{"id":12342,"date":"2023-07-08T20:00:02","date_gmt":"2023-07-08T17:00:02","guid":{"rendered":"https:\/\/iteach.ro\/experientedidactice\/?p=12342"},"modified":"2023-07-29T20:53:18","modified_gmt":"2023-07-29T17:53:18","slug":"masurari-si-unitati-de-masura-la-matematica-de-gimnaziu-observatii-metodologice-bazate-pe-experienta","status":"publish","type":"post","link":"https:\/\/iteach.ro\/experientedidactice\/masurari-si-unitati-de-masura-la-matematica-de-gimnaziu-observatii-metodologice-bazate-pe-experienta","title":{"rendered":"M\u0103sur\u0103ri \u0219i unit\u0103\u021bi de m\u0103sur\u0103 la matematica de gimnaziu \u2013 observa\u021bii metodologice bazate pe experien\u021b\u0103"},"content":{"rendered":"<p>Programa \u0219colar\u0103 de matematic\u0103 pentru clasa a V-a are un capitol intitulat \u201eElemente de geometrie \u0219i unit\u0103\u021bi de m\u0103sur\u0103\u201d. Unit\u0103\u021bile de m\u0103sur\u0103 reprezint\u0103 o unitate de \u00eenv\u0103\u021bare la finalul acestui capitol. C\u00e2nd c\u0103ut\u0103m informa\u021bii despre predarea lec\u021biilor cu unit\u0103\u021bi de m\u0103sur\u0103, de cele mai multe ori ne \u00eent\u00e2lnim cu urm\u0103toarele \u00eentreb\u0103ri: (1) Ce m\u0103sur\u0103m? (2) \u00cen ce m\u0103sur\u0103m? Ce unitate de m\u0103sur\u0103 folosim? (3) Cu ce m\u0103sur\u0103m? Ce instrumente folosim? (4) Cum efectu\u0103m transform\u0103rile \u00eentre unit\u0103\u021bi (\u00eentre multiplii \u0219i submultiplii unei unit\u0103\u021bi de m\u0103sur\u0103)?<br \/>\nAceste \u00eentreb\u0103ri \u00eentr-adev\u0103r sunt foarte importante, dar no\u021biunea de m\u0103surare \u00eenseamn\u0103 mai mult dec\u00e2t at\u00e2t. <!--more--><\/p>\n<p>O defini\u021bie a m\u0103sur\u0103rii raportat la lec\u021biile din aceast\u0103 unitate de \u00eenv\u0103\u021bare din clasa a V-a ar fi urm\u0103toarea:<\/p>\n<blockquote><p>Prin m\u0103surare \u00een general \u00een\u021belegem compararea unei m\u0103rimi pe care vrem s\u0103-o m\u0103sur\u0103m cu unitatea de m\u0103sur\u0103 aleas\u0103, adic\u0103 de c\u00e2te ori unitatea de m\u0103sur\u0103 este cuprins\u0103 \u00een m\u0103rimea respectiv\u0103.<\/p><\/blockquote>\n<p>Pornind \u00eens\u0103 de la experien\u021bele din via\u021ba copiilor de clasa a V-a, \u00een\u021belesul cuv\u00e2ntului a m\u0103sura este mai extins. Prezint c\u00e2teva exemple care pot fi discutate cu elevii, exemple de activit\u0103\u021bi care sunt legate de m\u0103surare:<\/p>\n<ul>\n<li>C\u00e2nd copiii \u00een gr\u0103dini\u021b\u0103 sau \u00een ciclul primar compar\u0103, selecteaz\u0103 obiectele dup\u0103 lungime, dup\u0103 form\u0103, dup\u0103 culoare etc., fac tot un fel de m\u0103surare.<\/li>\n<li>Juc\u00e2ndu-se pe balansoar, copiii observ\u0103 care dintre ei are masa corporal\u0103 mai mare sau mai mic\u0103, astfel ei au efectuat o m\u0103surare.<\/li>\n<li>Rezultatele competi\u021biei de dans sau patinaj artistic, dar \u00een general orice competi\u021bie \u0219i nu numai de sport este m\u0103surare.<\/li>\n<li>Evalu\u0103rile la \u0219coal\u0103, notele primite de c\u0103tre elevi la un test m\u0103soar\u0103 cuno\u0219tin\u021bele lor la materia respectiv\u0103 (nu cu precizia unui dispozitiv complex de m\u0103surare \u0219i nu totdeauna obiectiv).