{"id":36577,"date":"2019-10-31T22:12:27","date_gmt":"2019-10-31T19:12:27","guid":{"rendered":"https:\/\/prohoster.info\/blog\/vot-zachem-nuzhna-shkolnaya-algebra\/"},"modified":"2019-10-31T22:12:27","modified_gmt":"2019-10-31T19:12:27","slug":"vot-zachem-nuzhna-shkolnaya-algebra","status":"publish","type":"post","link":"https:\/\/prohoster.info\/ro\/blog\/news\/vot-zachem-nuzhna-shkolnaya-algebra","title":{"rendered":"De ce este necesar\u0103 algebra \u0219colar\u0103","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"<p>De obicei, la \u00eentrebarea \u201ede ce este necesar\u0103 matematica?\u201d se r\u0103spunde cu ceva de genul \u201egimnastic\u0103 pentru minte\u201d. \u00cen opinia mea, aceast\u0103 explica\u021bie nu este suficient\u0103. Atunci c\u00e2nd o persoan\u0103 face exerci\u021bii fizice, \u0219tie exact denumirea grupurilor musculare care se dezvolt\u0103. Dar discu\u021biile despre matematic\u0103 r\u0103m\u00e2n prea abstracte. Care sunt, mai exact, \u201emu\u0219chii min\u021bii\u201d care sunt antrena\u021bi de algebra \u0219colar\u0103? Aceasta nu seam\u0103n\u0103 deloc cu adev\u0103rata matematic\u0103, \u00een care se fac mari descoperiri. Ce aduce abilitatea de a c\u0103uta derivata unor func\u021bii complicate?<\/p>\n<p>Predarea program\u0103rii studen\u021bilor mai pu\u021bin capabili m-a condus spre un r\u0103spuns mai precis la \u00eentrebarea \u201ede ce?\u201d. \u00cen acest articol, voi \u00eencerca s\u0103 v\u0103 transmit acest r\u0103spuns.<\/p>\n<p><img decoding=\"async\" alt=\"De ce este necesar\u0103 algebra \u0219colar\u0103\" src=\"\/wp-content\/uploads\/2019\/07\/68c529ad50470860a474ba8d910ff00f.jpg\" style=\"display:block;margin: 0 auto;\" \/><noindex><a rel=\"nofollow\" name=\"habracut\"><\/a><\/noindex><br \/>\nLa \u0219coal\u0103, se acord\u0103 destul de mult timp transform\u0103rii \u0219i simplific\u0103rii expresiilor. De exemplu: 81\u00d72+126xy+49y2 trebuie transformat ca (9x+7y)2.<\/p>\n<p>\u00cen acest exemplu, de la elev se a\u0219teapt\u0103 s\u0103-\u0219i aminteasc\u0103 formula p\u0103tratului sumei. <\/p>\n<p><img decoding=\"async\" alt=\"De ce este necesar\u0103 algebra \u0219colar\u0103\" src=\"\/wp-content\/uploads\/2019\/07\/7b8f583cf587730de2f76011f83b05b2.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>\n\u00cen cazuri mai complexe, expresia ob\u021binut\u0103 poate fi utilizat\u0103 pentru alte transform\u0103ri. De exemplu:<\/p>\n<p><img decoding=\"async\" alt=\"De ce este necesar\u0103 algebra \u0219colar\u0103\" src=\"\/wp-content\/uploads\/2019\/07\/fe1570cc2f91020281abd22b47aad458.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>\nse transform\u0103 mai \u00eent\u00e2i \u00een<\/p>\n<p><img decoding=\"async\" alt=\"De ce este necesar\u0103 algebra \u0219colar\u0103\" src=\"\/wp-content\/uploads\/2019\/07\/0aaa7d8b4dbf3d4c8e331a44088fc863.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>\niar apoi, cu precizarea (a + 2b) != 0, se ob\u021bine a\u0219a<\/p>\n<p><img decoding=\"async\" alt=\"De ce este necesar\u0103 algebra \u0219colar\u0103\" src=\"\/wp-content\/uploads\/2019\/07\/a95f9f03442ae65be217f70d4039b433.