{"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\/news\/vot-zachem-nuzhna-shkolnaya-algebra","title":{"rendered":"Kuidas on kooli algebra vajalik?","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"<p>Tavaliselt vastatakse k\u00fcsimusele \"miks on matemaatika vajalik?\" midagi sellist nagu \"vaimu treening\". Minu arvates on see seletus ebapiisav. Kui inimene teeb f\u00fc\u00fcsilisi harjutusi, siis teab ta t\u00e4pselt, milliseid lihasgruppe ta treenib. Kuid matemaatika k\u00e4sitlemine j\u00e4\u00e4b liiga abstraktseks. Milliseid konkreetselt \"vaimu lihaseid\" kooli algebra treenib? See ei sarnane t\u00f5elise matemaatikaga, kus tehakse suuri avastusi. Mida annab oskus otsida tuletisi mingitest keerulistest funktsioonidest?<\/p>\n<p>Programmeerimise \u00f5petamine n\u00f5rkadele tudengitele on viinud mind t\u00e4psema vastuseni k\u00fcsimusele \"miks?\". Artiklis p\u00fc\u00fcan selle teie juurde tuua.<\/p>\n<p><img decoding=\"async\" alt=\"Kuidas on kooli algebra 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 p\u00fchendatakse \u00fcsna palju aega v\u00e4ljendite teisendamisele ja lihtsustamisele. N\u00e4iteks: 81\u00d72+126xy+49y\u00b2 tuleb teisendada j\u00e4rgmiselt: (9x+7y)\u00b2.<\/p>\n<p>Antud n\u00e4ites oodatakse \u00f5pilaselt, et ta meenutab summa ruudu valemit. <\/p>\n<p><img decoding=\"async\" alt=\"Kuidas on kooli algebra vajalik?\" src=\"\/wp-content\/uploads\/2019\/07\/7b8f583cf587730de2f76011f83b05b2.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>\nKardinaalsetes olukordades v\u00f5ib saadud v\u00e4ljendit kasutada teisteks transformatsioonideks. N\u00e4iteks:<\/p>\n<p><img decoding=\"async\" alt=\"Kuidas on kooli algebra vajalik?\" src=\"\/wp-content\/uploads\/2019\/07\/fe1570cc2f91020281abd22b47aad458.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>\ntransformeeritakse esmalt kujule<\/p>\n<p><img decoding=\"async\" alt=\"Kuidas on kooli algebra vajalik?\" src=\"\/wp-content\/uploads\/2019\/07\/0aaa7d8b4dbf3d4c8e331a44088fc863.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>\nja siis, t\u00e4iendusega (a + 2b) != 0, saadakse see nii<\/p>\n<p><img decoding=\"async\" alt=\"Kuidas on kooli algebra vajalik?\" src=\"\/wp-content\/uploads\/2019\/07\/a95f9f03442ae65be217f70d4039b433.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Selle tulemuse saavutamiseks peab \u00f5pilane algses v\u00e4ljendis \u00e4ra tundma ning seej\u00e4rel rakendama kolme valemit:<\/p>\n<ul>\n<li>Summa ruut<\/li>\n<li>Ruutude vahe<\/li>\n<li>Tavalise murru tegurite l\u00fchemus<\/li>\n<\/ul>\n<p>\nTavalisel koolis kulutasime peaaegu kogu aja algebra tunni ajal selliste avaldise transformeerimisele. K\u00f5rgkooli k\u00f5rgemal matemaatikas ei muutunud midagi oluliselt. Meile \u00f5petati, kuidas tuletisi (integraale jne) v\u00f5tta ja anti hulgaliselt \u00fclesandeid. Kas sellest oli kasu? Minu arvates \u2014 jah. Selliste harjutuste tulemuseks:<\/p>\n<ol>\n<li>Hakkasime avaldiseid transformeerima.<\/li>\n<li>Arenes t\u00e4helepanelikkus detailide suhtes.<\/li>\n<li>Kujunes ideaal \u2014 lakooniline v\u00e4ljend, mille poole p\u00fc\u00fcda.<\/li>\n<\/ol>\n<p>\nMinu arvates on sellise ideaali, kvaliteedi ja oskuse olemasolu igap\u00e4evases arendust\u00f6\u00f6s v\u00e4ga kasulik. L\u00f5ppude l\u00f5puks t\u00e4hendab avaldise lihtsustamine, et muuta selle struktuuri nii, et m\u00f5istmine oleks lihtsam, ilma m\u00f5tet m\u00f5jutamata. Kas see ei meenuta teile midagi?<\/p>\n<p>See on peaaegu Martin Fowlersi samanimelise raamatu refaktoreerimise m\u00e4\u00e4ratlemine.