<\/li>\n<li>Obiceiurile de cump\u0103rare: c\u00e2nd avem inten\u021bia s\u0103 cump\u0103r\u0103m ceva facem mai multe m\u0103sur\u0103ri (compar\u0103ri). Dac\u0103 dispunem de suma de bani necesar\u0103, deci compar\u0103m pre\u021bul produsului cu banii pe care \u00eei avem. Dac\u0103 ceea ce vrem s\u0103 cump\u0103r\u0103m este de calitatea dorit\u0103 sau dac\u0103 ne convine din toate punctele de vedere. Dac\u0103 sunt mai multe sortimente, le evalu\u0103m dup\u0103 criteriile noastre c\u0103rora trebuie s\u0103 le corespund\u0103 etc.<\/li>\n<li>Sistemul electoral, rezultatele alegerilor. Cu pu\u021bin\u0103 fantezie ne putem \u00eenchipui candida\u021bii \u0219i programele lor balans\u00e2ndu-se pe c\u00e2ntar.<\/li>\n<li>Rezultatele testelor IQ.<\/li>\n<\/ul>\n<p>Ultimele dou\u0103 exemple sunt mai pu\u021bin familiare elevilor din clasa a V-a \u0219i necesit\u0103\u00a0 explica\u021bii.<\/p>\n<p><strong>Alte observa\u021bii metodologice: <\/strong><\/p>\n<p>Este necesar s\u0103 le ar\u0103t\u0103m elevilor \u00een clasa a V-a folosirea instrumentelor de m\u0103surare. Cu toate c\u0103 au folosit liniarul \u0219i \u00een clasele primare, nu le este clar c\u0103 m\u0103surarea segmentului trebuie s\u0103 \u00eenceap\u0103 de la marcajul zero.<\/p>\n<p>Este util s\u0103-i obi\u0219nuim pe elevii s\u0103 fac\u0103 aproxim\u0103ri \u00eenainte de m\u0103surarea concret\u0103. Aceast\u0103 metod\u0103 o putem aplica nu numai la capitolul \u201dUnit\u0103\u021bi de m\u0103sur\u0103\u201d ci \u0219i la m\u0103surarea unghiurilor.<\/p>\n<p>Unit\u0103\u021bile de m\u0103sur\u0103 sunt plasate \u00een capitolul geometrie, dar le folosim \u0219i \u00een alte contexte \u00een matematic\u0103. De exemplu: axa numerelor, la problemele aritmetice, sau la clasa a VI-a la rapoarte \u0219i propor\u021bii, la numere \u00eentregi vorbim despre altitudine \u0219i ad\u00e2ncime etc. Unit\u0103\u021bile de m\u0103sur\u0103 se folosesc \u0219i la alte discipline.<\/p>\n<p>Men\u021bionez cu regret c\u0103 Programa \u0219colar\u0103 pentru disciplina matematic\u0103 clasele a V-a \u2013 a VIII-a din 2017 nu include printre con\u021binuturi unit\u0103\u021bile de m\u0103sur\u0103 pentru mas\u0103, m\u0103surarea timpului \u0219i unit\u0103\u021bile monetare. Conform programei, aceste unit\u0103\u021bi de m\u0103sur\u0103 sunt \u00eent\u00e2lnite de c\u0103tre elevi numai \u00een probleme aritmetice la finalul capitolului \u201eFrac\u021bii\u201d. Din p\u0103cate cuno\u0219tin\u021bele legate de m\u0103surarea acestor m\u0103rimi\u00a0 nu sunt \u00eensu\u0219ite \u00eentr-o m\u0103sur\u0103 necesar\u0103 de c\u0103tre elevi \u00een ciclul primar.<\/p>\n<p>Ce mai ascund m\u0103sur\u0103rile? Plec\u00e2nd de la m\u0103surare putem ajunge la no\u021biuni care dep\u0103\u0219esc nivelul matematicii predate la clasa a V-a.<\/p>\n<p>M\u0103surarea o putem concepe \u0219i ca o activitate prin care\u00a0 obiectelor (evenimentelor) m\u0103surate le asociem numere (m\u0103sura lor)\u00a0 care exprim\u0103 caracteristicile lor dintr-un anumit punct de vedere, \u0219i prin care ele devin comparabile cantitativ sau calitativ. De exemplu, dac\u0103 m\u0103sur\u0103m trei segmente de lungimi diferite cu liniarul ob\u021binem trei numere. La cele trei segmente ata\u0219\u0103m cele trei numere conform m\u0103sur\u0103rilor efectuate. Am ob\u021binut dou\u0103 mul\u021bimi cu o rela\u021bie \u00eentre elemente, care este chiar o func\u021bie.