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Pentru a ob\u021bine un astfel de rezultat, elevul trebuie s\u0103 recunoasc\u0103 \u00een expresia ini\u021bial\u0103 \u0219i apoi s\u0103 aplice trei formule:<\/p>\n<ul>\n<li>P\u0103tratul sumei<\/li>\n<li>Diferen\u021ba p\u0103tratelor<\/li>\n<li>Simplificarea factorilor \u00een frac\u021bii ordinare<\/li>\n<\/ul>\n<p>\n\u00cen \u0219coala obi\u0219nuit\u0103, la algebra, aproape tot timpul ne-am ocupat de astfel de transform\u0103ri ale expresiilor. La facultate, la matematicile superioare, nimic nu s-a schimbat semnificativ. Ni s-a explicat cum s\u0103 lu\u0103m derivatelor (integrale etc.) \u0219i ne-au fost date o mul\u021bime de exerci\u021bii. A fost benefic? \u00cen opinia mea \u2013 da. Ca rezultat al acestor exerci\u021bii:<\/p>\n<ol>\n<li>S-a rafinat abilitatea de a transforma expresii.<\/li>\n<li>A crescut aten\u021bia la detalii.<\/li>\n<li>S-a format un ideal \u2013 o expresie concis\u0103, la care putem aspira.<\/li>\n<\/ol>\n<p>\n\u00cen opinia mea, existen\u021ba unui astfel de ideal, calitate \u0219i abilitate este foarte util\u0103 \u00een munca zilnic\u0103 a unui dezvoltator. C\u0103ci a simplifica o expresie, \u00een esen\u021b\u0103, \u00eenseamn\u0103 a-i modifica structura pentru a facilita \u00een\u021belegerea, f\u0103r\u0103 a afecta sensul. \u021ai se pare cunoscut?<\/p>\n<p>Este practic defini\u021bia refactoriz\u0103rii din cartea omonim\u0103 a lui Martin Fowler.<\/p>\n<p>\u00cen lucrarea sa, autorul formuleaz\u0103 acestea astfel:<\/p>\n<blockquote><p>Refactorizarea (Refactoring) (substantiv): modificarea structurii interne a software-ului cu scopul de a facilita \u00een\u021belegerea func\u021bion\u0103rii acestuia \u0219i de a simplifica modificarea, f\u0103r\u0103 a afecta comportamentul observabil.\n<\/p><\/blockquote>\n<blockquote><p>A efectua refactorizarea (Refactor) (verb): a modifica structura software-ului, aplic\u00e2nd o serie de refactoriz\u0103ri, f\u0103r\u0103 a afecta comportamentul s\u0103u.\n<\/p><\/blockquote>\n<p>Cartea ofer\u0103 \u201eformule\u201d care trebuie recunoscute \u00een codul surs\u0103 \u0219i reguli pentru transformarea lor.<\/p>\n<p>Ca exemplu simplu, voi aduce \u201eintroducerea unei variabile explicative\u201d din carte:<\/p>\n<pre><code class=\"plaintext\">if ( (platform.toUpperCase().indexOf(\u201cMAC\u201d) &gt; -1 ) &amp;&amp;\n    (browser.toUpperCase().indexOf(\u201cIE\u201d) &gt; -1 )&amp;&amp;\n    wasInitialized() &amp;&amp; resize &gt; 0 ) {\n    \/\/ execut\u0103 ceva\n}<\/code><\/pre>\n<p>\nP\u0103r\u021bile expresiei trebuie \u00eenregistrate \u00eentr-o variabil\u0103, a c\u0103rei denumire explic\u0103 scopul acesteia.<\/p>\n<pre><code class=\"plaintext\">final boolean isMacOS = platform.toUpperCase().indexOf(\u201cMAC\u201d) &gt; -1;\nfinal boolean isIEBrowser = browser.toUpperCase().indexOf(\u201cIE\u201d) &gt; -1;\nfinal boolean isResized = resize &gt; 0;\nif(isMacOS &amp;&amp; isIEBrowser &amp;&amp; wasInitialized() &amp;&amp; isResized) {\n   \/\/ execut\u0103 ceva\n}\n<\/code><\/pre>\n<p>\nImagineaz\u0103-\u021bi o persoan\u0103 care nu poate simplifica expresiile algebrice folosind formula p\u0103tratului sumei \u0219i al diferen\u021bei p\u0103tratelor.<\/p>\n<p>Crezi c\u0103 aceast\u0103 persoan\u0103 poate refactoriza codul?<\/p>\n<p>Va putea s\u0103 scrie un cod clar pentru altele, dac\u0103 nu are format\u0103 ideea de concizie? Din punctul meu de vedere \u2014 nu.<\/p>\n<p>Totu\u0219i, la \u0219coal\u0103 \u00eenva\u021b\u0103 to\u021bi, iar programatori devin doar o minoritate. Este util\u0103 abilitatea de a transforma expresii pentru oamenii obi\u0219nui\u021bi? Cred c\u0103 da. Aceast\u0103 abilitate este aplicat\u0103 \u00eentr-o form\u0103 mai abstract\u0103: trebuie s\u0103 evaluezi situa\u021bia \u0219i s\u0103 alegi ac\u021biunea ulterioar\u0103 astfel \u00eenc\u00e2t s\u0103 te aproprii de scop. \u00cen pedagogie, acest fenomen se nume\u0219te <noindex><a rel=\"nofollow\" href=\"https:\/\/current_pedagogy.academic.ro\/1191\/\">transfer (de abilitate)<\/a><\/noindex>.