{"id":1562,"date":"2023-10-07T13:26:55","date_gmt":"2023-10-07T13:26:55","guid":{"rendered":"https:\/\/flatarmal.is\/?p=1562"},"modified":"2023-10-07T16:44:29","modified_gmt":"2023-10-07T16:44:29","slug":"reynsla-af-hugsandi-skolastofu-i-staerdfraedi","status":"publish","type":"post","link":"https:\/\/flatarmal.is\/?p=1562","title":{"rendered":"Reynsla af hugsandi sk\u00f3lastofu \u00ed st\u00e6r\u00f0fr\u00e6\u00f0i"},"content":{"rendered":"\n
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D\u00f3r\u00f3thea Margr\u00e9t Einarsd\u00f3ttir. <\/p>\n\n\n\n

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Fyrir nokkrum misserum fann \u00e9g \u00ed geymslunni bunka af g\u00f6mlum n\u00e1msb\u00f3kum fr\u00e1 \u00fev\u00ed \u00e9g var \u00ed grunnsk\u00f3la. Ein \u00feeirra vakti s\u00e9rstaka athygli m\u00edna en \u00fea\u00f0 var l\u00fai\u00f0 hefti \u00ed st\u00e6r\u00f0fr\u00e6\u00f0i. Utan \u00e1 heftinu st\u00f3\u00f0, me\u00f0 fallega skreyttum st\u00f6fum, nafni\u00f0 mitt. Fyrir ne\u00f0an \u00fea\u00f0 st\u00f3\u00f0 ,,St\u00e6rfr\u00e6\u00f0i\u201c og \u00fear fyrir ne\u00f0an haf\u00f0i veri\u00f0 b\u00e6tt vi\u00f0 ,,er lei\u00f0inleg\u201c. M\u00e9r br\u00e1 nokku\u00f0 vi\u00f0 vegna \u00feess a\u00f0 m\u00e9r finnst st\u00e6r\u00f0fr\u00e6\u00f0i \u00fevert \u00e1 m\u00f3ti mj\u00f6g skemmtileg og mundi ekki eftir \u00fev\u00ed a\u00f0 hafa nokkurn t\u00edmann \u00fe\u00f3tt h\u00fan lei\u00f0inleg. Og \u00fe\u00f3, \u00fea\u00f0 var j\u00fa \u00feetta me\u00f0 almennu brotin sem \u00e9g skildi aldrei almennilega. Or\u00f0ad\u00e6min voru l\u00edka alltaf frekar erfi\u00f0. Tugabrotin sem \u00e9g missti af. R\u00famfr\u00e6\u00f0in sem \u00e9g \u00e1tti erfitt me\u00f0 a\u00f0 sj\u00e1 fyrir m\u00e9r.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n

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Eitt og anna\u00f0 rifja\u00f0ist upp \u00feegar betur var a\u00f0 g\u00e1\u00f0. \u00c9g var ein af \u00feessum nemendum sem \u00e1tti au\u00f0velt me\u00f0 a\u00f0 muna hluti utanb\u00f3kar, l\u00e6ra a\u00f0fer\u00f0ina og muna svo \u00ed pr\u00f3finu hva\u00f0 \u00e1tti a\u00f0 gera og \u00ed hva\u00f0a r\u00f6\u00f0. \u00c9g var aftur \u00e1 m\u00f3ti ekki flj\u00f3t a\u00f0 ,,fatta\u201c hluti og ekki flj\u00f3t a\u00f0 reikna \u00ed huganum, \u00fe\u00e1 var n\u00fa betra a\u00f0 leggja \u00feetta bara \u00e1 minni\u00f0. \u00deannig gekk m\u00e9r oftast \u00e1g\u00e6tlega \u00ed st\u00e6r\u00f0fr\u00e6\u00f0i, en upplifunin var samt ekki alltaf j\u00e1kv\u00e6\u00f0. \u00deegar lei\u00f0 \u00e1 sk\u00f3lag\u00f6nguna f\u00f3r svo a\u00f0 ver\u00f0a erfi\u00f0ara a\u00f0 herma eftir s\u00fdnid\u00e6mum og l\u00e6ra fl\u00f3knar a\u00f0fer\u00f0ir \u00e1n \u00feess a\u00f0 skilja \u00fe\u00e6r. \u00de\u00e1 upplif\u00f0i \u00e9g oft b\u00e6\u00f0i pressu og pirring \u00feegar kennarinn var a\u00f0 \u00fatsk\u00fdra eitthva\u00f0 og \u00e9g skildi ekki \u00fea\u00f0 sem hann var a\u00f0 segja. Pressu \u00e1 a\u00f0 vera flj\u00f3t a\u00f0 n\u00e1 hlutunum og pirring yfir \u00fev\u00ed a\u00f0 geta \u00fea\u00f0 ekki. En, \u00e9g skrifa\u00f0i ni\u00f0ur \u00fea\u00f0 sem st\u00f3\u00f0 \u00e1 t\u00f6flunni og hermdi svo eftir s\u00fdnid\u00e6munum og \u00fe\u00e1 gekk \u00feetta n\u00fa oftast \u00feokkalega.<\/p>\n<\/div>\n\n\n\n

