{"id":794,"date":"2021-08-26T10:30:02","date_gmt":"2021-08-26T08:30:02","guid":{"rendered":"http:\/\/ucitel.kvcso.cz\/?p=794"},"modified":"2022-04-04T22:18:46","modified_gmt":"2022-04-04T20:18:46","slug":"skriptovani-v-geogebre","status":"publish","type":"post","link":"https:\/\/ucitel.kvcso.cz\/?p=794","title":{"rendered":"Skriptov\u00e1n\u00ed v Geogeb\u0159e"},"content":{"rendered":"\n<p>O Geogeb\u0159e jsem u\u017e n\u011bkolikr\u00e1t psal. Jednak ji pova\u017euji v dne\u0161n\u00ed dob\u011b za nezbytn\u00fd n\u00e1stroj u\u010ditel\u016f matematiky bez ohledu na vztah k ICT obecn\u011b, jednak jde skute\u010dn\u011b o \u0161irokou vzd\u011bl\u00e1vac\u00ed platformu p\u0159esahuj\u00edc\u00ed p\u016fvodn\u00ed geometrii. Berte tato slova pros\u00edm jako konstatov\u00e1n\u00ed faktu, by\u0165 subjektivn\u00ed. Nejde o technologick\u00e9 nad\u0161en\u00ed, ale o syst\u00e9movou v\u00fduku, kter\u00e1 je pln\u011b v rukou kantora.&nbsp;<\/p>\n\n\n\n<p>V Geogeb\u0159e m\u016f\u017eeme dokonce vytv\u00e1\u0159et <strong>vlastn\u00ed v\u00fdukov\u00e9 aplikace<\/strong>. Platforma (\u00famysln\u011b nepou\u017e\u00edv\u00e1m ozna\u010den\u00ed program) toti\u017e umo\u017e\u0148uje pr\u00e1ci s ud\u00e1lostmi podobn\u011b jako v jak\u00e9mkoli programov\u00e1n\u00ed. Jde vlastn\u011b o dv\u011b \u00farovn\u011b v p\u0159\u00edstupu.&nbsp;<\/p>\n\n\n\n<p>V t\u00e9 <strong>prvn\u00ed <\/strong>vyu\u017eijeme ud\u00e1lostn\u00ed prvky nap\u0159. tla\u010d\u00edtko, posuvn\u00edk nebo dynamick\u00fd text. Jakmile pochop\u00edme jednoduch\u00fd princip, u\u017e si m\u016f\u017eeme p\u0159ipravit jednoduchou vlastn\u00ed aplikaci, nap\u0159\u00edklad tr\u00e9ninkov\u00e9 h\u0159i\u0161t\u011b na procvi\u010dov\u00e1n\u00ed d\u011blitelnosti.&nbsp;<\/p>\n\n\n\n<p>V <strong>druh\u00e9<\/strong> \u00farovni zapoj\u00edme p\u0159ipraven\u00e9 skripty, kter\u00e9 jsou u\u017e naprogramov\u00e1ny a lze je kombinovat. Jejich pou\u017eit\u00ed nen\u00ed obt\u00ed\u017en\u00e9, jen je t\u0159eba m\u00edt smysl pro algoritmizaci. Ale tu matematici maj\u00ed, \u017ee? Snadno si sestav\u00edme dynamick\u00e9 \u00falohy, kter\u00e9 n\u00e1m slou\u017e\u00ed v hodin\u011b i pro p\u0159\u00edpravu.&nbsp;<\/p>\n\n\n\n<p>V dob\u011b zav\u0159en\u00fdch \u0161kol jsem podobn\u00e9 v\u00fdstupy vyu\u017eil pro vlastn\u00ed v\u00fdukov\u00e1 videa. Jedno je v uk\u00e1zce pod kapitolou (YouTube), v podstat\u011b kop\u00edruje m\u016fj zp\u016fsob v\u00fdkladu a p\u0159id\u00e1v\u00e1 nav\u00edc dynami\u010dnost. Nemluv\u011b o tom, \u017ee jej maj\u00ed moji \u017e\u00e1ci v Classroomu, proto\u017ee co kdyby\u2026<\/p>\n\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Funkce y = sin(x)\" width=\"644\" height=\"362\" src=\"https:\/\/www.youtube.com\/embed\/VNuUnR29D8A?