<\/p>\n<p>Cele mai vii exemple apar \u00een timpul repara\u021biilor casnice cu mijloace improvizate, \u00eentr-un mod \u201eamator\u201d. Ca rezultat, apar acele \u201etrucuri\u201d \u0219i life hack-uri, unul dintre ele este ilustrat \u00een CPDV. Autorul ideii a avut o bucat\u0103 de lemn, un fir \u0219i patru \u0219uruburi. Amintindu-\u0219i de modelul unei prize pentru lamp\u0103, a construit din ele o priz\u0103 f\u0103cut\u0103 manual.<\/p>\n<p>Chiar \u0219i atunci c\u00e2nd utilizeaz\u0103 transport auto, \u0219oferul recunoa\u0219te constant modele \u00een lumea \u00eenconjur\u0103toare \u0219i efectueaz\u0103 manevre corespunz\u0103toare pentru a ajunge la destina\u021bie.<\/p>\n<blockquote><p>C\u00e2nd ai murit, nu \u0219tii, ci doar altora le este greu. Acelasi lucru se \u00eent\u00e2mpl\u0103 c\u00e2nd nu ai st\u0103p\u00e2nit matematica...<\/p><\/blockquote>\n<p>Ce se \u00eent\u00e2mpl\u0103, dac\u0103 o persoan\u0103 nu reu\u0219e\u0219te s\u0103 \u00eenve\u021be transformarea expresiilor? Din c\u00e2nd \u00een c\u00e2nd, fac sesiuni individuale cu studen\u021bi care au avut dificult\u0103\u021bi cu matematica la \u0219coal\u0103. De obicei, ei se blocheaz\u0103 complet pe tema buclelor. At\u00e2t de mult, \u00eenc\u00e2t trebuie s\u0103 lucr\u0103m la \u201ealgebr\u0103\u201d, dar \u00een limbajul de programare.<br \/>\nAcest lucru se \u00eent\u00e2mpl\u0103 pentru c\u0103, atunci c\u00e2nd scriem bucle, principala tehnic\u0103 const\u0103 tocmai \u00een a transforma un grup de expresii identice.<\/p>\n<p>S\u0103 presupunem c\u0103 rezultatul programului ar trebui s\u0103 arate astfel:<\/p>\n<blockquote><p>Introducere<br \/>\nCapitolul 1<br \/>\nCapitolul 2<br \/>\nCapitolul 3<br \/>\nCapitolul 4<br \/>\nCapitolul 5<br \/>\nCapitolul 6<br \/>\nCapitolul 7<br \/>\nConcluzie<\/p><\/blockquote>\n<p> Un program trivial pentru a ob\u021bine acest rezultat arat\u0103 astfel:<\/p>\n<pre><code class=\"cs\">static void Main(string[] args)\n{\n    Console.WriteLine(\"Introducere\");\n    Console.WriteLine(\"Capitolul 1\");\n    Console.WriteLine(\"Capitolul 2\");\n    Console.WriteLine(\"Capitolul 3\");\n    Console.WriteLine(\"Capitolul 4\");\n    Console.WriteLine(\"Capitolul 5\");\n    Console.WriteLine(\"Capitolul 6\");\n    Console.WriteLine(\"Capitolul 7\");\n    Console.WriteLine(\"Concluzie\");\n}<\/code><\/pre>\n<p>\nDar aceast\u0103 solu\u021bie este departe de idealul concis. Mai \u00eent\u00e2i trebuie s\u0103 g\u0103sim grupul repetitiv de ac\u021biuni \u0219i apoi s\u0103-l transform\u0103m. \u00cen cele din urm\u0103, va ap\u0103rea o solu\u021bie de genul:<\/p>\n<pre><code class=\"cs\">static void Main(string[] args)\n{\n    Console.WriteLine(\"Introducere\");\n    for (int i = 1; i &lt;= 7; i++)\n    {\n        Console.WriteLine(&quot;Capitolul &quot; + i);\n    }\n    Console.WriteLine(&quot;Concluzie&quot;);\n}<\/code><\/pre>\n<p>\nDac\u0103 o persoan\u0103 nu a \u00eenv\u0103\u021bat matematica la vremea ei, atunci nu va putea efectua astfel de transform\u0103ri. Pur \u0219i simplu nu va avea abilit\u0103\u021bile necesare. De aceea, tema buclelor este prima barier\u0103 \u00een formarea unui dezvoltator.