\u0645\u0629 Precision and Rigor<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.difference.news\/edu\/%d9%84%d9%86%d8%aa%d8%b9%d8%b1%d9%81-%d8%b9%d9%84%d9%89-%d9%86%d9%85%d9%88%d8%b0%d8%ac-%d9%81%d8%a7%d9%86-%d9%87%d9%8a%d9%84-%d9%81%d9%8a-%d8%aa%d8%af%d8%b1%d9%8a%d8%b3-%d8%a7%d9%84%d9%87%d9%86%d8%af\/#%D9%83%D8%A7%D8%AA%D8%A8_%D8%A7%D9%84%D9%85%D9%82%D8%A7%D9%84\" title=\" \u0643\u0627\u062a\u0628 \u0627\u0644\u0645\u0642\u0627\u0644 \"> \u0643\u0627\u062a\u0628 \u0627\u0644\u0645\u0642\u0627\u0644 <\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n\n<div class=\"post-inner\">\n<div class=\"entry\">\n<span style=\"color: #333399;\"><strong>\u062a\u0648\u0637\u0626\u0629\u00a0<\/strong><\/span><\/p>\n<p>\u062a\u0645\u062a\u0632\u062c \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0628\u062d\u064a\u0627\u062a\u0646\u0627 \u0627\u0644\u064a\u0648\u0645\u064a\u0629 \u0648\u0641\u064a \u0643\u0644 \u0645\u0627 \u064a\u062d\u064a\u0637 \u0628\u0646\u0627 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621\u060c 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\u0644\u0647\u0630\u0627 \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u064a\u0635\u0644\u0647 \u0625\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u0627\u062a \u0627\u0644\u0639\u0644\u064a\u0627: \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644 \u0643\u062a\u0627\u0628\u0629 \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u060c \u0641\u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0647\u0646\u062f\u0633\u064a \u0641\u0643\u0631\u0629 \u0645\u0639\u0642\u062f\u0629 \u062a\u062a\u0637\u0644\u0628 \u0645\u0633\u062a\u0648\u064a\u0627\u062a \u0628\u0635\u0631\u064a\u0629 \u0648\u062a\u062d\u0644\u064a\u0644\u064a\u0629 \u0639\u062f\u0629 \u0643\u064a \u062a\u064f\u0643\u062a\u0633\u0628.<\/p>\n<p>\u0644\u0642\u062f \u0644\u0641\u062a \u0646\u0645\u0648\u0630\u062c \u0641\u0627\u0646 \u0647\u064a\u0644 (Van Hiele) \u0623\u0646\u0638\u0627\u0631 \u0627\u0644\u0645\u0634\u062a\u063a\u0644\u064a\u0646 \u0641\u064a \u0645\u062c\u0627\u0644 \u062a\u0639\u0644\u064a\u0645 \u0648\u062a\u0639\u0644\u0645 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0641\u064a \u0643\u0644 \u0645\u0646 \u0647\u0648\u0644\u0646\u062f\u0627 \u0648\u0627\u0644\u0627\u062a\u062d\u0627\u062f \u0627\u0644\u0633\u0648\u0641\u064a\u062a\u064a \u0633\u0627\u0628\u0642\u0627 \u0648\u062f\u0648\u0644 \u0623\u0648\u0631\u0628\u0627\u060c \u0641\u0642\u0627\u0645\u062a \u0647\u0630\u0647 \u0627\u0644\u062f\u0648\u0644 \u0628\u0645\u0631\u0627\u062c\u0639\u0629 \u0645\u0648\u0636\u0648\u0639\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u0645\u062a\u0639\u0644\u0642\u0629 \u0628\u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0641\u064a \u0638\u0644 \u0645\u0628\u0627\u062f\u0626 \u0647\u0630\u0627 \u0627\u0644\u0646\u0645\u0648\u0630\u062c\u060c \u0648\u0623\u0638\u0647\u0631\u062a \u0647\u0630\u0647 \u0627\u0644\u0645\u0631\u0627\u062c\u0639\u0629 \u0623\u0646 \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u064a\u062a\u0645\u062a\u0639 \u0628\u0642\u0627\u0628\u0644\u064a\u0629 \u0639\u0627\u0644\u064a\u0629 \u0644\u0644\u062a\u0637\u0628\u064a\u0642 \u0641\u064a \u0646\u0637\u0627\u0642 \u0648\u0627\u0633\u0639 \u0648\u063a\u064a\u0631 \u0645\u062d\u062f\u0648\u062f. (\u0633\u0639\u064a\u062f\u060c 2007\u060c 170)<\/p>\n<p>\u0625\u0646 \u0645\u0646 \u0623\u0647\u0645 \u0627\u0644\u0639\u0648\u0627\u0645\u0644 \u0627\u0644\u062a\u064a \u0633\u0627\u0647\u0645\u062a \u0641\u064a \u0627\u0646\u062a\u0634\u0627\u0631 \u0648\u062a\u0637\u0648\u064a\u0631 \u0646\u0645\u0648\u0630\u062c (\u0641\u0627\u0646 \u0647\u064a\u0644) \u0647\u0648: \u0627\u0639\u062a\u0645\u0627\u062f\u0647 \u0639\u0644\u0649 \u0645\u0633\u062a\u0648\u064a\u0627\u062a \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0647\u0646\u062f\u0633\u064a \u0641\u064a\u0645\u0627 \u064a\u062e\u0635 \u062a\u0642\u062f\u0645 \u0627\u0644\u062a\u0644\u0627\u0645\u064a\u0630 \u0641\u064a \u062a\u0639\u0644\u0645 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0628\u062f\u0644\u0627\u064b \u0645\u0646 \u0627\u0639\u062a\u0645\u0627\u062f\u0647 \u0641\u0642\u0637 \u0639\u0644\u0649 \u0627\u0644\u0633\u0646 \u0648\u0627\u0644\u0646\u0636\u062c \u0627\u0644\u0628\u064a\u0648\u0644\u0648\u062c\u064a\u060c \u0648\u0643\u0630\u0644\u0643 \u062f\u0639\u0645\u062a \u0627\u0644\u0628\u062d\u0648\u062b \u062f\u0642\u0629 \u0647\u0630\u0627 \u0627\u0644\u0646\u0645\u0648\u0630\u062c\u060c \u0648\u062f\u0639\u0648\u062a\u0647\u0645 \u0644\u062a\u0637\u0648\u064a\u0631 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0648\u062a\u0646\u0641\u064a\u0630\u0647\u0627 \u0641\u064a \u0627\u0644\u0641\u0635\u0648\u0644 \u0627\u0644\u062f\u0631\u0627\u0633\u064a\u0629 \u0628\u0645\u0627 \u064a\u062a\u0648\u0627\u0641\u0642 \u0645\u0639\u0647.<\/p>\n<div class=\"code-block code-block-1\" style=\"margin: 8px auto; text-align: center; display: block; clear: both;\">\n<\/div>\n<p>\u0648\u0642\u062f \u0623\u0648\u0635\u0649 \u0627\u0644\u062a\u0642\u0631\u064a\u0631 \u0627\u0644\u0645\u0639\u0644\u0646 \u0645\u0646 (NCTM, 1989) \u0628\u0625\u062f\u062e\u0627\u0644 \u0646\u0645\u0648\u0630\u062c (\u0641\u0627\u0646 \u0647\u064a\u0644) \u0644\u0644\u0645\u0645\u0627\u0631\u0633\u0629 \u0627\u0644\u0641\u0639\u0644\u064a\u0629 \u0648\u0648\u0636\u0639\u0647 \u0645\u062d\u0644 \u0627\u0644\u062a\u0646\u0641\u064a\u0630 \u0641\u064a \u0623\u0645\u0631\u064a\u0643\u0627\u060c \u0643\u0645\u0627 \u0623\u0648\u0635\u0649 \u0643\u0630\u0644\u0643 \u0627\u0644\u0643\u0648\u0646\u062c\u0631\u0633 \u0627\u0644\u0639\u0627\u0644\u0645\u064a \u0644\u062a\u0639\u0644\u064a\u0645 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a\u00a0 \u0641\u064a \u0645\u0624\u062a\u0645\u0631\u0647 \u0627\u0644\u0633\u0627\u0628\u0639 \u0627\u0644\u0645\u0646\u0639\u0642\u062f \u0628\u0645\u062f\u064a\u0646\u0629 \u0643\u064a\u0648\u0628\u064a\u0643 (Quebic) \u0627\u0644\u0643\u0646\u062f\u064a\u0629 (1992) \u0628\u062a\u062f\u0631\u064a\u0633 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0641\u064a \u0636\u0648\u0621 \u0646\u0645\u0648\u0630\u062c (\u0641\u0627\u0646 \u0647\u064a\u0644).(\u0639\u0628\u064a\u062f\u060c 1993\u060c 198).<\/p>\n<p>\u0648\u0641\u064a \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0646\u0641\u0633\u0647 \u064a\u0648\u0635\u064a (NCTM, 2000) \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0646\u0645\u0648\u0630\u062c (\u0641\u0627\u0646 \u0647\u064a\u0644) \u0644\u0645\u0633\u0627\u0639\u062f\u0629 \u0627\u0644\u062a\u0644\u0627\u0645\u064a\u0630 \u0641\u064a \u0627\u0644\u062a\u063a\u0644\u0628 \u0639\u0644\u0649 \u0627\u0644\u0635\u0639\u0648\u0628\u0627\u062a \u0627\u0644\u062a\u064a \u064a\u0648\u0627\u062c\u0647\u0648\u0646\u0647\u0627 \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a.<\/p>\n<p>\u064a\u0631\u0649 \u0643\u062b\u064a\u0631 \u0645\u0646 \u0627\u0644\u0628\u0627\u062d\u062b\u064a\u0646: \u0628\u0623\u0646 \u0645\u0633\u062a\u0648\u064a\u0627\u062a ( \u0641\u0627\u0646 \u0647\u064a\u0644 ) \u0645\u0641\u064a\u062f\u0629 \u0641\u064a \u062a\u062d\u062f\u064a\u062f \u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u0644\u0627\u0645\u064a\u0630 \u0641\u064a \u0641\u0647\u0645 \u0627\u0644\u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629 \u0648\u062a\u0642\u064a\u0645 \u0647\u064a\u0643\u0644 \u0623\u0648 \u062a\u0637\u0648\u064a\u0631 \u0648\u062a\u0648\u062c\u064a\u0647 \u0627\u0644\u0645\u062d\u062a\u0648\u0649 \u0627\u0644\u0647\u0646\u062f\u0633\u064a \u0641\u064a \u0643\u062a\u0628 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u0645\u062f\u0631\u0633\u064a\u0629 \u0627\u0644\u062b\u0627\u0646\u0648\u064a\u0629.