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Fyzika v Geogeb\u0159e<\/h2>\n\n\n\n<p>Zaj\u00edmavou fyzik\u00e1ln\u00ed \u00falohu m\u016f\u017eeme vytvo\u0159it i pomoc\u00ed Geogebry. Ona to je vlastn\u011b po\u0159\u00e1d matematika, nebo\u0165 se jedn\u00e1 o pohyb rovnom\u011brn\u00fd p\u0159\u00edmo\u010dar\u00fd, tj. o <strong>\u00falohu o pohybu<\/strong>. Nejde ale ani tak o v\u00fdpo\u010det, ale o experiment\u00e1ln\u00ed hr\u00e1tky. V podstat\u011b jde o doh\u00e1n\u011bn\u00ed jednoho objektu druh\u00fdm a ot\u00e1zku, jak nastavit parametry, aby oba dob\u011bhly do c\u00edle sou\u010dasn\u011b.&nbsp;<\/p>\n\n\n\n<p>Prvn\u00edmu objektu (b\u011b\u017eci) ur\u010d\u00edme rychlost, klidn\u011b z\u00e1vislou na dal\u0161\u00edm parametru &#8211; viz posuvn\u00edk <em>b<\/em>. U druh\u00e9ho (cyklisty) zvol\u00edme zpo\u017ed\u011bn\u00ed startu pomoc\u00ed podm\u00ednky z\u00e1visl\u00e9 na ura\u017een\u00e9 vzd\u00e1lenosti b\u011b\u017ece. Jednoduch\u00fdm experimentov\u00e1n\u00edm (zm\u011bnou podm\u00ednky) se budeme sna\u017eit dos\u00e1hnout stejn\u00e9ho okam\u017eiku pro dosa\u017een\u00ed c\u00edle.&nbsp;<\/p>\n\n\n\n<p>Jde opravdu o experiment\u00e1ln\u00ed hru. Pokud ale chceme se \u017e\u00e1ky ov\u011b\u0159it v\u00fdsledek v\u00fdpo\u010dtem, p\u016fjde o jednoduchou rovnici z \u00faloh o pohybu. P\u0159\u00edklad je o fyzice i matematice. Ur\u010dit\u011b je vhodn\u00e9 v\u00e9st \u017e\u00e1ky k tomu, aby se sna\u017eili pochopit, co vlastn\u011b po\u010d\u00edtaj\u00ed.&nbsp;<\/p>\n\n\n\n<p>Jak dojdeme k tomu, \u017ee cyklista vyjede, kdy\u017e m\u00e1 b\u011b\u017eec za sebou pr\u00e1v\u011b 6&nbsp;metr\u016f? Celkov\u00fd \u010das je 5&nbsp;s pro dr\u00e1hu 15&nbsp;m. Tak\u017ee zpo\u017ed\u011bn\u00ed o a = 2&nbsp;s (v druh\u00e9 rovnici) vyn\u00e1sob\u00edme 3 (jeho rychlost).<\/p>\n\n\n\n<p><em>s = v . t<br>15 = 3x&nbsp; &#8211; (b\u011b\u017eec)<br>15 = 5(x &#8211; a) &#8211; (cyklista)<br>a = (2\/5).x (\u010das b\u011b\u017ece, zde v sekund\u00e1ch, x = 5&nbsp;s, a = 2&nbsp;s)<\/em><\/p>\n\n\n\n<p>Dal\u0161\u00ed mo\u017enost je v \u0159e\u0161en\u00ed \u00falohy <em>grafickou metodou<\/em>. To ji\u017e experiment nen\u00ed, proto\u017ee \u017e\u00e1ci pracuj\u00ed s line\u00e1rn\u00ed funkc\u00ed, resp. s grafick\u00fdm \u0159e\u0161en\u00edm soustavy line\u00e1rn\u00edch rovnic. Je opravdu d\u016fle\u017eit\u00e9, aby pochopili rozd\u00edl mezi modelov\u00e1n\u00edm \u00falohy a \u0159e\u0161en\u00edm. Pro ob\u011b situace pou\u017e\u00edv\u00e1me Geogebru, poka\u017ed\u00e9 ale s jin\u00fdm c\u00edlem.&nbsp; Propojen\u00ed experiment\u00e1ln\u00ed hry a grafick\u00e9ho \u0159e\u0161en\u00ed je ve videu pod kapitolou (YouTube).