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Mynd 1: Brostnar vonir greinarh\u00f6fundar \u00ed st\u00e6r\u00f0fr\u00e6\u00f0i<\/em>
5. bekkjar<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n
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\u00cd minni sk\u00f3lastofu vil \u00e9g leggja \u00e1herslu \u00e1 a\u00f0 nemendur hugsi frekar en hermi, tali saman og r\u00f6kr\u00e6\u00f0i, \u00e9g vil a\u00f0 \u00feau giski \u00e1n \u00feess a\u00f0 vita, \u00e9g vil l\u00edka a\u00f0 \u00feau giski vitlaust og skilji ekki, \u00e9g vil a\u00f0 \u00feau komi me\u00f0 till\u00f6gur \u00e1n \u00feess a\u00f0 vera d\u00e6md, r\u00f6ksty\u00f0ji og \u00fatsk\u00fdri fyrir hvert \u00f6\u00f0ru og byggi \u00feannig upp sameiginlegan skilning \u00e1 st\u00e6r\u00f0fr\u00e6\u00f0ilegum fyrirb\u00e6rum og a\u00f0fer\u00f0um. \u00c9g vil ekki a\u00f0 \u00feeim finnist \u00feau \u00feurfa a\u00f0 vera flj\u00f3t a\u00f0 n\u00e1 einhverju, flj\u00f3t a\u00f0 reikna e\u00f0a flj\u00f3t a\u00f0 hugsa. \u00c9g vil ekki a\u00f0 \u00feau upplifi a\u00f0 \u00feau \u00feurfi a\u00f0 segja r\u00e9tta svari\u00f0, vita r\u00e9ttu lei\u00f0ina og a\u00f0 h\u00e6st s\u00e9 klappa\u00f0 fyrir \u00feeim sem eru n\u00f3gu sn\u00f6gg a\u00f0 \u00fev\u00ed. Svo vil \u00e9g n\u00e1tt\u00farulega ekki a\u00f0 \u00feau s\u00e9u a\u00f0 hanga \u00e1hugalaus \u00ed s\u00edmunum s\u00ednum e\u00f0a t\u00f6lvunni. \u00c9g vil a\u00f0 \u00feau s\u00e9u virk, \u00e1hugas\u00f6m, spennt og \u00e6st \u00ed a\u00f0 gl\u00edma vi\u00f0 st\u00e6r\u00f0fr\u00e6\u00f0ilegar spurningar.<\/p>\n\n\n\n

