{"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\/et\/blog\/novosti-interneta\/vot-zachem-nuzhna-shkolnaya-algebra","title":{"rendered":"Siit on koolialgebra vajalik","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"<p>Tavaliselt vastatakse k\u00fcsimusele \"miks on matemaatika vajalik?\" midagi sellist nagu \"vaimne spordiharjutus\". Minu arvates on see seletus ebapiisav. Kui inimene tegeleb f\u00fc\u00fcsiliste harjutustega, teab ta t\u00e4pselt, milliste lihasgruppide arengut see h\u00f5lmab. Kuid matemaatikast r\u00e4\u00e4kimine j\u00e4\u00e4b liiga abstraktseks. Millised konkreetsed \"vaimu lihased\" treenivad koolialgebra? See ei sarnane sugugi t\u00f5elise matemaatikaga, kus tehakse suuri avastusi. Mida annab oskus otsida tuletist mingitest keerulistest funktsioonidest?<\/p>\n<p>Programmeerimise \u00f5petamine n\u00f5rkadele \u00f5pilastele on viinud mind t\u00e4psema vastuseni k\u00fcsimusele \"miks?\". Artiklis p\u00fc\u00fcan seda teieni tuua.<\/p>\n<p><img decoding=\"async\" alt=\"Siit on koolialgebra vajalik\" src=\"\/wp-content\/uploads\/2019\/07\/68c529ad50470860a474ba8d910ff00f.jpg\" style=\"display:block;margin: 0 auto;\" \/><noindex><a rel=\"nofollow\" name=\"habracut\"><\/a><\/noindex><br \/>\nKoolis kulub \u00fcsna palju aega v\u00e4ljendite muutmisele ja lihtsustamisele. N\u00e4iteks: 81\u00d72+126xy+49y2 tuleb \u00fcmber kujundada j\u00e4rgmiselt: (9x+7y)2.<\/p>\n<p>Antud n\u00e4ites oodatakse \u00f5pilaselt, et ta m\u00e4letab summa ruutfunktsiooni valemit. <\/p>\n<p><img decoding=\"async\" alt=\"Siit on koolialgebra vajalik\" src=\"\/wp-content\/uploads\/2019\/07\/7b8f583cf587730de2f76011f83b05b2.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>\nRaskemates olukordades saab saadud avaldist kasutada teiste transformatsioonide jaoks. N\u00e4iteks:<\/p>\n<p><img decoding=\"async\" alt=\"Siit on koolialgebra vajalik\" src=\"\/wp-content\/uploads\/2019\/07\/fe1570cc2f91020281abd22b47aad458.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>\nmuudetakse esmalt kujule<\/p>\n<p><img decoding=\"async\" alt=\"Siit on koolialgebra vajalik\" src=\"\/wp-content\/uploads\/2019\/07\/0aaa7d8b4dbf3d4c8e331a44088fc863.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>\nja seej\u00e4rel, t\u00e4psustusega (a + 2b) != 0, saadakse nii<\/p>\n<p><img decoding=\"async\" alt=\"Siit on koolialgebra vajalik\" src=\"\/wp-content\/uploads\/2019\/07\/a95f9f03442ae65be217f70d4039b433.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Sellise tulemuse saavutamiseks peab \u00f5pilane tuvastama algses avaldises ja seej\u00e4rel rakendama kolme valemit:<\/p>\n<ul>\n<li>Summa ruut<\/li>\n<li>Ruutude erinevus<\/li>\n<li>Tavap\u00e4rase murdosa kordajate l\u00fchendamine<\/li>\n<\/ul>\n<p>\nTavakoolis tegelesime algebras peaaegu kogu aeg just selliste avaldiste \u00fcmberkujundamisega. \u00dclikoolis k\u00f5rgemat matemaatikat \u00f5ppides ei muutunud peaaegu midagi. Meile r\u00e4\u00e4giti, kuidas leida tuletisi (integraale jne) ja anti hunnik \u00fclesandeid. Kas see oli kasulik? Minu arvates \u2014 jah. Nende harjutuste t\u00e4itmisel:<\/p>\n<ol>\n<li>Hakkas v\u00e4ljendite \u00fcmberkujundamise oskus teravduma.<\/li>\n<li>Ainult detailide j\u00e4lgimise oskus arenes.<\/li>\n<li>Kujunes idee \u2014 lakooniline v\u00e4ljendus, mille poole p\u00fc\u00fcelda.<\/li>\n<\/ol>\n<p>\nMinu arvates on sellise ideaali, kvaliteedi ja oskuse olemasolu arendaja igap\u00e4evat\u00f6\u00f6s v\u00e4ga kasulik. L\u00f5ppude l\u00f5puks t\u00e4hendab v\u00e4ljendi lihtsustamine p\u00f5him\u00f5tteliselt selle struktuuri muutmist eesm\u00e4rgiga h\u00f5lbustada arusaamist, m\u00f5jutamata t\u00e4hendust. Kas see ei meenuta teile midagi?