<\/p>\n<p>Probleme similare apar \u0219i \u00een alte domenii. Dac\u0103 o persoan\u0103 nu \u0219tie s\u0103 foloseasc\u0103 un instrument la \u00eendem\u00e2n\u0103, nu va putea s\u0103 demonstreze ingeniozitate \u00een via\u021ba de zi cu zi. Limbile rele vor spune c\u0103 m\u00e2inile nu cresc din locul potrivit. Pe drum, acest lucru se manifest\u0103 prin incapacitatea de a evalua corect situa\u021bia \u0219i de a alege manevra. Ceva ce uneori poate duce la consecin\u021be tragice.<\/p>\n<p>Concluzii:<\/p>\n<ol>\n<li>Matematica \u0219colar\u0103 \u0219i universitar\u0103 ne este necesar\u0103 pentru a putea face lumea mai bun\u0103 cu resursele pe care le avem.<\/li>\n<li>Dac\u0103 studiezi \u0219i \u00eent\u00e2mpini probleme \u00een \u00eenv\u0103\u021barea buclelor, \u00eencearc\u0103 s\u0103 te \u00eentorci la originile tale - algebra \u0219colar\u0103. Ia un caiet de exerci\u021bii pentru clasa a 9-a \u0219i rezolv\u0103 exerci\u021biile din acesta.<\/li>\n<\/ol>\n<p>Sursa: <a content=\"nofollow\" rel=\"nofollow\" href=\"https:\/\/habr.com\/ru\/post\/456156\/\">habr.com<\/a><\/p>","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"<p>\u041e\u0431\u044b\u0447\u043d\u043e \u043d\u0430 \u0432\u043e\u043f\u0440\u043e\u0441 \u00ab\u0437\u0430\u0447\u0435\u043c \u043d\u0443\u0436\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430?\u00bb \u043e\u0442\u0432\u0435\u0447\u0430\u044e\u0442 \u0447\u0442\u043e-\u0442\u043e \u0432\u0440\u043e\u0434\u0435 \u00ab\u0433\u0438\u043c\u043d\u0430\u0441\u0442\u0438\u043a\u0430 \u0434\u043b\u044f \u0443\u043c\u0430\u00bb. \u041d\u0430 \u043c\u043e\u0439 \u0432\u0437\u0433\u043b\u044f\u0434, \u044d\u0442\u043e\u0433\u043e \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u044f \u043d\u0435\u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e. \u041a\u043e\u0433\u0434\u0430 \u0447\u0435\u043b\u043e\u0432\u0435\u043a \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442 \u0444\u0438\u0437\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f, \u0442\u043e \u043e\u043d \u0437\u043d\u0430\u0435\u0442 \u0442\u043e\u0447\u043d\u043e\u0435 \u043d\u0430\u0437\u0432\u0430\u043d\u0438\u0435 \u0433\u0440\u0443\u043f\u043f \u043c\u044b\u0448\u0446, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u0440\u0438 \u044d\u0442\u043e\u043c \u0440\u0430\u0437\u0432\u0438\u0432\u0430\u044e\u0442\u0441\u044f. \u041d\u043e \u0440\u0430\u0437\u0433\u043e\u0432\u043e\u0440\u044b \u043f\u0440\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0443 \u043e\u0441\u0442\u0430\u044e\u0442\u0441\u044f \u0441\u043b\u0438\u0448\u043a\u043e\u043c \u0430\u0431\u0441\u0442\u0440\u0430\u043a\u0442\u043d\u044b\u043c\u0438. \u041a\u0430\u043a\u0438\u0435 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u043e \u00ab\u043c\u044b\u0448\u0446\u044b \u0443\u043c\u0430\u00bb \u0442\u0440\u0435\u043d\u0438\u0440\u0443\u044e\u0442\u0441\u044f \u0448\u043a\u043e\u043b\u044c\u043d\u043e\u0439 \u0430\u043b\u0433\u0435\u0431\u0440\u043e\u0439? \u041e\u043d\u0430 \u0432\u0435\u0434\u044c \u0441\u043e\u0432\u0441\u0435\u043c \u043d\u0435 \u043f\u043e\u0445\u043e\u0436\u0430 \u043d\u0430 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0443\u044e [&hellip;]<\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":27386,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[702],"tags":[],"class_list":["post-36577","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-news"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.4 - aioseo.com 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