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\u00deegar \u00e9g kynntist a\u00f0fer\u00f0um hugsandi sk\u00f3lastofu fann \u00e9g \u00feessum gildum m\u00ednum \u00ed kennslu farveg. \u00dev\u00ed meira sem \u00e9g sko\u00f0a\u00f0i \u00feetta \u00fev\u00ed heilla\u00f0ri var\u00f0 \u00e9g af n\u00e1lguninni. Sm\u00e1tt og sm\u00e1tt f\u00f3r \u00e9g a\u00f0 pikka upp atri\u00f0in, \u00fatf\u00e6ra og innlei\u00f0a \u00ed m\u00edna kennslu.<\/p>\n\n\n\n

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Hva\u00f0 er hugsandi sk\u00f3lastofa?<\/strong><\/p>\n\n\n\n

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Hugsandi sk\u00f3lastofu m\u00e1 rekja til st\u00e6r\u00f0fr\u00e6\u00f0imenntunarfr\u00e6\u00f0ingsins Peter Liljedahl sem hefur rannsaka\u00f0 og \u00fer\u00f3a\u00f0 hugmyndafr\u00e6\u00f0i sem byggir \u00e1 a\u00f0 skapa r\u00fdmi \u00fear sem hugsun er \u00ed fyrirr\u00fami. \u00cd hugsandi sk\u00f3lastofu vinna nemendur a\u00f0 verkefnum sem krefjast hugsunar og byggja \u00feannig sameiginlega upp skilning \u00e1 n\u00fdjum hugt\u00f6kum og hugmyndum \u00ed gegnum samr\u00e6\u00f0ur s\u00edn \u00e1 milli og vi\u00f0 kennara. (Liljedahl, 2020).<\/p>\n\n\n\n

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Peter hefur n\u00fdtt ni\u00f0urst\u00f6\u00f0ur ranns\u00f3kna sinna til a\u00f0 setja saman lista af 14 prakt\u00edskum lei\u00f0um til a\u00f0 byggja upp hugsandi sk\u00f3lastofu. \u00cd b\u00f3k sinni Building thinking classroom fr\u00e1 2020 fer hann \u00edtarlega \u00ed gegnum atri\u00f0in 14 og hvernig \u00fatf\u00e6ra m\u00e1 \u00feau \u00ed kennslu en h\u00e9r er stikla\u00f0 \u00e1 st\u00f3ru:<\/p>\n<\/div>\n<\/div>\n\n\n\n

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1. Ver\u00f0ug verkefni sem krefjast hugsunar<\/strong> – Verkefni sem nemendur f\u00e1st vi\u00f0 ver\u00f0a a\u00f0 vera sett \u00feannig fram a\u00f0 ekki s\u00e9 h\u00e6gt a\u00f0 leysa \u00feau \u00e1n \u00feess a\u00f0 hugsa, vinna saman, r\u00f6kr\u00e6\u00f0a, koma me\u00f0 till\u00f6gur, kanna, rannsaka o.s.frv.<\/p>\n\n\n\n

2. S\u00fdnilega slembnir h\u00f3par<\/strong> \u2013 Dregi\u00f0 er \u00ed tveggja til \u00feriggja nemenda h\u00f3pa \u00e1 handah\u00f3fskenndan h\u00e1tt og lykilatri\u00f0i er a\u00f0 nemendur s\u00e9u vitni a\u00f0 \u00fev\u00ed a\u00f0 vali\u00f0 s\u00e9 slembi\u00f0. N\u00fdir h\u00f3par eru mynda\u00f0ir \u00ed upphafi hverrar kennslustundar.<\/p>\n\n\n\n

3. L\u00f3\u00f0r\u00e9ttir \u00fatstrokanlegir fletir<\/strong> \u2013 Nemendur vinna verkefnin s\u00edn standandi vi\u00f0 t\u00fasst\u00f6flur e\u00f0a a\u00f0ra fleti sem m\u00e1 au\u00f0veldlega stroka \u00fat af. Hver h\u00f3pur f\u00e6r einn penna sem l\u00e1tinn er ganga milli nemendanna.<\/p>\n\n\n\n

