{"id":128,"date":"2019-06-04T13:11:10","date_gmt":"2019-06-04T11:11:10","guid":{"rendered":"https:\/\/suomi.luma.fi\/sv\/?page_id=128"},"modified":"2019-06-05T10:20:01","modified_gmt":"2019-06-05T08:20:01","slug":"aritmetik-med-nya-ogon-for-lagstadiet","status":"publish","type":"page","link":"https:\/\/suomi.luma.fi\/sv\/projekt\/aritmetik-med-nya-ogon-for-lagstadiet\/","title":{"rendered":"Aritmetik med nya \u00f6gon f\u00f6r l\u00e5gstadiet"},"content":{"rendered":"<h5>Introduktion<\/h5>\n<p>Projektet omfattar utveckling av pedagogiska tillv\u00e4gag\u00e5ngss\u00e4tt och id\u00e9er som baserar sig p\u00e5 internationell forskning. Syftet med dessa \u00e4r att redan i l\u00e5gstadiet l\u00e4gga grunden till den algebraundervisning som inleds i h\u00f6gstadiet. Konstrueringen av grundl\u00e4ggande matematiska begrepp och betydelser samt inledandet av studier i algebra kan st\u00f6das genom i praktiken sm\u00e5, men teoretiskt viktiga \u00e4ndringar i l\u00e5gstadiets aritmetikundervisning. S\u00e5dana \u00e4ndringar \u00e4r till exempel att m\u00e5ngsidigt utnyttja numeriska ekvationer redan i nyb\u00f6rjarundervisningen f\u00f6r att eleverna ska ha m\u00f6jlighet att uppfatta likhetstecknets strukturella betydelse, olika forskningsinriktade uppgifter, problem och lekar genom vilka man f\u00f6rbereder variabelns och den algebraiska ekvationens begrepp samt principerna f\u00f6r algebraisk ekvationsl\u00f6sning, huvudr\u00e4kning som genomf\u00f6rs p\u00e5 ett lite annorlunda s\u00e4tt, etc.<\/p>\n<p>Elevernas aktiva deltagande leder till en reflektiv undervisningsdiskussion som vi \u00e4nnu inte har l\u00e4rt oss utnyttja tillr\u00e4ckligt inom den finl\u00e4ndska skolmatematikens kultur. I denna diskussion l\u00e4gger eleverna fram sina egna, genuina tankar, motiverar dem, lyssnar p\u00e5 andras tankar samt relaterar sitt eget t\u00e4nkande till diskussionen. Projektet tar fram olika s\u00e4tt att st\u00f6da l\u00e5gstadiel\u00e4rares f\u00f6rm\u00e5ga att skapa och styra h\u00f6gklassiga matematiska diskussioner i hela klassen. Matematiklektionernas diskussionskultur kan utvecklas genom att f\u00f6rhandla fram till\u00e4mpliga sociala och sociomatematiska normer. Dessa beskriver de f\u00f6rv\u00e4ntningar som klassgemenskapens medlemmar har p\u00e5 varandra om deltagande i diskussionen och specifikt om vilka s\u00e4tt att delta som v\u00e4rdes\u00e4tts matematiskt.<\/p>\n<p>Projektet producerar elektroniskt k\u00e4llmaterial f\u00f6r l\u00e5gstadiel\u00e4rare, l\u00e4romaterial f\u00f6r l\u00e5gstadieelever samt l\u00e4romaterial f\u00f6r l\u00e4rare och l\u00e4rarstuderande f\u00f6r att skapa och utveckla en matematisk diskussionskultur i klassrummet.<\/p>\n<p>Projektet inleddes 1.1.2017.