<\/p>\n<p>\u0644\u0642\u062f \u0623\u0635\u0628\u062d \u0646\u0645\u0648\u0630\u062c \u0641\u0627\u0646 \u0647\u064a\u0644 \u0641\u064a \u0627\u0644\u0643\u062b\u064a\u0631 \u0645\u0646 \u0627\u0644\u062f\u0648\u0644 \u0627\u0644\u0639\u0627\u0645\u0644 \u0627\u0644\u0623\u0643\u062b\u0631 \u062a\u0623\u062b\u064a\u0631\u0627 \u0641\u064a \u062a\u0637\u0648\u064a\u0631 \u0645\u062d\u062a\u0648\u0649 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0641\u064a \u0643\u062a\u0628 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a\u060c \u0641\u0641\u064a \u062c\u0646\u0648\u0628 \u0623\u0641\u0631\u064a\u0642\u064a\u0627 \u062d\u0627\u0648\u0644\u062a \u0645\u0646\u0638\u0645\u0629 \u062a\u0639\u0644\u0645 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0648\u0645\u0628\u0627\u062f\u0631\u0629 \u0627\u0644\u062a\u0639\u0644\u0645 \u0625\u0639\u0627\u062f\u0629 \u062a\u0635\u0648\u0631 \u0644\u062a\u0639\u0644\u064a\u0645 \u0648\u062a\u0639\u0644\u0645 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0648\u0627\u0642\u062a\u0631\u062d\u0648\u0627 \u062a\u063a\u064a\u0631\u0627\u062a \u0639\u0644\u0649 \u0645\u062d\u062a\u0648\u0649 \u0627\u0644\u0647\u0646\u062f\u0633\u0629\u060c \u062d\u064a\u062b \u0631\u0623\u0649 \u0627\u0644\u0641\u0631\u064a\u0642 \u0623\u0646 \u0646\u0645\u0648\u0630\u062c \u0641\u0627\u0646 \u0647\u064a\u0644 \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647 \u0643\u0625\u0637\u0627\u0631 \u0644\u0641\u0647\u0645 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0644\u062f\u0649 \u0627\u0644\u062a\u0644\u0627\u0645\u064a\u0630\u060c \u0648\u0643\u0641\u0643\u0631\u0629 \u0644\u0648\u0636\u0639 \u0645\u062d\u062a\u0648\u0649 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0641\u064a \u0643\u062a\u0628 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a.( Alex &amp; Mammen, 2016, 2225 )<\/p>\n<p><span style=\"color: #333399;\"><strong>3- \u0645\u0633\u062a\u0648\u064a\u0627\u062a \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0647\u0646\u062f\u0633\u064a<\/strong><\/span><\/p>\n<p>\u0643\u0645\u0627 \u0648\u0631\u062f\u062a \u0641\u064a: (\u0627\u0644\u0631\u0645\u062d\u064a\u060c2009 \u061b Usiskin, 1982 \u061b Fuys, et,1995<\/p>\n<div class=\"code-block code-block-6\" style=\"margin: 8px auto; text-align: center; display: block; clear: both;\">\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"%D8%A7%D9%84%D9%85%D8%B3%D8%AA%D9%88%D9%89_1_%D8%A7%D9%84%D9%85%D8%B3%D8%AA%D9%88%D9%89_%D8%A7%D9%84%D8%AA%D8%B5%D9%88%D8%B1%D9%8A_Visualization\"><\/span><span style=\"color: #008000;\"><strong>\u0627\u0644\u0645\u0633\u062a\u0648\u0649 (1): \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u062a\u0635\u0648\u0631\u064a <\/strong><strong>Visualization<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0648\u0641\u064a\u0647 \u064a\u062d\u0643\u0645 \u0627\u0644\u062a\u0644\u0645\u064a\u0630 \u0639\u0644\u0649 \u0627\u0644\u0623\u0634\u0643\u0627\u0644 \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629 \u0648\u062a\u0635\u0646\u064a\u0641\u0647\u0627 \u0645\u0646 \u0645\u0638\u0647\u0631\u0647\u0627 \u0627\u0644\u0639\u0627\u0645\u060c \u0648\u064a\u0645\u064a\u0632\u0647\u0627 \u0643\u0643\u0644\u060c \u0648\u0644\u0627 \u064a\u0639\u0631\u0641 \u0634\u064a\u0626\u0627\u064b \u0639\u0646 \u062e\u0635\u0627\u0626\u0635\u0647\u0627\u060c \u0648\u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0647 \u0641\u0625\u0646 \u0627\u0644\u0645\u062b\u0644\u062b \u064a\u062e\u062a\u0644\u0641 \u0639\u0646 \u0627\u0644\u0645\u0631\u0628\u0639\u060c \u0627\u0644\u0645\u0631\u0628\u0639 \u064a\u062e\u062a\u0644\u0641 \u0639\u0646 \u0627\u0644\u0645\u0633\u062a\u0637\u064a\u0644\u060c \u0648\u0644\u0627 \u064a\u0633\u062a\u0637\u064a\u0639 \u0627\u0644\u062a\u0644\u0645\u064a\u0630 \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0631\u0628\u0637 \u0628\u064a\u0646 \u0627\u0644\u062e\u0635\u0627\u0626\u0635\u060c \u0643\u0645\u0627 \u0623\u0646\u0647 \u0644\u0627 \u064a\u0639\u0631\u0641 \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0628\u064a\u0646\u0647\u0627.