4. Svi\u00f0slj\u00f3si\u00f0 kvatt<\/strong> \u2013 Kennarinn \u00e1varpar h\u00f3pinn \u00far mismunandi \u00e1ttum og uppr\u00f6\u00f0un \u00ed stofunni er \u00e1n svi\u00f0s, nemendabor\u00f0um ra\u00f0a\u00f0 \u00ed eyjur sem h\u00e6gt er a\u00f0 ganga \u00ed kringum.<\/p>\n<\/div>\n\n\n\n

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5. A\u00f0eins spurningum sem lei\u00f0a til \u00e1framhaldandi hugsunar er svara\u00f0<\/strong> \u2013 Nemendur eru hvattir til a\u00f0 spyrja hvert anna\u00f0 frekar en kennarann. Kennarinn hlustar \u00e1 \u00feann sem spyr en gefur a\u00f0eins \u00fea\u00f0 upp sem nemendurnir \u00feurfa a\u00f0 heyra til a\u00f0 hugsun \u00feeirra geti haldi\u00f0 \u00e1fram.<\/p>\n\n\n\n

6. Stutt munnleg fyrirm\u00e6li \u00ed upphafi kennslustundar<\/strong> \u2013 Verkefnum er ekki dreift skriflega heldur kynnir kennari \u00feau munnlega \u00ed eins stuttu m\u00e1li og h\u00e6gt er.<\/p>\n\n\n\n

7. ,,G\u00e1\u00f0u hva\u00f0 \u00fe\u00fa kannt n\u00fana\u201c verkefni<\/strong> \u2013 Sem heimavinnu e\u00f0a \u00ed lok kennslustunda f\u00e1 nemendur verkefni sem reyna \u00e1 \u00feau n\u00e1msmarkmi\u00f0 sem undir eru hverju sinni og gefa nemendum uppl\u00fdsingar um hvar \u00feau standa.<\/p>\n\n\n\n

8. Nemendasj\u00e1lfst\u00e6\u00f0i<\/strong> \u2013 Nemendur a\u00f0sto\u00f0a hvert anna\u00f0, \u00feau taka sameiginlega \u00e1byrg\u00f0 \u00e1 a\u00f0 allir \u00ed h\u00f3pnum skilji \u00fea\u00f0 sem um er a\u00f0 vera. \u00deau leita til annarra eftir a\u00f0sto\u00f0 og \u00e1liti.<\/p>\n<\/div>\n\n\n\n

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Mynd 2: Atri\u00f0in 14 sem ranns\u00f3knir s\u00fdna a\u00f0 hafi \u00e1hrif \u00e1 hugsun nemenda. Mynd fengin \u00far b\u00f3kinni Building thinking classrooms eftir Peter Liljedahl<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n
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9. V\u00edsbendingar og \u00fatv\u00edkkanir vi\u00f0 h\u00e6fi<\/strong> \u2013 Kennari gefur v\u00edsbendingar og \u00fatv\u00edkkar verkefnin \u00feannig a\u00f0 hver nemandi f\u00e1 h\u00e6filega \u00e1skorun hverju sinni, ekki of au\u00f0velda og ekki of erfi\u00f0a.<\/p>\n\n\n\n

10. Samantekt<\/strong> \u2013 \u00cd lokin tekur kennarinn umr\u00e6\u00f0ur me\u00f0 \u00f6llum um \u00fea\u00f0 sem nemendur hafa veri\u00f0 a\u00f0 f\u00e1st vi\u00f0 og festir \u00feannig sameiginlegan skilning \u00e1 n\u00e1msefninu. H\u00e9r fyrst eru kynnt til s\u00f6gunnar n\u00fd hugt\u00f6k og a\u00f0fer\u00f0ir sem nemendur hafa \u00fe\u00e1 \u00feegar upplifa\u00f0 og m\u00f3ta\u00f0 \u00ed vinnu sinni.<\/p>\n\n\n\n