<\/p>\n<p>Oma t\u00f6\u00f6s s\u00f5nastab autor need j\u00e4rgmiselt:<\/p>\n<blockquote><p>Refactoring (s\u00f5na): tarkvara sisemise struktuuri muutmine eesm\u00e4rgiga muuta selle toimimist arusaadavamaks ja lihtsustada muutmist, m\u00f5jutamata n\u00e4htavat k\u00e4itumist.\n<\/p><\/blockquote>\n<blockquote><p>Refaktoreerima (verbi): tarkvara struktuuri muutmine, rakendades mitmeid refaktoreerimisi, ilma et see m\u00f5jutaks selle k\u00e4itumist.\n<\/p><\/blockquote>\n<p>Raamatus esitatakse \u00abvalemid\u00bb, mida tuleb tuvastada l\u00e4htekoodis ning nende muutmise reegleid.<\/p>\n<p>Lihtsama n\u00e4itena toon raamatus toodud \u00abselgitava muutuja sisseviimise\u00bb:<\/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    \/\/ tee midagi\n}<\/code><\/pre>\n<p>\nV\u00e4ljendi osad tuleb kirjutada muutujasse, mille nimi selgitab selle eesm\u00e4rki.<\/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   \/\/ tee midagi\n}\n<\/code><\/pre>\n<p>\nKujutage ette inimest, kes ei oska algebralisi v\u00e4ljendeid lihtsustada, kasutades ruutude summa ja erinevuse valemit.<\/p>\n<p>Kuidas arvatavasti arvate, et see inimene suudab koodi refaktoreerida?<\/p>\n<p>Kas ta suudab \u00fcldse kirjutada teistele arusaadavat koodi, kui tal ei ole kujunenud ideaalset arusaama sellest, mis on kokkuv\u00f5tlik? Minu arvates \u2014 ei.<\/p>\n<p>Siiski \u00f5pivad k\u00f5ik koolis, aga programmeerijateks saavad v\u00e4hesed. Kas oskus v\u00e4ljendeid muuta on tavalistele inimestele kasulik? Ma arvan, et jah. Ainult oskus rakendatakse rohkem abstraktsel viisil: tuleb hinnata olukorda ja valida edasine tegevus, et l\u00e4heneda eesm\u00e4rgile. Pedagoogikas nimetatakse seda fenomeni <noindex><a rel=\"nofollow\" href=\"https:\/\/current_pedagogy.academic.ru\/1191\/\">edasi\u00fclekanne (oskus)<\/a><\/noindex>.<\/p>\n<p>K\u00e4rgimad n\u00e4iteks tekivad kodustes remondit\u00f6\u00f6des odava meetodi abil, \u00abkolhooslikult\u00bb tehtuna. Selle tulemusena ilmuvad need \u00abnipid\u00bb ja eluh\u00e4kid, millest \u00fcks on kujutatud \u041a\u041f\u0414\u0412-l. Idee autoril oli puut\u00fckk, juhe ja neli kruvi. Meelde tuletades lampide patendi mustrit, kokkutas ta neist isetehtud patendi.<\/p>\n<p>Isegi autoga s\u00f5ites tegeleb juht pidevalt \u00fcmbritseva maailma mustrite tuvastamise ja vastavate man\u00f6\u00f6vrite tegemisega, et j\u00f5uda sihtkohta.<\/p>\n<blockquote><p>Kui sa oled surnud, siis sa sellest ei tea, ainult teistel on raske. Samamoodi on, kui sa ei ole matemaatikat selgeks saanud\u2026<\/p><\/blockquote>\n<p>Mis juhtub, kui inimene ei \u00f5pi v\u00e4ljendite muutmist? Aeg-ajalt viin l\u00e4bi individuaalseid tunde \u00fcli\u00f5pilastega, kellel koolis matemaatikaga kehvasti l\u00e4ks. T\u00fc\u00fcpiliselt takerduvad nad rangelt ts\u00fcklite teema peale. Nii palju, et nendega tuleb tegeleda \"algebraga\", kuid programmeerimiskeele kontekstis.<br \/>\nSee juhtub sellep\u00e4rast, et ts\u00fcklite kirjutamisel p\u00f5hitekst seisneb just selles, et muuta sama v\u00e4\u00e4rtustega r\u00fchm v\u00e4ljendeid.