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%D8%A7%D9%84%D9%85%D8%B3%D8%AA%D9%88%D9%89_2_%D8%A7%D9%84%D9%85%D8%B3%D8%AA%D9%88%D9%89_%D8%A7%D9%84%D8%AA%D8%AD%D9%84%D9%8A%D9%84%D9%8A_Analysis\"><\/span><span style=\"color: #008000;\"><strong>\u0627\u0644\u0645\u0633\u062a\u0648\u0649<\/strong><strong> (2): \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a <\/strong><strong>Analysis<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u064a\u0633\u062a\u0637\u064a\u0639 \u0627\u0644\u062a\u0644\u0645\u064a\u0630 \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0623\u0634\u0643\u0627\u0644 \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629 \u0628\u062f\u0644\u0627\u0644\u0629 \u062e\u0635\u0627\u0626\u0635\u0647\u0627 \u0648\u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u0647\u0630\u0647 \u0627\u0644\u062e\u0635\u0627\u0626\u0635\u060c \u0643\u0645\u0627 \u064a\u0639\u062a\u0645\u062f \u0635\u0641\u0627\u062a \u0645\u0645\u064a\u0632\u0629 \u0644\u0643\u0644 \u0641\u0626\u0629 \u0645\u0646 \u0627\u0644\u0623\u0634\u0643\u0627\u0644\u060c \u0648\u064a\u0633\u062a\u062e\u062f\u0645 \u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0623\u0634\u0643\u0627\u0644 \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629 \u0641\u064a \u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u0647\u0646\u062f\u0633\u064a\u0629 \u0639\u0644\u0649 \u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0634\u0643\u0644 \u0627\u0644\u0648\u0627\u062d\u062f\u060c \u0648\u0644\u0643\u0646 \u0644\u0627 \u064a\u0633\u062a\u0637\u064a\u0639 \u0627\u0644\u062a\u0644\u0645\u064a\u0630 \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0631\u0628\u0637 \u0628\u064a\u0646 \u0627\u0644\u062e\u0635\u0627\u0626\u0635. \u0645\u062b\u0644\u0627\u064b\u060c \u0644\u0627 \u064a\u0633\u062a\u0646\u062a\u062c \u0627\u0644\u062a\u0644\u0645\u064a\u0630 \u0623\u0646 \u0627\u0644\u0645\u0631\u0628\u0639 \u062d\u0627\u0644\u0629 \u062e\u0627\u0635\u0629 \u0645\u0646 \u0645\u062a\u0648\u0627\u0632\u064a \u0623\u0636\u0644\u0627\u0639.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%D8%A7%D9%84%D9%85%D8%B3%D8%AA%D9%88%D9%89_3_%D9%85%D8%B3%D8%AA%D9%88%D9%89_%D8%A7%D9%84%D8%A7%D8%B3%D8%AA%D9%86%D8%AA%D8%A7%D8%AC_%D8%BA%D9%8A%D8%B1_%D8%A7%D9%84%D8%B4%D9%83%D9%84%D9%8A_Informal_deduction\"><\/span><span style=\"color: #008000;\"><strong>\u0627\u0644\u0645\u0633\u062a\u0648\u0649 (3): \u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c \u063a\u064a\u0631 \u0627\u0644\u0634\u0643\u0644\u064a <\/strong><strong>Informal deduction<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u064a\u0633\u062a\u0637\u064a\u0639 \u0627\u0644\u062a\u0644\u0645\u064a\u0630 \u0627\u0633\u062a\u062e\u062f\u0645 \u062e\u0648\u0627\u0635 \u0627\u0644\u0623\u0634\u0643\u0627\u0644 \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629 \u0641\u064a \u0635\u064a\u0627\u063a\u0629 \u062a\u0639\u0631\u064a\u0641 \u062a\u0644\u0643 \u0627\u0644\u0623\u0634\u0643\u0627\u0644\u060c \u0643\u0645\u0627 \u0623\u0646\u0647 \u064a\u0633\u062a\u0637\u064a\u0639 \u0631\u0628\u0637\u00a0 \u062e\u0648\u0627\u0635 \u0627\u0644\u0623\u0634\u0643\u0627\u0644 \u0639\u0644\u0649 \u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0634\u0643\u0644 \u0627\u0644\u0648\u0627\u062d\u062f\u060c \u0623\u0648 \u0639\u0644\u0649 \u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0623\u0634\u0643\u0627\u0644 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629\u060c \u0643\u0645\u0627 \u064a\u062a\u0645\u0643\u0646 \u0627\u0644\u062a\u0644\u0627\u0645\u064a\u0630 \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0645\u0646 \u0625\u0643\u0645\u0627\u0644 \u0628\u0631\u0647\u0627\u0646 \u0644\u0645\u0634\u0643\u0644\u0629 \u0647\u0646\u062f\u0633\u064a\u0629\u060c \u0648\u064a\u0633\u062a\u0637\u064a\u0639 \u0627\u0644\u062a\u0644\u0645\u064a\u0630 \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0641\u0647\u0645 \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0628\u064a\u0646 \u0627\u0644\u0646\u0638\u0631\u064a\u0627\u062a \u0648\u0627\u0644\u0645\u0633\u0644\u0645\u0627\u062a\u060c \u0648\u062a\u062a\u0636\u062d \u0644\u062f\u064a\u0647 \u0628\u0639\u0636 \u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0634\u0631\u0648\u0637 \u0627\u0644\u0636\u0631\u0648\u0631\u064a\u0629 \u0648\u0627\u0644\u0643\u0627\u0641\u064a\u0629.