11. Gl\u00f3sur fyrir framt\u00ed\u00f0arsj\u00e1lf<\/strong> \u2013 Nemendur eru hvattir til a\u00f0 punkta ni\u00f0ur atri\u00f0i og gl\u00f3sa \u00fea\u00f0 sem \u00feau hafa unni\u00f0 \u00ed t\u00edmanum me\u00f0 \u00fea\u00f0 \u00ed huga hva\u00f0 muni n\u00fdtast \u00feeim s\u00ed\u00f0ar.<\/p>\n\n\n\n

Atri\u00f0i 12 \u2013 14 fjalla um hvernig n\u00e1msmati <\/strong>er h\u00e1tta\u00f0 \u00ed hugsandi sk\u00f3lastofu. L\u00f6g\u00f0 er \u00e1hersla \u00e1 a\u00f0 n\u00fdta lei\u00f0sagnarmat til a\u00f0 sj\u00e1 st\u00f6\u00f0u og stefnu nemandans hverju sinni. Mikilv\u00e6gt er a\u00f0 n\u00e1msmat byggi \u00e1 g\u00f6gnum og a\u00f0 veri\u00f0 s\u00e9 a\u00f0 meta \u00feau atri\u00f0i sem okkur \u00feykja eftirs\u00f3knarver\u00f0 \u00ed hugsandi sk\u00f3lastofu.<\/p>\n\n\n\n

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Mynd 3: Nemendur \u00ed hugsandi sk\u00f3lastofu reikna aukastafi \u00ed p\u00ed<\/em><\/figcaption><\/figure>\n<\/div>\n\n\n\n
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Til a\u00f0 byrja me\u00f0 hvetur Peter kennara til \u00feess a\u00f0 tileinka s\u00e9r a\u00f0eins efstu \u00ferj\u00fa atri\u00f0in \u00e1 listanum og fikra sig s\u00ed\u00f0an ne\u00f0ar sm\u00e1tt og sm\u00e1tt. M\u00f6rgum kennurum finnst \u00ed upphafi fl\u00f3ki\u00f0 a\u00f0 finna n\u00f3gu ver\u00f0ug verkefni sem krefjast hugsunar. Ma\u00f0ur kemst \u00fe\u00f3 flj\u00f3tt upp \u00e1 lag me\u00f0 a\u00f0 umor\u00f0a hef\u00f0bundin verkefni, til d\u00e6mis \u00far kennslub\u00f3kum, \u00ed ver\u00f0ug verkefni sem krefjast hugsunar. Oft er lykillinn f\u00f3lginn \u00ed \u00fev\u00ed a\u00f0 byrja \u00e1 d\u00e6mi sem allir r\u00e1\u00f0a vi\u00f0 og fikra sig svo \u00ed h\u00e6filegum skrefum \u00ed \u00e1tt a\u00f0 n\u00e1msmarkmi\u00f0inu hverju sinni. \u00cd \u00f6llum tilfellum \u00e6tti a\u00f0 setja fram verkefni \u00e1n \u00feess a\u00f0 b\u00fai\u00f0 s\u00e9 a\u00f0 kenna a\u00f0fer\u00f0ina til \u00feess a\u00f0 leysa \u00fea\u00f0. Gott er a\u00f0 hafa \u00ed huga a\u00f0 markmi\u00f0i\u00f0 me\u00f0 hugsandi sk\u00f3lastofu er ekki a\u00f0 finna upp n\u00f3gu \u00e1hugaver\u00f0 verkefni fyrir nemendur til a\u00f0 hugsa um heldur byggja upp \u00e1hugasama nemendur sem eru tilb\u00fanir til a\u00f0 hugsa um hva\u00f0a verkefni sem er.<\/p>\n<\/div>\n<\/div>\n\n\n\n

D\u00e6mi um verkefni<\/strong><\/p>\n\n\n\n

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\u00c9g l\u00e6t fylgja me\u00f0 sem d\u00e6mi nokkur verkefni sem \u00e9g hef nota\u00f0. Athugi\u00f0 a\u00f0 verkefnin voru ekki l\u00f6g\u00f0 fyrir skriflega heldur munnlega en \u00e9g skrifa \u00feau h\u00e9r upp nokkurn veginn eins og \u00e9g lag\u00f0i \u00feau fyrir.<\/p>\n\n\n\n