<\/p>\n\n\n\n<p>A to nejlep\u0161\u00ed nakonec. V \u00faloze je nastavena rychlost b\u011b\u017ece jako konstanta. Ale pokud ji zad\u00e1me tak\u00e9 jako m\u011bn\u00edc\u00ed se parametr (<em>b<\/em>), dostaneme dal\u0161\u00ed mo\u017en\u00e1 \u0159e\u0161en\u00ed. Ve videu jsem zvolil zm\u011bnu jen v p\u0159irozen\u00fdch \u010d\u00edslech, aby mohli \u017e\u00e1ci doj\u00edt k rozumn\u00fdm v\u00fdsledk\u016fm. A v dal\u0161\u00ed \u00farovni m\u016f\u017eeme nazna\u010dit b\u011b\u017eci, aby na cel\u00e9m \u00faseku zrychloval.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"B\u011b\u017eec a cyklista\" width=\"644\" height=\"483\" src=\"https:\/\/www.youtube.com\/embed\/dDVWVDrE0RE?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p><strong>Autor: Petr Chlebek <\/strong><\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>O Geogeb\u0159e jsem u\u017e n\u011bkolikr\u00e1t psal. Jednak ji pova\u017euji v dne\u0161n\u00ed dob\u011b za nezbytn\u00fd n\u00e1stroj u\u010ditel\u016f matematiky bez ohledu na vztah k ICT obecn\u011b, jednak jde skute\u010dn\u011b o \u0161irokou vzd\u011bl\u00e1vac\u00ed platformu p\u0159esahuj\u00edc\u00ed p\u016fvodn\u00ed geometrii. Berte tato slova pros\u00edm jako konstatov\u00e1n\u00ed faktu, by\u0165 subjektivn\u00ed. Nejde o technologick\u00e9 nad\u0161en\u00ed, ale o syst\u00e9movou v\u00fduku, kter\u00e1 je pln\u011b v&#8230;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,7,8],"tags":[108,44,37,15,34,94],"class_list":["post-794","post","type-post","status-publish","format-standard","hentry","category-sekce-ict","category-sekce-matematiky-a-informatiky","category-sekce-prirodovedna","tag-digitalni-kompetence-2","tag-fyzika","tag-geogebra","tag-ict","tag-matematika","tag-programovani"],"_links":{"self":[{"href":"https:\/\/ucitel.kvcso.cz\/index.php?rest_route=\/wp\/v2\/posts\/794","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ucitel.kvcso.cz\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ucitel.kvcso.cz\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ucitel.kvcso.cz\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/ucitel.kvcso.cz\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=794"}],"version-history":[{"count":7,"href":"https:\/\/ucitel.kvcso.cz\/index.php?rest_route=\/wp\/v2\/posts\/794\/revisions"}],"predecessor-version":[{"id":802,"href":"https:\/\/ucitel.kvcso.cz\/index.php?rest_route=\/wp\/v2\/posts\/794\/revisions\/802"}],"wp:attachment":[{"href":"https:\/\/ucitel.kvcso.cz\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=794"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ucitel.kvcso.cz\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=794"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ucitel.kvcso.cz\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=794"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}