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%D8%A7%D9%84%D9%85%D8%B3%D8%AA%D9%88%D9%89_4_%D9%85%D8%B3%D8%AA%D9%88%D9%89_%D8%A7%D9%84%D8%A7%D8%B3%D8%AA%D9%86%D8%AA%D8%A7%D8%AC_%D8%A7%D9%84%D8%B4%D9%83%D9%84%D9%8A_Formal_deduction\"><\/span><span style=\"color: #008000;\"><strong>\u0627\u0644\u0645\u0633\u062a\u0648\u0649 (4): \u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0627\u0644\u0634\u0643\u0644\u064a <\/strong><strong>Formal deduction<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u064a\u062a\u062d\u062f\u062f \u0647\u0630\u0627 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0628\u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0646\u0638\u0631\u064a \u0648\u0628\u0646\u0627\u0621 \u0627\u0644\u0628\u0631\u0627\u0647\u064a\u0646 \u0644\u0644\u0646\u0638\u0631\u064a\u0627\u062a \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629 \u0648\u0627\u0633\u062a\u062e\u0644\u0627\u0635 \u0646\u062a\u0627\u0626\u062c \u0645\u0646 \u062e\u0648\u0627\u0635 \u0648\u0645\u0639\u0637\u064a\u0627\u062a \u0645\u062d\u062f\u062f\u0629\u060c \u0648\u064a\u0633\u062a\u0637\u064a\u0639 \u0627\u0644\u062a\u0644\u0645\u064a\u0630 \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u062a\u0645\u064a\u064a\u0632 \u0628\u064a\u0646 \u0627\u0644\u0639\u0646\u0627\u0635\u0631 \u063a\u064a\u0631 \u0627\u0644\u0645\u0639\u0631\u0651\u064e\u0641\u0629 \u0648\u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a \u0648\u0627\u0644\u0645\u0633\u0644\u0645\u0627\u062a \u0648\u0627\u0644\u0628\u0631\u0647\u0627\u0646\u060c \u0648\u064a\u0630\u0643\u0631 \u0627\u0644\u0633\u0628\u0628 \u0628\u0639\u0628\u0627\u0631\u0627\u062a \u0645\u0646\u0637\u0642\u064a\u0629 \u0648\u0628\u0627\u0644\u0627\u0639\u062a\u0645\u0627\u062f \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u0644\u0645\u0627\u062a \u0648\u0627\u0644\u0646\u0638\u0631\u064a\u0627\u062a.<\/p>\n<div class=\"code-block code-block-7\" style=\"margin: 8px auto; text-align: center; display: block; clear: both;\">\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"%D8%A7%D9%84%D9%85%D8%B3%D8%AA%D9%88%D9%89_5_%D9%85%D8%B3%D8%AA%D9%88%D9%89_%D8%A7%D9%84%D8%AF%D9%82%D8%A9_%D9%88%D8%A7%D9%84%D8%B5%D8%B1%D8%A7%D9%85%D8%A9_Precision_and_Rigor\"><\/span><span style=\"color: #008000;\"><strong>\u0627\u0644\u0645\u0633\u062a\u0648\u0649 (5): \u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u062f\u0642\u0629 \u0648\u0627\u0644\u0635\u0631\u0627\u0645\u0629 <\/strong><strong>Precision and Rigor<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u064a\u0634\u062a\u063a\u0644 \u0627\u0644\u062a\u0644\u0627\u0645\u064a\u0630 \u0641\u064a \u0623\u0646\u0638\u0645\u0629 \u0628\u062f\u064a\u0647\u064a\u0629 \u0645\u062e\u062a\u0644\u0641\u0629\u060c \u0648\u064a\u0635\u064a\u0631 \u0648\u0628\u0625\u0645\u0643\u0627\u0646\u0647\u0645 \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u0645\u0648\u0627\u0636\u064a\u0639 \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629\u060c \u0648\u0627\u0644\u0645\u0642\u0627\u0631\u0646\u0629 \u0628\u064a\u0646 \u0645\u062e\u062a\u0644\u0641 \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629\u060c \u0648 \u0645\u0642\u0627\u0631\u0646\u0629 \u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c\u0627\u062a \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629\u060c \u0648\u0627\u0644\u062a\u0644\u0627\u0645\u064a\u0630 \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u064a\u0641\u0647\u0645\u0648\u0646 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u063a\u064a\u0631 \u0627\u0644\u0625\u0642\u0644\u064a\u062f\u064a\u0629\u060c \u0643\u0645\u0627 \u0623\u0646\u0647 \u064a\u0643\u0648\u0646 \u0628\u0645\u0642\u062f\u0648\u0631\u0647\u0645 \u0648\u0639\u064a \u0648\u0641\u0647\u0645 \u062f\u0648\u0631 \u0627\u0644\u0645\u0646\u0637\u0642 \u0648\u0627\u0644\u0637\u0631\u0642 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629 \u0644\u0644\u0628\u0631\u0647\u0627\u0646.<\/p>\n<p><span style=\"color: #333399;\"><strong>4- \u062e\u0635\u0627\u0626\u0635 \u0645\u0633\u062a\u0648\u064a\u0627\u062a \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u00a0<\/strong><\/span><\/p>\n<p>\u0643\u0645\u0627 \u0648\u0631\u062f\u062a \u0641\u064a: (Usiskin, 1982,5-6)<\/p>\n<ul>\n<li>\u0627\u0644\u062a\u062a\u0627\u0628\u0639 \u0627\u0644\u062b\u0627\u0628\u062a (fixed sequence): \u0648\u0647\u064a \u0636\u0631\u0648\u0631\u0629 \u0623\u0646 \u064a\u0645\u0631 \u0627\u0644\u062a\u0644\u0645\u064a\u0630 \u0641\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u0649 (N-1) \u0642\u0628\u0644 \u0627\u0644\u0648\u0635\u0648\u0644 \u0625\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 (N).