Onkraj formule: zakaj bodoči učitelji naletijo na težave pri matematični indukciji v besedilnih nalogah
Povzetek
Ta študija preučuje izzive, s katerimi se bodoči učitelji spoprijemajo pri uporabi matematične indukcije za dokazovanje zapletenih besedilnih nalog. Reševanje problemov, zlasti z neobičajnimi besedilnimi nalogami, razvija veščine mišljenja višjega reda, dokazovanje, zlasti matematična indukcija, pa je osrednja matematična praksa. Za študente in bodoče učitelje matematična indukcija kljub svoji pomembnosti predstavlja velike izzive. Ta študija opredeljuje tehnične, matematične in konceptualne težave, s katerimi se spoprijemajo bodoči učitelji. Izvedli smo kvalitativno študijo s 34 bodočimi učitelji (starimi 19–20 let). Podatki so bili zbrani s pisnim testom (z neobičajno matematično indukcijsko besedilno nalogo), z vprašalniki in s polstrukturiranimi intervjuji. Analiza, ki je temeljila na klasifikaciji Avitala in Libeskinda, je pokazala, da tehnične težave vključujejo napačno določitev prvega primera in nezmožnost posplošitve vzorcev pri koraku indukcije. Matematične težave izhajajo iz napačne razlage problema in napačne opredelitve trditve P(n). Konceptualne težave vključujejo napačno razumevanje deduktivne narave matematične indukcije, strogo upoštevanje prvega primera n = 1 in podcenjevanje pomena osnovnega koraka. Ugotovitve kažejo, da so za izboljšanje modeliranja, konceptualnega razumevanja matematične indukcije in veščin splošnega vzorca pri bodočih učiteljih potrebni ciljni pedagoški ukrepi v okviru usposabljanja učiteljev.
Prenosi
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