{"id":535,"date":"2019-08-05T11:37:58","date_gmt":"2019-08-05T09:37:58","guid":{"rendered":"https:\/\/suomi.luma.fi\/sv\/?page_id=535"},"modified":"2019-10-28T17:46:28","modified_gmt":"2019-10-28T15:46:28","slug":"flexibel-ekvationslosning","status":"publish","type":"page","link":"https:\/\/suomi.luma.fi\/sv\/projekt\/flexibel-ekvationslosning\/","title":{"rendered":"Flexibel ekvationsl\u00f6sning"},"content":{"rendered":"<h5>Introduktion<\/h5>\n<p>Projektet Flexibel ekvationsl\u00f6sning (2015\u20132019) utvecklar h\u00f6gstadiets matematikundervisning med betoning p\u00e5 line\u00e4ra ekvationer.<\/p>\n<p>Utvecklingsarbetet baserar sig p\u00e5 professor Jon Stars (Harvards universitet) och hans kollegers unders\u00f6kningar om inl\u00e4rningen av line\u00e4ra ekvationer och erfarenheterna hos de l\u00e4rare som har deltagit i Finlands f\u00f6rh\u00e5llanden. Tillsammans med de l\u00e4rare som har deltagit i projektet har projektgruppen vid Ule\u00e5borgs universitet utvecklat ett materialpaket f\u00f6r studier i ekvationer och l\u00e4mpliga inl\u00e4rningss\u00e4tt. Fokus \u00e4r p\u00e5 grundandet av begrepp och sammanfattning av det inl\u00e4rda stoffet under ledning av l\u00e4raren, matematikstudier i sm\u00e5 grupper, att beskriva sitt tankearbete h\u00f6gt, presentation av de omvandlingar som beh\u00f6vs f\u00f6r ekvationsl\u00f6sning som en helhet, sj\u00e4lvbed\u00f6ming och anv\u00e4ndning av olika l\u00f6sningss\u00e4tt. M\u00e5let \u00e4r att \u00f6ka f\u00f6rst\u00e5elsen, flexibiliteten och studiemotivationen.<\/p>\n<p>Materialet och metoden utvecklas vidare p\u00e5 basis av anv\u00e4ndningserfarenheter och unders\u00f6kningar. Vi ber er anv\u00e4nda den blankett som finns i anknytning till materialet f\u00f6r att anm\u00e4la n\u00e4r ni bekantar er med det eller tar det i bruk.<\/p>\n<h5>Video<\/h5>\n<p><iframe loading=\"lazy\" src=\"https:\/\/www.youtube.com\/embed\/vFaYWQ0__7E\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h5>Material som st\u00f6der undervisning<\/h5>\n<p><strong>Niv\u00e5er:<\/strong> grundundervisning: \u00e5rskurs 7\u20139<br \/>\n<strong>L\u00e4ro\u00e4mnen:<\/strong> matematik<br \/>\n<strong>Beskrivning:<\/strong> Materialet omfattar cirka 10 lektioner och \u00e4r en metod f\u00f6r att studera ekvationsl\u00f6sning antingen p\u00e5 \u00e5rskurs 7 eller 8 i grundskolan. Metodens fokus \u00e4r p\u00e5 grundandet av begrepp och sammanfattning av det inl\u00e4rda stoffet under ledning av l\u00e4raren, matematikstudier i sm\u00e5 grupper, att beskriva sitt tankearbete h\u00f6gt, presentation av de omvandlingar som beh\u00f6vs f\u00f6r ekvationsl\u00f6sning som en helhet, sj\u00e4lvbed\u00f6ming och anv\u00e4ndning av olika l\u00f6sningss\u00e4tt.<br \/>\n<strong>Typ:<\/strong> beskrivning \/ redog\u00f6relse av den pedagogiska modellen, \u00f6vrigt st\u00f6dmaterial f\u00f6r l\u00e4rare, (l\u00e4ro)material f\u00f6r elever<br \/>\n<strong>Nyckelord:<\/strong> matematik f\u00f6r h\u00f6gstadiet, 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:\/\/ouluma.fi\/joustava-yhtalonratkaisu\/materiaali\/\">Till materialet \u00bb<\/a><\/strong><\/p>\n<h5>Publikationer<\/h5>\n<ul>\n<li> H\u00e4st\u00f6, P. &amp; Palkki, R. (2019). Finnish students\u2019 flexibility and its relation to speed and accuracy in equation solving. Nordic Studies in Mathematics Education, 24(3-4). In press.