<\/li>\n<li>\u0627\u0644\u062a\u0642\u062f\u0645 (Advancement): \u0648\u0647\u0648 \u0643\u0644 \u0645\u0627 \u064a\u0643\u0648\u0646 \u0636\u0645\u0646\u064a\u0627 \u0641\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u0649 (N-1) \u064a\u0635\u064a\u0631 \u0635\u0631\u064a\u062d\u0627 \u0641\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u0649 (N) \u0648\u0627\u0644\u062a\u0642\u062f\u0645 \u0645\u0646 \u0645\u0633\u062a\u0648\u0649 \u0625\u0644\u0649 \u0645\u0633\u062a\u0648\u0649 \u0623\u0639\u0644\u0649 \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0623\u0633\u0627\u0644\u064a\u0628 \u062a\u0639\u0644\u064a\u0645\u064a\u0629 \u0645\u0646\u0627\u0633\u0628\u0629.<\/li>\n<li>\u0627\u0644\u0644\u063a\u0629 (Linguistics): \u0644\u0643\u0644 \u0645\u0633\u062a\u0648\u0649 \u062a\u0641\u0643\u064a\u0631 \u0631\u0645\u0648\u0632 \u062e\u0627\u0635\u0629 \u0648\u0644\u063a\u0629 \u062e\u0627\u0635\u0629 \u0648\u0639\u0644\u0627\u0642\u0627\u062a\u0647 \u0627\u0644\u062e\u0627\u0635\u0629 \u0627\u0644\u062a\u064a \u062a\u0631\u0628\u0637 \u0628\u064a\u0646 \u0627\u0644\u0631\u0645\u0648\u0632\u060c \u0641\u0627\u0644\u0644\u063a\u0629 \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645\u0629 \u0641\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u0649 (N-1) \u062a\u0635\u0628\u062d \u0623\u0643\u062b\u0631 \u062f\u0642\u0629 \u0641\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u0649(N)\u060c \u0623\u064a \u0623\u0646\u0647 \u064a\u0648\u062c\u062f \u0628\u0646\u0627\u0621 \u0644\u063a\u0648\u064a \u0644\u0643\u0644 \u0645\u0633\u062a\u0648\u0649 \u0645\u0646 \u0645\u0633\u062a\u0648\u064a\u0627\u062a \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0647\u0646\u062f\u0633\u064a.<\/li>\n<li>\u0627\u0644\u0641\u0635\u0644 (Separation): \u0644\u0627 \u064a\u064f\u0645\u0643\u0646 \u0644\u0634\u062e\u0635\u064a\u0646 \u0641\u064a \u0645\u0633\u062a\u0648\u0649 \u062a\u0641\u0643\u064a\u0631 \u0645\u062e\u062a\u0644\u0641 \u0641\u0647\u0645 \u0628\u0639\u0636\u0647\u0645\u0627 \u0627\u0644\u0628\u0639\u0636. \u0641\u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u062a\u0644\u0645\u064a\u0630 \u0641\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u0649 (N-1) \u0648\u0627\u0644\u0645\u0639\u0644\u0645 \u064a\u0634\u0631\u062d \u0641\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u0649 (N) \u0641\u0644\u0646 \u064a\u062a\u0645\u0643\u0646 \u0627\u0644\u062a\u0644\u0645\u064a\u0630 \u0645\u0646 \u0641\u0647\u0645 \u0645\u0627 \u064a\u0642\u0648\u0644\u0647 \u0627\u0644\u0645\u0639\u0644\u0645.<\/li>\n<li>\u0627\u0644\u0627\u0643\u062a\u0633\u0627\u0628 (Acquisition): \u0648\u062a\u0639\u0646\u064a \u0623\u0646\u0647 \u064a\u0645\u0643\u0646 \u0644\u0639\u0645\u0644\u064a\u0629 \u0627\u0644\u062a\u0639\u0644\u0645 \u0646\u0642\u0644 \u0627\u0644\u062a\u0644\u0645\u064a\u0630 \u0645\u0646 \u0645\u0633\u062a\u0648\u0649 \u062a\u0641\u0643\u064a\u0631 \u0625\u0644\u0649 \u0622\u062e\u0631.<\/li>\n<\/ul>\n<p><span style=\"color: #333399;\">5- \u0645\u0631\u0627\u062d\u0644 \u0646\u0645\u0648\u0630\u062c \u0641\u0627\u0646 \u0647\u064a\u0644<\/span><\/p>\n<ul>\n<li>\u0643\u0645\u0627 \u0648\u0631\u062f\u062a \u0641\u064a: ( \u0627\u0644\u0631\u0645\u062d\u064a\u060c 2009\u060c 88)<\/li>\n<\/ul>\n<p>\u0627\u0644\u0627\u0646\u062a\u0642\u0627\u0644 \u0645\u0646 \u0645\u0633\u062a\u0648\u0649 \u062a\u0641\u0643\u064a\u0631 \u0625\u0644\u0649 \u0622\u062e\u0631 \u064a\u062a\u0645 \u0645\u0646 \u062e\u0644\u0627\u0644 \u062e\u0645\u0633\u0629 \u0645\u0631\u0627\u062d\u0644 \u0648\u0647\u064a:<\/p>\n<ul>\n<li><span style=\"color: #008000;\"><strong>\u0627\u0644\u0645\u0639\u0644\u0648\u0645\u0627\u062a:<\/strong> <\/span>\u064a\u062c\u0628 \u0623\u0646 \u064a\u0628\u062f\u0623 \u0627\u0644\u062a\u062f\u0631\u064a\u0633 \u0628\u0645\u0648\u0627\u062f \u062a\u0642\u062f\u0645 \u0644\u0644\u0637\u0641\u0644 \u0648\u062a\u0642\u0648\u062f\u0647 \u0644\u0627\u0643\u062a\u0634\u0627\u0641 \u0628\u064f\u0646\u0649 \u0645\u0639\u064a\u0646\u0629.