<\/p>\n<p>See on praktiliselt refaktoringu m\u00e4\u00e4ratlus Martin Fowler'i samanimelisest raamatust.<\/p>\n<p>Oma t\u00f6\u00f6s s\u00f5nastab autor need j\u00e4rgmiselt:<\/p>\n<blockquote><p>Refaktooring (s\u00f5na): tarkvara sisemise struktuuri muutmine, mille eesm\u00e4rk on lihtsustada selle toimimise m\u00f5istmist ja muudatuste tegemist, m\u00f5jutamata n\u00e4htavat k\u00e4itumist.\n<\/p><\/blockquote>\n<blockquote><p>Refaktoori (tegus\u00f5na): tarkvara struktuuri muutmine, rakendades mitmeid refaktoore, m\u00f5jutamata selle k\u00e4itumist.\n<\/p><\/blockquote>\n<p>Raamat sisaldab 'valemeid', mida tuleb tuvastada l\u00e4htekoodist ja nende muutmise reegleid.<\/p>\n<p>Lihtsaima n\u00e4itena toon 'selgitava muutujaga tutvumise' raamatust:<\/p>\n<pre><code class=\"plaintext\">if ( (platform.toUpperCase().indexOf(\"MAC\") &gt; -1 ) &amp;&amp;\n    (browser.toUpperCase().indexOf(\"IE\") &gt; -1 )&amp;&amp;\n    wasInitialized() &amp;&amp; resize &gt; 0 ) {\n    \/\/ tee midagi\n}<\/code><\/pre>\n<p>\nV\u00e4ljendi osad tuleb salvestada muutujasse, mille nimi selgitab selle eesm\u00e4rki.<\/p>\n<pre><code class=\"plaintext\">final boolean isMacOS = platform.toUpperCase().indexOf(\"MAC\") &gt; -1;\nfinal boolean isIEBrowser = browser.toUpperCase().indexOf(\"IE\") &gt; -1;\nfinal boolean isResized = resize &gt; 0;\nif(isMacOS &amp;&amp; isIEBrowser &amp;&amp; wasInitialized() &amp;&amp; isResized) {\n   \/\/ tee midagi\n}\n<\/code><\/pre>\n<p>\nKujudage inimest, kes ei suuda algebrailisi lauseid lihtsustada ruudi summa ja vahe valemi abil.<\/p>\n<p>Kuidas arvate, kas see inimene suudab koodi refaktoorida?<\/p>\n<p>Kas ta suudab \u00fcldse kirjutada teistele arusaadavat koodi, kui tal ei ole kujunenud ideaalne selgus? Minu arvates - ei.<\/p>\n<p>Kuid koolis \u00f5pivad k\u00f5ik, samas kui programmeerijateks saavad v\u00e4hemus. Kas tavalistele inimestele on kasulik oskus v\u00e4ljendite \u00fcmberkujundamine? Arvan, et jah. Kuid see oskus rakendub enamasti abstraktsemal viisil: tuleb hinnata olukorda ja valida edasine tegevus nii, et l\u00e4heneda eesm\u00e4rgile. Pedagoogikas nimetatakse seda n\u00e4htust <noindex><a rel=\"nofollow\" href=\"https:\/\/current_pedagogy.academic.ru\/1191\/%D0%9F%D0%95%D0%A0%D0%95%D0%9D%D0%9E%D0%A1\">\u00fclekandeks (oskusest)<\/a><\/noindex>.<\/p>\n<p>K\u00f5ige silmatorkavamad n\u00e4ited ilmnevad igap\u00e4evase kodu remondi k\u00e4igus improviseeritud vahenditega. Selle tulemusel tekivad need kuulsad \"nippide\" ja elu h\u00e4kkide n\u00e4ited, millest \u00fcks on kujutatud KPDA-s. Idee autoril oli puut\u00fckk, keerdliin ja neli kruvi. Meeles pidades lampide pesade mustrit, kogus ta neist kokku isetehtud pesa.<\/p>\n<p>Isegi autot transpordis s\u00f5ites tegeleb juht pidevalt \u00fcmbritseva maailma mustrite \u00e4ra tundmise ja vastavate man\u00f6\u00f6verdustega, et j\u00f5uda eesm\u00e4rgini.<\/p>\n<blockquote><p>Kui sa olid surnud, ei tea sa sellest, ainult teistel on raske. Sama on siis, kui sa ei ole matemaatikat selgeks saanud...<\/p><\/blockquote>\n<p>Mida siis teha, kui inimene ei \u00f5nnestu v\u00e4ljendite \u00fcmberkujunemisel? Aeg-ajalt viin l\u00e4bi individuaalseid tunde tudengitega, kellel koolis matemaatika h\u00e4sti ei l\u00e4inud. \u00dcldiselt j\u00e4\u00e4vad nad t\u00e4iesti kinni ts\u00fcklite teema juurde. Nii palju, et nendega tuleb tegeleda 'algebra' k\u00fcsimustega, kuid programmeerimiskeeles.<br \/>\nSee juhtub seet\u00f5ttu, et ts\u00fcklite kirjutamise peamine tehnika seisneb just sama gruppi kuju muutmise osas.