Verkefni sett fyrir \u00e1\u00f0ur en fjalla\u00f0 er um v\u00edsisf\u00f6ll<\/strong><\/p>\n\n\n\n

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1. \u00d3nefndur st\u00e6r\u00f0fr\u00e6\u00f0ikennari er or\u00f0inn lang\u00fereyttur \u00e1 vi\u00f0varandi metna\u00f0arleysi nemenda sinna og \u00e1kve\u00f0ur a\u00f0 m\u00fata \u00feeim til \u00feess a\u00f0 l\u00e6ra heima \u00e1 hverjum degi \u00ed heilan m\u00e1nu\u00f0. Nemendurnir f\u00e1 a\u00f0 velja um \u00fea\u00f0 a\u00f0 f\u00e1 100.000.000 kr. \u00ed lok m\u00e1na\u00f0arins e\u00f0a a\u00f0 f\u00e1 greidda 1 kr. fyrir fyrsta dag, 2 kr. fyrir n\u00e6sta dag og svo \u00e1vallt tv\u00f6falda upph\u00e6\u00f0 n\u00e6sta dag \u00fat m\u00e1nu\u00f0inn.

a) Hvora lei\u00f0ina myndu\u00f0 \u00fei\u00f0 velja?
b) Hve langt \u00feyrfti t\u00edmabili\u00f0 a\u00f0 vera til \u00feess a\u00f0 \u00fei\u00f0 myndu\u00f0 velja hina lei\u00f0ina? <\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n

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2. \u00de\u00fa leggur 1 kr. inn \u00e1 bankareikning sem hefur 100% vexti \u00e1 \u00e1ri. Hva\u00f0 \u00e1ttu miki\u00f0 \u00ed lok \u00e1rs ef vextirnir eru reikna\u00f0i<\/p>\n\n\n\n

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a) einu sinni \u00e1 \u00e1ri?
b) tvisvar \u00e1 \u00e1ri?
c) \u00ferisvar \u00e1 \u00e1ri?
d) fj\u00f3rum sinnum \u00e1 \u00e1ri?
e) sex sinnum \u00e1 \u00e1ri?
f) m\u00e1na\u00f0arlega?
g) vikulega?
h) daglega?
i) tvisvar \u00e1 s\u00f3larhring?
j) fj\u00f3rum sinnum \u00e1 s\u00f3larhring?
k) \u00e1 klukkustundar fresti?
l) \u00e1 m\u00edn\u00fatu fresti?
m) \u00e1 sek\u00fandu fresti?<\/p>\n\n\n\n

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Mynd 4 a, b, c: Nemendur r\u00e6\u00f0a saman um aflei\u00f0ur hornafalla. H\u00e9r f\u00e9kk hver h\u00f3pur \u00fathluta\u00f0 einhvers konar s\u00ednus e\u00f0a k\u00f3s\u00ednus falli og \u00e1ttu a\u00f0 athuga hvort hallatala \u00feeirra fylgdi mynstri. Endanleg ni\u00f0ursta\u00f0a f\u00e9kkst ekki fyrr en h\u00f3parnir h\u00f6f\u00f0u sko\u00f0a\u00f0 t\u00f6flur hj\u00e1 \u00f6\u00f0rum til samanbur\u00f0ar<\/em><\/p>\n<\/div>\n\n\n\n

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Verkefni sett fyrir \u00e1\u00f0ur en fjalla\u00f0 er um lograf\u00f6ll<\/strong><\/p>\n\n\n\n

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Sko\u00f0um a\u00f0eins t\u00f6luna 10 og athugum hva\u00f0 gerist \u00feegar vi\u00f0 setjum hana \u00ed veldi.<\/p>\n\n\n\n

a) \u00cd hva\u00f0a veldi \u00fearf a\u00f0 setja t\u00f6luna 10 til \u00feess a\u00f0 f\u00e1 \u00fat 1000?