<\/p>\n<h5>Material som st\u00f6der undervisningen<\/h5>\n<p><strong>Niv\u00e5er:<\/strong> grundundervisning: \u00e5rskurs 3\u20136<br \/>\n<strong>L\u00e4ro\u00e4mnen:<\/strong> matematik<br \/>\n<strong>Beskrivning:<\/strong> l\u00e4romaterial i ekvationsl\u00f6sning f\u00f6r l\u00e5gstadieeveler<br \/>\n<strong>Typ:<\/strong> (l\u00e4ro)material f\u00f6r elever<br \/>\n<strong>Nyckelord:<\/strong> multilitteracitet, grundl\u00e4ggande r\u00e4knekunskap, r\u00e4kna genom gruppering, enkel algebra, matematik f\u00f6r l\u00e5gstadiet, ekvationsl\u00f6sning, flexibilitet, j\u00e4mf\u00f6relse av l\u00f6sningss\u00e4tt, fel, sj\u00e4lvbed\u00f6mning, begreppsf\u00f6rst\u00e5else, diskussion, verbalisering<\/p>\n<p><strong><a class=\"button\" href=\"https:\/\/suomi.luma.fi\/sv\/files\/2019\/05\/AAUS-6-Ekvationsl\u00f6sning-\u2013-material-till-elever.pdf\"> Till materialet (elevens guide) \u00bb<\/a><\/strong><\/p>\n<p><strong><a class=\"button\" href=\"https:\/\/suomi.luma.fi\/sv\/files\/2019\/05\/AAUS-kopieringsunderlag.pdf\">Till materialet (kopieringsunderlag) \u00bb<\/a><\/strong><\/p>\n<p><strong><a class=\"button\" href=\"https:\/\/suomi.luma.fi\/sv\/files\/2019\/05\/Aritmetik-med-nya-\u00f6gon-f\u00f6r-l\u00e5gstadiet-material.pdf\"> \u00d6vrigt material \u00bb<\/a><\/strong><\/p>\n<h5>Publikationer<\/h5>\n<ul>\n<li>Partanen, A.-M. &amp; Tolvanen, P. (in press). Developing a frame for analysing different meanings of the concept of variable mediated by tasks in elementary-school mathematics textbooks. <em>NOMAD<\/em>.<\/li>\n<li>Partanen, A.-M. &amp; Tolvanen, P. (2017). <a href=\"https:\/\/www.researchgate.net\/publication\/322754306_Conceptions_and_skills_of_fifth_graders_related_to_algebraic_equation_solving_in_three_pilot_tests\"><em>Conceptions and skills of fifth graders related to algebraic equation solving in three pilot tests.<\/em><\/a> NORMA 17, The Eighth Nordic Conference on Mathematics Education, Stockholm, Sweden.<\/li>\n<li>Partanen, A.-M. &amp; Tolvanen, P. (2018). <a href=\"https:\/\/lacris.ulapland.fi\/fi\/publications\/uncategorizable-cases-in-developing-a-frame-for-analyzing-different-meanings-of-the-concept-of-the-variable-mediated-by-mathematical-tasks(293f7d39-4d32-4860-b77a-2ec1d1332f98).html\">Uncategorizable cases in developing a frame for analyzing different meanings of the concept of the variable mediated by mathematical tasks.<\/a> In Bergqvist, E., \u00d6sterholm, M., Granberg, C. &amp; Sumpter, L. (Eds.), <em>Proceedings of the 42th Conference of the International Group for the Psychology of Mathematics Education (Vol. 5, p. 132)<\/em>. Ume\u00e5, Sweden: PME.<\/li>\n<\/ul>\n<h6>Konferenspresentationer<\/h6>\n<ul>\n<li>Tolvanen, P. (2017). Mixed methods in mathematics and science education research (stem) (EERA-ECER Season School), 2.-4.3.2017, Barcelona, Spain.<\/li>\n<li>Tolvanen, P. (2016). Implementing Early Algebra in Two Finnish Elementary Schools \u2013 A preliminary research plan. <em>Miniconference of the Nordic Network for Algebra Learning, N2AL<\/em>, Vaasa, Finland, 30.\u201331.5.<\/li>\n<li>Tolvanen, P. (2016). Developing a test for 5th graders on meanings and skills related to equation solving. <em>Miniconference of the Nordic Network for Algebra Learning, N2AL<\/em>, Uppsala, Sweden, 6.