<\/p>\n<p>Oletame, et programmi t\u00f6\u00f6 tulemus peab v\u00e4lja n\u00e4gema selline:<\/p>\n<blockquote><p>Sissejuhatus<br \/>\nPeat\u00fckk 1<br \/>\nPeat\u00fckk 2<br \/>\nPeat\u00fckk 3<br \/>\nPeat\u00fckk 4<br \/>\nPeat\u00fckk 5<br \/>\nPeat\u00fckk 6<br \/>\nPeat\u00fckk 7<br \/>\nKokkuv\u00f5te<\/p><\/blockquote>\n<p> Lihtne programm, et saavutada see tulemus, n\u00e4eb v\u00e4lja j\u00e4rgmine:<\/p>\n<pre><code class=\"cs\">static void Main(string[] args)\n{\n    Console.WriteLine(\"Sissejuhatus\");\n    Console.WriteLine(\"Peat\u00fckk 1\");\n    Console.WriteLine(\"Peat\u00fckk 2\");\n    Console.WriteLine(\"Peat\u00fckk 3\");\n    Console.WriteLine(\"Peat\u00fckk 4\");\n    Console.WriteLine(\"Peat\u00fckk 5\");\n    Console.WriteLine(\"Peat\u00fckk 6\");\n    Console.WriteLine(\"Peat\u00fckk 7\");\n    Console.WriteLine(\"Kokkuv\u00f5te\");\n}<\/code><\/pre>\n<p>\nKuid see lahendus on kaugel lakoonilisest ideaalist. Esiteks peab selles leidma korduva tegevuste grupi ja seej\u00e4rel \u00fcmber kujundama. L\u00f5ppkokkuv\u00f5ttes saab selline lahendus:<\/p>\n<pre><code class=\"cs\">static void Main(string[] args)\n{\n    Console.WriteLine(\"Sissejuhatus\");\n    for (int i = 1; i &lt;= 7; i++)\n    {\n        Console.WriteLine(&quot;Peat\u00fckk &quot; + i);\n    }\n    Console.WriteLine(&quot;Kokkuv\u00f5te&quot;);\n}<\/code><\/pre>\n<p>\nKui inimene ei ole oma ajal matemaatikat valdama \u00f5ppinud, ei saa ta ka selliseid transformatsioone teostada. Tal ei ole lihtsalt vastavaid oskusi. Just sellep\u00e4rast on ts\u00fcklite teema arendaja hariduses esmane takistus.<\/p>\n<p>Sarnased probleemid tekivad ka teistes valdkondades. Kui inimene ei oska kasutada k\u00e4ep\u00e4rast t\u00f6\u00f6riista, ei saa ta n\u00e4idata kodust leidlikkust. Kurjad keeled \u00fctlevad, et k\u00e4ed ei kasva \u00f5igest kohast. Teel v\u00e4ljendub see oskuseta olukorda \u00f5igesti hinnata ja man\u00f6\u00f6vrit valida. Mis m\u00f5nikord v\u00f5ib viia traagiliste tagaj\u00e4rgedeni.<\/p>\n<p>J\u00e4reldused:<\/p>\n<ol>\n<li>Kooli ja \u00fclikooli matemaatika on vajalik, et oskaksime maailma paremaks muuta olemasolevate vahenditega.<\/li>\n<li>Kui \u00f5pite ja teil on ts\u00fcklite \u00f5ppimisega probleeme, proovige naasta algusesse \u2014 kooli algebra juurde. V\u00f5tke 9. klassi \u00fclesannete kogu ja lahendage sealt n\u00e4ited.<\/li>\n<\/ol>\n<p>Allikas: <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-novosti-interneta"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.0.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"\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? 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\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\" \/>\n\t\t<meta property=\"og:url\" content=\"https:\/\/prohoster.info\/et\/blog\/novosti-interneta\/vot-zachem-nuzhna-shkolnaya-algebra\" \/>\n\t\t<meta property=\"og:image\" content=\"https:\/\/prohoster.info\/wp-content\/uploads\/2021\/11\/logo-350.jpg\" \/>\n\t\t<meta property=\"og:image:secure_url\" content=\"https:\/\/prohoster.info\/wp-content\/uploads\/2021\/11\/logo-350.jpg\" \/>\n\t\t<meta property=\"og:image:width\" content=\"350\" \/>\n\t\t<meta property=\"og:image:height\" content=\"350\" \/>\n\t\t<meta property=\"article:published_time\" content=\"2019-10-31T19:12:27+00:00\" \/>\n\t\t<meta property=\"article:modified_time\" content=\"2019-10-31T19:12:27+00:00\" \/>\n\t\t<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/prohoster\" \/>\n\t\t<meta property=\"article:author\" content=\"https:\/\/www.facebook.com\/prohoster\" \/>\n\t\t<!-- All in One SEO -->\n\n","aioseo_head_json":{"title":"\ud83e\udd47Miks on kooli algebra vajalik | ProHoster","description":"Tavaliselt vastatakse k\u00fcsimusele \u00abmiks on matemaatikat vaja?\u00bb midagi sellist nagu \u00abvaimne treening\u00bb. 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