b) \u00cd hva\u00f0a veldi \u00fearf a\u00f0 setja t\u00f6luna 10 til \u00feess a\u00f0 f\u00e1 \u00fat 10000?

c) \u00cd hva\u00f0a veldi \u00fearf a\u00f0 setja t\u00f6luna 10 til \u00feess a\u00f0 f\u00e1 \u00fat 10?

d) \u00cd hva\u00f0a veldi \u00fearf a\u00f0 setja t\u00f6luna 10 til \u00feess a\u00f0 f\u00e1 \u00fat 1?

e) \u00cd hva\u00f0a veldi \u00fearf a\u00f0 setja t\u00f6luna 10 til \u00feess a\u00f0 f\u00e1 \u00fat 0,1?

f) \u00cd hva\u00f0a veldi \u00fearf a\u00f0 setja t\u00f6luna 10 til \u00feess a\u00f0 f\u00e1 \u00fat 0,01?

g) \u00cd hva\u00f0a veldi \u00fearf a\u00f0 setja t\u00f6luna 10 til \u00feess a\u00f0 f\u00e1 \u00fat 0?

h) \u00cd hva\u00f0a veldi \u00fearf a\u00f0 setja t\u00f6luna 10 til \u00feess a\u00f0 f\u00e1 \u00fat 2?<\/p>\n\n\n\n

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H\u00e9r er einfaldlega veri\u00f0 a\u00f0 l\u00e1ta nemendur f\u00e1 hef\u00f0bundi\u00f0 d\u00e6mi \u00e1n \u00feess a\u00f0 kenna \u00feeim a\u00f0fer\u00f0ina. Fyrstu d\u00e6min eru flestum au\u00f0veld en svo fl\u00e6kist m\u00e1li\u00f0 i\u00f0ulega \u00ed g) og h) li\u00f0. \u00c1 \u00feessum t\u00edmapunkti \u00feekkja \u00feau ekki log<\/em> takkann \u00e1 reikniv\u00e9linni og dettur ekki \u00ed hug a\u00f0 nota hann heldur fara a\u00f0 giska. \u00de\u00e1 er oft kappsm\u00e1l a\u00f0 athuga hversu n\u00e1l\u00e6gt \u00feau komast \u00fatkomunni sem \u00feau vilja.<\/p>\n<\/div>\n<\/div>\n\n\n\n

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Mynd 5: Hugsandi sk\u00f3lastofa \u00ed \u00e1fanga um f\u00f6ll og deildun<\/em><\/figcaption><\/figure>\n<\/div>\n<\/div>\n\n\n\n

Verkefni sett fyrir \u00e1\u00f0ur en regla um fjarl\u00e6g\u00f0 punkts fr\u00e1 l\u00ednu er sett fram<\/strong><\/p>\n\n\n\n

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a) Hugsum okkar a\u00f0 l\u00ednan y=3 s\u00e9 markl\u00edna \u00ed hlaupakeppni og punkturinn (-6,-1) s\u00e9 hlaupari.
Hva\u00f0 er langt fr\u00e1 hlauparanum \u00ed markl\u00ednuna?

b) Hugum okkur a\u00f0 l\u00ednan y=x s\u00e9 markl\u00edna \u00ed hlaupakeppni og punkturinn (4,0) s\u00e9 hlaupari.
Hva\u00f0 er langt fr\u00e1 hlauparanum \u00ed markl\u00ednuna?

c) Hugsum okkur a\u00f0 l\u00ednan 7x+2y+5=0 s\u00e9 markl\u00edna \u00ed hlaupakeppni og punkturinn (2,3) s\u00e9 hlaupari.
Hva\u00f0 er langt fr\u00e1 hlauparanum \u00ed markl\u00ednuna?

d) Hugsum okkur a\u00f0 l\u00ednan ax+by+c=0 s\u00e9 markl\u00edna og punkturinn (x0, y0) s\u00e9 hlaupari.
Hva\u00f0 er langt fr\u00e1 hlauparanum \u00ed markl\u00ednuna?<\/p>\n\n\n\n