<\/li>\n<li>H\u00e4st\u00f6, P., Palkki, R., Tuomela, D. &amp; Star, J.R. (2019). <a href=\"http:\/\/scimath.net\/articles\/71\/711.pdf\">Relationship between flexibility and success in national examinations.<\/a> <em>European Journal of Science and Mathematics Education, 7(1), 1-13.<\/em><\/li>\n<li>Kostama, V. (2016). <a href=\"http:\/\/jultika.oulu.fi\/files\/nbnfioulu-201611223095.pdf\"><em>\u201dMiten n\u00e4\u00e4 pit\u00e4is teh\u00e4? Tapaustutkimus seitsem\u00e4nnen luokan pienryhmien ensikosketuksesta yht\u00e4l\u00f6nratkaisuun.<\/em><\/a> Avhandling pro gradu. Ule\u00e5borgs universitet.<\/li>\n<li>Palkki, R. &amp; H\u00e4st\u00f6, P. (2018). <a href=\"http:\/\/jultika.oulu.fi\/files\/nbnfi-fe2019041011718.pdf\">Mathematics teachers\u2019 reasons to use (or not) intentional errors.<\/a><em>Teaching Mathematics and Computer Science, 16(2), 263-282.<\/em><\/li>\n<li>Palkki, R. (2018).  <a href=\"https:\/\/doi.org\/10.31129\/LUMAT.6.1.327\">Matematiikan opettajien ja opettajaopiskelijoiden k\u00e4sityksi\u00e4 vertailumenetelm\u00e4st\u00e4.<\/a> <em>LUMAT: International Journal on Math, Science and Technology Education, 6(1), 105-128.<\/em><\/li>\n<li>Palkki, R. (2016). Joustava yht\u00e4l\u00f6nratkaisu. <em>Dimensio, 1(6), 16-19.<\/em><\/li>\n<li>Palkki, R. (2014).  <a href=\"http:\/\/ouluma.fi\/2014\/09\/joustavuus-yhtalonratkaisussa-jon-r-starin-mukaan\/\">Joustavuus yht\u00e4l\u00f6nratkaisussa Jon R. Starin mukaan.<\/a> <em>OuLUMA-verkkolehti.<\/em><\/li>\n<li>Palkki, R. (2016).  <a href=\"https:\/\/www.protsv.fi\/mlseura\/julkaisut\/MALU2015_Final.pdf\">Virheellinen esimerkki matematiikan luokkahuonekeskustelussa.<\/a> In Silfverberg, H. &amp; H\u00e4st\u00f6, P. (Eds.). <em>Proceedings of Annual Symposium of the Finnish Mathematics and Science Education Research Association 2015<\/em>. Turku, Finland.<\/li>\n<li>Palkki, R. (2016). Features effecting success in Flexible Equation solving \u2013 A Case study. In Cs\u00edkos, C., Rausch, A. &amp; Szit\u00e1nyi, J. (Eds.). <em>Proceedings of the 40th Conference of the International 1\u2013218 Group for the Psychology of Mathematics Education, 1(4), 218<\/em>. Szeged, Hungary: PME. (pidennetty abstrakti konferenssijulkaisussa)<\/li>\n<li> Tuomela, D. &amp; H\u00e4hki\u00f6niemi, M. (2018). Variation of student engagement between different algebra tasks. In <em>Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education. Vol. 4, pp. 307-314<\/em>. Ume\u00e5, Sweden: PME.<\/li>\n<li> Tuomela, T. D. (2016).  <a href=\"https:\/\/wiki.oulu.fi\/download\/attachments\/65110841\/TuomelaMalu2016_revised.pdf?version=1&amp;modificationDate=1467097000000&amp;api=v2\">Task Potential of Reversed Equation Solving.<\/a> In Silfverberg, H. &amp; H\u00e4st\u00f6, P. (Eds.). <em>Proceedings of Annual Symposium of the Finnish Mathematics and Science Education Research Association 2015<\/em>. Turku, Finland.<\/li>\n<\/ul>\n<h6>Konferenspresentationer<\/h6>\n<ul>\n<li>H\u00e4st\u00f6, P. (10\/2019). Exploring Students\u2019 Mathematical Flexibility in Three Countries. Matematiikan ja luonnontieteiden opetuksen tutkimusseuran tutkimusp\u00e4iv\u00e4t, Helsinki.