<\/p>\n<p>Oletame, et programmi v\u00e4ljundi tulemus peaks v\u00e4lja n\u00e4gema j\u00e4rgmiselt:<\/p>\n<blockquote><p>Sissejuhatus<br \/>\nPeat\u00fckk 1<br \/>\nPeat\u00fckk 2<br \/>\nL\u00fchipeat\u00fckk 3<br \/>\nL\u00fchipeat\u00fckk 4<br \/>\nL\u00fchipeat\u00fckk 5<br \/>\nL\u00fchipeat\u00fckk 6<br \/>\nL\u00fchipeat\u00fckk 7<br \/>\nKokkuv\u00f5te<\/p><\/blockquote>\n<p> Lihtne programmiline lahendus selle tulemuse saavutamiseks n\u00e4eb v\u00e4lja j\u00e4rgmiselt:<\/p>\n<pre><code class=\"cs\">static void Main(string[] args)\n{\n    Console.WriteLine(\"Sissejuhatus\");\n    Console.WriteLine(\"L\u00fchipeat\u00fckk 1\");\n    Console.WriteLine(\"L\u00fchipeat\u00fckk 2\");\n    Console.WriteLine(\"L\u00fchipeat\u00fckk 3\");\n    Console.WriteLine(\"L\u00fchipeat\u00fckk 4\");\n    Console.WriteLine(\"L\u00fchipeat\u00fckk 5\");\n    Console.WriteLine(\"L\u00fchipeat\u00fckk 6\");\n    Console.WriteLine(\"L\u00fchipeat\u00fckk 7\");\n    Console.WriteLine(\"Kokkuv\u00f5te\");\n}<\/code><\/pre>\n<p>\nKuid see lahendus on kaugel elegantsest ideaalist. Esiteks tuleb leida korduv tegevuser\u00fchm ja seej\u00e4rel muuta. L\u00f5pptulemusena saame j\u00e4rgmise lahenduse:<\/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;L\u00fchipeat\u00fckk &quot; + i);\n    }\n    Console.WriteLine(&quot;Kokkuv\u00f5te&quot;);\n}<\/code><\/pre>\n<p>\nKuid kui inimene ei \u00f5ppinud nooremana matemaatikat, ei suuda ta ka selliseid muudatusi teha. Tal ei ole lihtsalt vastavaid oskusi. Seet\u00f5ttu on ts\u00fcklite teema esimene takistus arendajate koolitamisel.<\/p>\n<p>Sarnased probleemid esinevad ka teistes valdkondades. Kui inimene ei oska t\u00f6\u00f6riistu kasutada, ei suuda ta ka n\u00e4idata igap\u00e4evast leidlikkust. \u00dcksk\u00f5ik, mida nad \u00fctlevad, et k\u00e4ed ei kasva sealt, kus vaja. Teel v\u00e4ljendub see oskuses \u00f5igesti olukorda hinnata ja man\u00f6\u00f6verdada, mis m\u00f5nikord v\u00f5ib tuua traagilisi tagaj\u00e4rgi.<\/p>\n<p>Kokkuv\u00f5tted:<\/p>\n<ol>\n<li>Kooli ja \u00fclikooli matemaatika on vajalik, et oskaksime muuta maailma paremaks olemasolevate vahenditega.<\/li>\n<li>Kui \u00f5pid ja sul on probleemide tekkimisega ts\u00fcklite \u00f5ppimisel, proovi naasta juurte juurde \u2014 koolialgebra juurde. V\u00f5ta 9. klassi \u00fclesannete kogu ja lahenda sealt n\u00e4iteid.<\/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-news"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.1.1 - 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.\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"Yuri Gagarin\"\/>\n\t<link rel=\"canonical\" href=\"https:\/\/prohoster.info\/et\/blog\/news\/vot-zachem-nuzhna-shkolnaya-algebra\" \/>\n\t<meta name=\"generator\" content=\"All in One SEO (AIOSEO) 5.0.1.1\" \/>\n\t\t<meta property=\"og:locale\" content=\"et_EE\" \/>\n\t\t<meta property=\"og:site_name\" content=\"ProHoster | \u041a\u0443\u043f\u0438\u0442\u044c \u043d\u0430\u0434\u0435\u0436\u043d\u044b\u0439 \u0445\u043e\u0441\u0442\u0438\u043d\u0433 \u0434\u043b\u044f \u0441\u0430\u0439\u0442\u043e\u0432 \u0441 \u0437\u0430\u0449\u0438\u0442\u043e\u0439 \u043e\u0442 DDoS, VPS VDS \u0441\u0435\u0440\u0432\u0435\u0440\u044b\" \/>\n\t\t<meta property=\"og:type\" content=\"article\" \/>\n\t\t<meta property=\"og:title\" content=\"\ud83e\udd47\u0412\u043e\u0442 \u0437\u0430\u0447\u0435\u043c \u043d\u0443\u0436\u043d\u0430 \u0448\u043a\u043e\u043b\u044c\u043d\u0430\u044f \u0430\u043b\u0433\u0435\u0431\u0440\u0430 | ProHoster\" \/>\n\t\t<meta property=\"og: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.\" \/>\n\t\t<meta property=\"og:url\" content=\"https:\/\/prohoster.info\/et\/blog\/news\/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\udd47N\u00e4e, miks on kooli algebral oma v\u00e4\u00e4rtus | ProHoster","description":"Tavaliselt vastatakse k\u00fcsimusele \u201emiks on matemaatikat vaja?\u201d midagi sellist nagu \u201evaimu sport\u201d. 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