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Fyrstu tveir li\u00f0irnir eru einskonar upphitun fyrir c) li\u00f0inn \u00fear sem markmi\u00f0i\u00f0 er a\u00f0 b\u00faa nemendur undir \u00fatlei\u00f0slu \u00e1 j\u00f6fnu fyrir fjarl\u00e6g\u00f0 punkts fr\u00e1 l\u00ednu sem kemur \u00ed d) li\u00f0. \u00deau sem fengu \u00feetta verkefni \u00ed t\u00edma hj\u00e1 m\u00e9r g\u00e1tu flest komi\u00f0 me\u00f0 einhverjar till\u00f6gur a\u00f0 \u00fev\u00ed hvernig m\u00e6tti byrja \u00e1 c) li\u00f0 en \u00feurftu svo v\u00edsbendingar til a\u00f0 komast \u00e1 lei\u00f0arenda. A\u00f0eins einn h\u00f3pur komst vel \u00e1 veg me\u00f0 d) li\u00f0 og gat fullm\u00f3ta\u00f0 j\u00f6fnuna sem veri\u00f0 var a\u00f0 b\u00faa til.<\/p>\n\n\n\n

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Upplifun nemenda og kennara<\/strong><\/p>\n\n\n\n

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M\u00edn upplifun af a\u00f0fer\u00f0um hugsandi sk\u00f3lastofu er s\u00fa a\u00f0 nemendur eru mun virkari, vinna betur saman, verja meiri t\u00edma \u00ed a\u00f0 byggja upp skilning \u00e1 n\u00e1msefninu og eru \u00e1hugasamari og r\u00e6\u00f0nari heldur en \u00feegar \u00e9g nota a\u00f0rar a\u00f0fer\u00f0ir. M\u00f6rg vilja helst bara vinna \u00e1 t\u00fasst\u00f6flurnar og bi\u00f0ja um \u00fea\u00f0 af fyrra brag\u00f0i. \u00d6\u00f0rum finnst \u00f3\u00fe\u00e6gilegt a\u00f0 vinna \u00ed h\u00f3p og eiga erfi\u00f0ara me\u00f0 samskipti. Flest virtust \u00fe\u00f3 pluma sig \u00e1g\u00e6tlega og ekki verr heldur en a\u00f0 sitja ein vi\u00f0 bor\u00f0 me\u00f0 bla\u00f0 og bl\u00fdant e\u00f0a t\u00f6lvu.<\/p>\n\n\n\n

\u00cd vor \u00feegar nemendur m\u00ednir voru u.\u00fe.b. h\u00e1lfnu\u00f0 me\u00f0 \u00e1fanga um f\u00f6ll og deildun t\u00f3k \u00e9g b\u00e6\u00f0i samtal vi\u00f0 \u00feau um hugsandi sk\u00f3lastofu og lag\u00f0i fyrir stutta vi\u00f0horfsk\u00f6nnun. \u00de\u00e1 haf\u00f0i sami h\u00f3pur veri\u00f0 hj\u00e1 m\u00e9r \u00f6nnina \u00e1 undan \u00ed vigrum og hornaf\u00f6llum og h\u00f6f\u00f0u \u00fev\u00ed fengi\u00f0 d\u00e1g\u00f3\u00f0a \u00e6fingu \u00ed m\u00f6rgum \u00fe\u00e1ttum sem eru \u00f3l\u00edk \u00fev\u00ed sem g\u00e6ti kallast hef\u00f0bundin kennslustofa.<\/p>\n<\/div>\n\n\n\n

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Mynd 6: Hugsandi sk\u00f3lastofa \u00ed \u00e1fanga um vigra og hornaf\u00f6ll<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n
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Spur\u00f0 hva\u00f0 \u00feau g\u00e6tu sagt j\u00e1kv\u00e6tt um \u00feessa kennslua\u00f0fer\u00f0 nefndu \u00feau eftirfarandi atri\u00f0i:<\/strong><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n

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