<\/li>\n<li>H\u00e4st\u00f6, P. (5\/2016). Spontaneous and induced flexible equation solving, Uppsala, Sweden.<\/li>\n<li>Palkki, R. (10\/2019). Kriittisi\u00e4 tekij\u00f6it\u00e4 oppilaan menestymiselle joustavuudessa ja pienryhm\u00e4ty\u00f6skentelyss\u00e4 &#8211; Matin ja Annin tapaukset Matematiikan ja luonnontieteiden opetuksen tutkimusseuran tutkimusp\u00e4iv\u00e4t, Helsinki.<\/li>\n<li>Palkki, R. (5\/2019). Critical factors for student flexibility and productive small group work &#8211; The cases of Anni and Matti. Mini conference in teaching and learning algebra. Oulu, Finland.<\/li>\n<li>Palkki, R. (11\/2017). Vertailumenetelm\u00e4 matematiikan oppimisen tueksi? Matematiikan ja luonnontieteiden opetuksen tutkimusseuran tutkimusp\u00e4iv\u00e4t, Rovaniemi.<\/li>\n<li> Palkki, R. (5\/2017). Mathematics teachers, errors and intentional errors, NORMA, Stockholm, Sweden.<\/li>\n<li> Palkki, R. (11\/2016). Mathematics teachers&#8217; beliefs about errors, Mini conference in teaching and learning algebra, Uppsala, Sweden.<\/li>\n<li> Palkki, R. (10\/2016). Matematiikan opettajien virheisiin liittyvi\u00e4 uskomuksia, Matematiikan ja luonnontieteiden opetuksen tutkimusseuran tutkimusp\u00e4iv\u00e4t, Joensuu.<\/li>\n<li> Palkki, R. (9\/2016). Virheellinen esimerkki matematiikan luokkahuonekeskustelussa. Pohjois-Suomen MALU-opetuksen seminaari, Oulu.<\/li>\n<li> Palkki, R. (7\/2016). Comparing right and wrong solutions in algebra, ICME-13, Hamburg, Germany.<\/li>\n<li> Palkki, R. (5\/2016). Using intentional errors &#8211; A classroom discussion on equation solving, Mini conference in teaching and learning algebra, Vasa, Finland.<\/li>\n<li> Palkki, R. (11\/2015). Mathematics teachers and errors, Colloquium, University of Oulu.<\/li>\n<li> Palkki, R. (10\/2015). V\u00e4\u00e4rin ratkaistu yht\u00e4l\u00f6 &#8211; oppimisen mahdollisuus? Matematiikan ja luonnontieteiden opetuksen tutkimusseuran tutkimusp\u00e4iv\u00e4t, Turku.<\/li>\n<li> Palkki, R. (9\/2015). Learning mathematics through Flexible equation solving \u2013 two cases of 7th graders, presentation in Pro Math &#8211; conference in Halle, Germany.<\/li>\n<li> Palkki, R. ja Tuomela, D. (10\/2017). Strateginen joustavuus suomalaisoppilailla, Pohjois-Suomen MALU-opetuksen seminaari, Oulu.<\/li>\n<li> Palkki, R. ja Tuomela, D. (9\/2017). Flexibility among Finnish students, EARLI, Tampere, Finland.<\/li>\n<li>Tuomela, D. (7\/2018). Variation of student engagement between different algebra tasks. The 42nd Conference of the International Group for the Psychology of Mathematics Education (PME42), Ume\u00e5, Sweden.<\/li>\n<li>Tuomela, D. (11\/2017). How characteristics of mathematical tasks can influence interaction and engagement in peer-to-peer small group work.  Matematiikan ja luonnontieteiden opetuksen tutkimusseuran tutkimusp\u00e4iv\u00e4t, Rovaniemi, Finland.<\/li>\n<li> Tuomela, D. (5\/2016). Creating learning opportunities through Reversed Equation Solving, Vasa, Finland.<\/li>\n<li> Tuomela, D. (11\/2015). Designing Reversed Equation Solving, Colloquium, University of Oulu.<\/li>\n<li> Tuomela, D. (10\/2015). Explorative study of reversed equation solving, Matematiikan ja luonnontieteiden opetuksen tutkimusseuran tutkimusp\u00e4iv\u00e4t, Turku, Finland.