<\/li>\n<li><span style=\"color: #008000;\"><strong>\u0627\u0644\u0648\u0636\u0648\u062d:<\/strong> <\/span>\u064a\u0642\u062f\u0645 \u0627\u0644\u0645\u0639\u0644\u0645 \u0627\u0644\u0645\u0635\u0637\u0644\u062d\u0627\u062a \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629\u060c \u0648\u064a\u0634\u062c\u0639 \u0627\u0644\u062a\u0644\u0627\u0645\u064a\u0630 \u0639\u0644\u0649 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647\u0627 \u0641\u064a \u0643\u062a\u0627\u0628\u0627\u062a\u0647\u0645 \u0641\u064a \u062d\u0635\u0635 \u0627\u0644\u0647\u0646\u062f\u0633\u0629.<\/li>\n<li><span style=\"color: #008000;\"><strong>\u0627\u0644\u062a\u0648\u062c\u064a\u0647 \u0627\u0644\u0645\u0628\u0627\u0634\u0631:<\/strong><\/span> \u0648\u0647\u064a \u0623\u0646 \u062a\u0642\u062f\u0645 \u0627\u0644\u0645\u0647\u0627\u0645 \u0644\u0644\u062a\u0644\u0627\u0645\u064a\u0630 \u0628\u0637\u0631\u064a\u0642\u0629 \u062a\u062c\u0639\u0644 \u0627\u0644\u0628\u064f\u0646\u0649 \u0627\u0644\u0645\u062a\u0639\u0644\u0645\u0629 \u0645\u0623\u0644\u0648\u0641\u0629 \u0644\u062f\u064a\u0647\u0645.<\/li>\n<li><span style=\"color: #008000;\"><strong>\u0627\u0644\u062a\u0648\u062c\u064a\u0647 \u0627\u0644\u062d\u0631:<\/strong><\/span> \u064a\u0642\u062f\u0645 \u0627\u0644\u0645\u0639\u0644\u0645 \u0645\u0647\u0645\u0627\u062a \u064a\u0645\u0643\u0646 \u0625\u062a\u0645\u0627\u0645\u0647\u0627 \u0628\u0637\u0631\u0642 \u0645\u062e\u062a\u0644\u0641\u0629\u060c \u0648\u064a\u0643\u062a\u0633\u0628 \u0627\u0644\u062a\u0644\u0627\u0645\u064a\u0630 \u062e\u0628\u0631\u0627\u062a \u0641\u064a \u062d\u0644 \u0645\u062a\u0637\u0644\u0628\u0627\u062a \u0628\u0645\u0641\u0631\u062f\u0647\u0645 \u0628\u0627\u0644\u0627\u0639\u062a\u0645\u0627\u062f \u0639\u0644\u0649 \u0645\u0627 \u062f\u0631\u0633\u0648\u0647 \u0633\u0627\u0628\u0642\u0627.<\/li>\n<li><span style=\"color: #008000;\"><strong>\u0627\u0644\u062a\u0643\u0627\u0645\u0644:<\/strong><\/span> \u064a\u064f\u0639\u0637\u0649 \u0627\u0644\u062a\u0644\u0627\u0645\u064a\u0630 \u0641\u0631\u0635\u0627 \u0644\u062a\u062c\u0645\u064a\u0639 \u0645\u0627 \u062f\u0631\u0633\u0648\u0647 \u0633\u0627\u0628\u0642\u0627\u060c \u0643\u0623\u0646 \u064a\u0635\u0645\u0645\u0648\u0627 \u0623\u0646\u0634\u0637\u062a\u0647\u0645 \u0628\u0623\u0646\u0641\u0633\u0647\u0645\u060c \u064a\u0645\u0643\u0646 \u0645\u0646 \u062e\u0644\u0627\u0644\u0647\u0627 \u062e\u0644\u0642 \u0641\u0643\u0631\u0629 \u062e\u0627\u0635\u0629 \u0628\u0647\u0645.<\/li>\n<\/ul>\n<p><span style=\"color: #333399;\"><strong>\u0627\u0644\u0645\u0631\u0627\u062c\u0639:<\/strong><\/span><\/p>\n<ul>\n<li><span style=\"font-size: 10pt;\">\u0627\u0644\u0631\u0645\u062d\u064a\u060c \u0631\u0641\u0627\u0621\u060c (2009)\u060c \u0646\u0638\u0631\u064a\u0629 \u0641\u0627\u0646 \u0647\u064a\u0644 \u0641\u064a \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u060c <strong>\u0645\u0644\u0641 \u0627\u0644\u062b\u0642\u0627\u0641\u0629 \u0627\u0644\u0639\u0644\u0645\u064a\u0629\u060c \u0631\u0624\u0649 \u062a\u0631\u0628\u0648\u064a\u0629\u060c<\/strong> \u0627\u0644\u0639\u062f\u062f (29)\u060c \u0635 87- 90.<\/span><\/li>\n<li><span style=\"font-size: 10pt;\">\u0633\u0639\u064a\u062f\u060c \u0631\u062f\u0645\u0627\u0646 \u0645\u062d\u0645\u062f\u060c (2007)\u060c \u0645\u062f\u0649 \u0627\u062a\u0633\u0627\u0642 \u0645\u062d\u062a\u0648\u0649 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0641\u064a \u0643\u062a\u0628 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u0645\u062f\u0631\u0633\u064a\u0629 \u0644\u0644\u0635\u0641\u0648\u0641\u060c \u0645\u0646 7-9 \u0641\u064a \u0627\u0644\u062c\u0645\u0647\u0648\u0631\u064a\u0629 \u0627\u0644\u064a\u0645\u0646\u064a\u0629 \u0645\u0639 \u0627\u0644\u0623\u0633\u0633 \u0627\u0644\u062a\u0639\u0644\u064a\u0645\u064a\u0629 \u0644\u0646\u0638\u0631\u064a\u0629 \u0641\u0627\u0646 \u0647\u064a\u0644 \u0644\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0647\u0646\u062f\u0633\u064a<strong>\u060c <\/strong><strong>\u0645\u062c\u0644\u0629 \u0627\u0644\u0639\u0644\u0648\u0645 \u0627\u0644\u062a\u0631\u0628\u0648\u064a\u0629 \u0648\u0627\u0644\u0646\u0641\u0633\u064a\u0629<\/strong>\u060c \u0627\u0644\u0645\u062c\u0644\u062f (8) \u0627\u0644\u0639\u062f\u062f (3)\u060c 166- 185.