<\/p>\n<p>Un exemplu asem\u0103n\u0103tor: Prima mul\u021bime con\u021bine elevii unei clase, a doua mul\u021bime este format\u0103 din numerele matricole ale elevilor din clasa respectiv\u0103. \u0218i aici exist\u0103 o func\u021bie conform c\u0103reia fiec\u0103rui elev corespunde num\u0103rul lui matricol.<\/p>\n<p>Ultimul exemplu are sau nu are leg\u0103tur\u0103 cu m\u0103sur\u0103rile?<\/p>\n<p>\u00cen concluzie cu abordarea problemelor legate de m\u0103sur\u0103ri \u0219i unit\u0103\u021bi de m\u0103sur\u0103 le oferim elevilor cuno\u0219tin\u021be practice necesare \u00een toate domeniile vie\u021bii \u0219i contribuim la dezvoltarea g\u00e2ndirii lor critice.<\/p>\n<p><em><strong>Bibliografie<\/strong><\/em><br \/>\nPrograma \u0219colar\u0103 pentru disciplina matematic\u0103 clasele a V-a \u2013 a VIII-a \u2013 2017<br \/>\nDr. T\u00f6r\u00f6k Tam\u00e1s: M\u00e9r\u00e9sek elm\u00e9lete \u00e9s m\u00f3dszertana a matematika tan\u00edt\u00e1s\u00e1ban (M\u0103sur\u0103ri teorie \u0219i metodologie \u00een predarea matematicii)\u00a0 Editura Calibra<br \/>\nStevens, S.S: Handbook of Experimental Psyhology New York, Wiley, 1951<br \/>\n\u00c1goston Gy, Nagy J, Orosz S:\u00a0 M\u00e9r\u00e9ses m\u00f3dszerek a pedag\u00f3gi\u00e1ban (Metode de m\u0103surare \u00een pedagogie), Ed. Tank\u00f6nyvkiad\u00f3 1979<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Programa \u0219colar\u0103 de matematic\u0103 pentru clasa a V-a are un capitol intitulat \u201eElemente de geometrie \u0219i unit\u0103\u021bi de m\u0103sur\u0103\u201d. Unit\u0103\u021bile de m\u0103sur\u0103 reprezint\u0103 o unitate de \u00eenv\u0103\u021bare la finalul acestui capitol. C\u00e2nd c\u0103ut\u0103m informa\u021bii despre predarea lec\u021biilor cu unit\u0103\u021bi de &hellip; <a href=\"https:\/\/iteach.ro\/experientedidactice\/masurari-si-unitati-de-masura-la-matematica-de-gimnaziu-observatii-metodologice-bazate-pe-experienta\">Cite\u0219te continuarea <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1225,1160,890,781,778,1704,1629],"tags":[1732],"class_list":["post-12342","post","type-post","status-publish","format-standard","hentry","category-competente-cheie","category-competente-pentru-viata","category-curriculum","category-didactica-matematicii","category-metode-didactice","category-mijloace-didactice","category-programa-scolara","tag-jolan-csuszner"],"_links":{"self":[{"href":"https:\/\/iteach.ro\/experientedidactice\/wp-json\/wp\/v2\/posts\/12342","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/iteach.ro\/experientedidactice\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/iteach.ro\/experientedidactice\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/iteach.ro\/experientedidactice\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/iteach.ro\/experientedidactice\/wp-json\/wp\/v2\/comments?post=12342"}],"version-history":[{"count":2,"href":"https:\/\/iteach.ro\/experientedidactice\/wp-json\/wp\/v2\/posts\/12342\/revisions"}],"predecessor-version":[{"id":12419,"href":"https:\/\/iteach.ro\/experientedidactice\/wp-json\/wp\/v2\/posts\/12342\/revisions\/12419"}],"wp:attachment":[{"href":"https:\/\/iteach.ro\/experientedidactice\/wp-json\/wp\/v2\/media?parent=12342"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/iteach.ro\/experientedidactice\/wp-json\/wp\/v2\/categories?post=12342"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/iteach.ro\/experientedidactice\/wp-json\/wp\/v2\/tags?post=12342"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}