<\/li>\n<\/ul>\n<h6>Publikationer som \u00e4r p\u00e5 g\u00e5ng<\/h6>\n<ul>\n<li> Matematiikanopettajien ja oppilaiden n\u00e4k\u00f6kulmia vertailuteht\u00e4vien k\u00e4ytt\u00f6\u00f6n: menetelm\u00e4 joustavuuden, keskustelun, analysointitaitojen ja virheist\u00e4 oppimisen tukemiseen. Doktorsavhandling.<\/li>\n<li> Tuomela, D. Implementation of reform material to create engaging and reasoning-oriented mathematics classroom culture. Doktorsavhandling.<\/li>\n<li> Palkki, R. The cases of Matti and Anni in Flexible Equation-solving (artikel)<\/li>\n<li> Tuomela, D. &amp; Paradis, A. The struggles and success of Ms. Icy when implementing reform material (artikel)<\/li>\n<li> Tuomela, D. &amp; H\u00e4hki\u00f6niemi, M. Individual or collaborative engagement? The case of 7th grade students implementing reform equation solving material (artikel)<\/li>\n<li> Joustava yht\u00e4l\u00f6nratkaisu -projektissa testimenestys (ei julkaisuja vireill\u00e4)<\/li>\n<li> Kansainv\u00e4linen vertailututkimus joustavuudesta 8.-luokkalaisilla ja lukion kakkosluokkalaisilla<\/li>\n<\/ul>\n<h5>Kontaktpersoner<\/h5>\n<ul>\n<li>Riikka Palkki, Ule\u00e5borgs universitet, riikka.palkki@oulu.fi<\/li>\n<li>Dimitri Tuomela, Ule\u00e5borgs universitet, tatu.tuomela@oulu.fi<\/li>\n<\/ul>\n<h5>Arbetsgrupp<\/h5>\n<ul>\n<li>Peter H\u00e4st\u00f6, Ule\u00e5borgs universitet \/ \u00c5bo universitet<\/li>\n<li>Riikka Palkki, Ule\u00e5borgs universitet<\/li>\n<li>Dimitri Tuomela, Ule\u00e5borgs universitet<\/li>\n<\/ul>\n<ul>\nMed i projektet 2015\/2016:<\/p>\n<li>Virpi Kostama, forskningsassistent<\/li>\n<li>Marko Leinonen, universitetsl\u00e4rare<\/li>\n<li>Juha Jaako, TkT, planerare, LUMA-center i Ule\u00e5bors universitet<\/li>\n<li>Hannu Suvanto, FM, praktikant<\/li>\n<\/ul>\n<h5>Samarbetsprojekt<\/h5>\n<p>Utbildning inom projektet g\u00f6rs i samband med projekt <a href=\"https:\/\/suomi.luma.fi\/sv\/projekt\/aritmetik-med-nya-ogon-for-lagstadiet\/\">Aritmetik med nya \u00f6gon f\u00f6r l\u00e5gstadiet<\/a> och<br \/>\n<a href=\"https:\/\/suomi.luma.fi\/sv\/projekt\/grundlaggande-raknekunskaper-med-flyt-och-flexibilitet\/\">Grundl\u00e4ggande r\u00e4knekunskaper med flyt och flexibilitet!<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introduktion Projektet Flexibel ekvationsl\u00f6sning (2015\u20132019) utvecklar h\u00f6gstadiets matematikundervisning med betoning p\u00e5 line\u00e4ra ekvationer. Utvecklingsarbetet baserar sig p\u00e5 professor Jon Stars (Harvards universitet) och hans kollegers unders\u00f6kningar om inl\u00e4rningen av line\u00e4ra ekvationer och erfarenheterna hos de l\u00e4rare som har deltagit i Finlands f\u00f6rh\u00e5llanden. Tillsammans med de l\u00e4rare som har deltagit i projektet har projektgruppen vid Ule\u00e5borgs [&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-535","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/suomi.luma.fi\/sv\/wp-json\/wp\/v2\/pages\/535","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=535"}],"version-history":[{"count":4,"href":"https:\/\/suomi.luma.fi\/sv\/wp-json\/wp\/v2\/pages\/535\/revisions"}],"predecessor-version":[{"id":590,"href":"https:\/\/suomi.luma.fi\/sv\/wp-json\/wp\/v2\/pages\/535\/revisions\/590"}],"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=535"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}