<\/span><\/li>\n<li><span style=\"font-size: 10pt;\">\u0639\u0628\u064a\u062f\u060c \u0648\u0644\u064a\u0645\u060c (1993)\u060c \u062a\u0642\u0631\u064a\u0631 \u0639\u0646 \u0645\u0624\u062a\u0645\u0631 \u0627\u0644\u0643\u0648\u0646\u062c\u0631\u0633 \u0627\u0644\u0639\u0627\u0644\u0645\u064a \u0644\u062a\u0639\u0644\u064a\u0645 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u0645\u0646\u0639\u0642\u062f \u0628\u0643\u0646\u062f\u0627 \u0641\u064a \u0627\u0644\u0641\u062a\u0631\u0629 \u0645\u0646 17- 23 \u0623\u063a\u0633\u0637\u0633<strong> 1992<\/strong>\u060c <strong>\u0627\u0644\u0645\u062c\u0644\u0629 \u0627\u0644\u062a\u0631\u0628\u0648\u064a\u0629\u060c \u062c\u0627\u0645\u0639\u0629 \u0627\u0644\u0643\u0648\u064a\u062a<\/strong>\u060c \u0627\u0644\u0645\u062c\u0644\u062f (8)\u060c \u0627\u0644\u0639\u062f\u062f (27)\u060c 193-204.<\/span><\/li>\n<li><span style=\"font-size: 10pt;\">\u2013 Fuys, D. etal (1995<strong>): The Van Hiele Model of Thinking in Geometry<\/strong>, J. of Research in Mathematics Education, Monograph3, NCTM, Vi, U.S.A<\/span><\/li>\n<li><span style=\"font-size: 10pt;\">\u2013 Usiskin, Z. (1982). <strong>Van Hiele levels and achievement in Secondary School Geometry<\/strong>, Department of Education the University of Chicago, 5835 s. Kimbark\u00a0 Avenue Chicago, IL 60637.<\/span><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p><\/p>\n<h3><span class=\"ez-toc-section\" id=\"%D9%83%D8%A7%D8%AA%D8%A8_%D8%A7%D9%84%D9%85%D9%82%D8%A7%D9%84\"><\/span> \u0643\u0627\u062a\u0628 \u0627\u0644\u0645\u0642\u0627\u0644 <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u062f. \u0639\u0628\u062f\u0647 \u0635\u0627\u0644\u062d \u0645\u062d\u0633\u0646 \u0628\u0647\u0648\u062b <\/p>\n<p>\u062f\u0643\u062a\u0648\u0631\u0627\u0647 \u0641\u064a \u062a\u062d\u0644\u064a\u0644 \u0648\u062a\u0642\u064a\u064a\u0645 \u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u062a\u0631\u0628\u064a\u0629 \u0648\u0627\u0644\u062a\u0643\u0648\u064a\u0646 (\u062a\u0639\u0644\u064a\u0645 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0646\u0645\u0648\u0630\u062c) \u0645\u0646 \u0643\u0644\u064a\u0629 \u0639\u0644\u0648\u0645 \u0627\u0644\u062a\u0631\u0628\u064a\u0629 -\u062c\u0627\u0645\u0639\u0629 \u0645\u062d\u0645\u062f 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&hellip;<\/p>\n","protected":false},"author":1,"featured_media":29147,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[21043],"tags":[21117,4346,4249,786,4,21114,21116,672,9069,200,21123,21115,29,21122,21113,343,9038],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/www.difference.news\/edu\/wp-content\/uploads\/2021\/12\/\u0644\u0646\u062a\u0639\u0631\u0641-\u0639\u0644\u0649-\u0646\u0645\u0648\u0630\u062c-\u0641\u0627\u0646-\u0647\u064a\u0644-\u0641\u064a-\u062a\u062f\u0631\u064a\u0633-\u0627\u0644\u0647\u0646\u062f\u0633\u0629.jpg?fit=660%2C330&ssl=1","jetpack-related-posts":[],"jetpack_shortlink":"https:\/\/wp.me\/pdhObK-7A6","_links":{"self":[{"href":"https:\/\/www.difference.news\/edu\/wp-json\/wp\/v2\/posts\/29146"}],"collection":[{"href":"https:\/\/www.difference.news\/edu\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.difference.news\/edu\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.difference.news\/edu\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.difference.news\/edu\/wp-json\/wp\/v2\/comments?post=29146"}],"version-history":[{"count":0,"href":"https:\/\/www.difference.news\/edu\/wp-json\/wp\/v2\/posts\/29146\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.difference.news\/edu\/wp-json\/wp\/v2\/media\/29147"}],"wp:attachment":[{"href":"https:\/\/www.difference.news\/edu\/wp-json\/wp\/v2\/media?parent=29146"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.difference.news\/edu\/wp-json\/wp\/v2\/categories?post=29146"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.difference.news\/edu\/wp-json\/wp\/v2\/tags?post=29146"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}