\u20139.9.<\/li>\n<li>Tolvanen, P. (2019). Preliminary results from Early Algebra study: 5th graders paper-pencil test. <em> Miniconference of the Nordic Network for Algebra Learning, N2AL<\/em>, Oulu, Finland, 22.\u201324.5.<\/li>\n<\/ul>\n<h6>Publikationer p\u00e5 g\u00e5ng<\/h6>\n<ul>\n<li> Tolvanen, P. Development of Early Algebraic Thinking of Finnish Elementary School  Pupils. Doktorsavhandling.<\/li>\n<li>Muotka, P. M\u00e4\u00e4r\u00e4llist\u00e4 ajattelua ja p\u00e4\u00e4ttely\u00e4 kehitt\u00e4minen oppimateriaalien avulla. Avhandling pro gradu.<\/li>\n<li>Pantsar, V. Varhaisalgebran teht\u00e4v\u00e4t alakoulun matematiikan oppikirjoissa. Avhandling pro gradu.<\/li>\n<\/ul>\n<h5>Kontaktpersoner<\/h5>\n<ul>\n<li>Anna-Maija Partanen, Lapplands universitet, anna-maija.partanen@ulapland.fi<\/li>\n<\/ul>\n<h5>Arbetsgrupp<\/h5>\n<ul>\n<li>Anna-Maija Partanen, Lapplands universitet, anna-maija.partanen@ulapland.fi<\/li>\n<li>Pieti Tolvanen, Lapplands universitet, pieti.tolvanen@ulapland.fi<\/li>\n<\/ul>\n<h5>Samarbetsprojekt<\/h5>\n<p>Projektets utbildning genomf\u00f6rs i samarbete med projekten  <a href=\"https:\/\/suomi.luma.fi\/hankkeet\/joustava-yhtalonratkaisu\/\">Joustava yht\u00e4l\u00f6nratkaisu<\/a> och <a href=\"https:\/\/suomi.luma.fi\/hankkeet\/sujuvuutta-ja-joustavuutta-peruslaskutaitoon\/\">Sujuvuutta ja joustavuutta peruslaskutaitoon!<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introduktion Projektet omfattar utveckling av pedagogiska tillv\u00e4gag\u00e5ngss\u00e4tt och id\u00e9er som baserar sig p\u00e5 internationell forskning. Syftet med dessa \u00e4r att redan i l\u00e5gstadiet l\u00e4gga grunden till den algebraundervisning som inleds i h\u00f6gstadiet. Konstrueringen av grundl\u00e4ggande matematiska begrepp och betydelser samt inledandet av studier i algebra kan st\u00f6das genom i praktiken sm\u00e5, men teoretiskt viktiga \u00e4ndringar [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":13,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"class_list":["post-128","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/suomi.luma.fi\/sv\/wp-json\/wp\/v2\/pages\/128","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/suomi.luma.fi\/sv\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/suomi.luma.fi\/sv\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/suomi.luma.fi\/sv\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/suomi.luma.fi\/sv\/wp-json\/wp\/v2\/comments?post=128"}],"version-history":[{"count":7,"href":"https:\/\/suomi.luma.fi\/sv\/wp-json\/wp\/v2\/pages\/128\/revisions"}],"predecessor-version":[{"id":419,"href":"https:\/\/suomi.luma.fi\/sv\/wp-json\/wp\/v2\/pages\/128\/revisions\/419"}],"up":[{"embeddable":true,"href":"https:\/\/suomi.luma.fi\/sv\/wp-json\/wp\/v2\/pages\/13"}],"wp:attachment":[{"href":"https:\/\/suomi.luma.fi\/sv\/wp-json\/wp\/v2\/media?parent=128"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}