[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-455655-105":3,"detail-sidebar-cat-0-en-105":80,"doc-detail-455655-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"sv","academic-dissertation-for-a-phd-in-philosophy-algorithmic-intuitive-and-formal-aspects-of-mathematics-in-dynamic-interplay","AKADEMISK AVHANDLING FÖR FILOSOFIE DOKTORSEXAMEN - Algoritmiska, intuitiva och formella aspekter av matematik i dynamiskt samspel","","Avhandling som undersöker hur studenter i matematik behandlar matematiskt material genom sin begreppsuppfattning inom matematisk analys. Fokuset ligger på studenters förmåga att använda och omforma förståelse när de arbetar med uppgifter i kalkyl. Två fallstudier analyserar förståelse av tröskelbegrepp: en intervjustudie om gränsvärde och integral samt en problemlösningsstudie om funktion, derivata och bevisföring genom induktion.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/academic-dissertation-for-a-phd-in-philosophy-algorithmic-intuitive-and-formal-aspects-of-mathematics-in-dynamic-interplay/455655/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/academic-dissertation-for-a-phd-in-philosophy-algorithmic-intuitive-and-formal-aspects-of-mathematics-in-dynamic-interplay/455655.png","ImageObject",300,407,{"name":42,"@type":43},"Rizky","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-08","2026-09-30",true,{"@type":52,"interactionType":53,"userInteractionCount":30},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"Vilket område och vilken typ av uppgifter undersöker avhandlingen?","Question",{"text":62,"@type":63},"Avhandlingen undersöker begreppsuppfattning i matematisk analys och hur studenter använder sin förståelse när de arbetar med kalkyluppgifter, inklusive utmanande uppgifter med funktion, derivata och induktionsbevis.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"Hur är de två fallstudierna upplagda?",{"text":67,"@type":63},"Den första studien är en intervjustudie om ingenjörsstudenters förståelse av gräns- och integralbegrepp. Den andra är en problemlösningsstudie där studenter inom matematikprogrammet arbetar med en uppgift som kräver proof by induction.",{"name":69,"@type":60,"acceptedAnswer":70},"Vilka skillnader i kontextualisering framträder mellan studentgrupperna?",{"text":71,"@type":63},"Resultaten visar att matematikprogrammets studenter uttrycker förståelse i en formell kontext där intuitiva idéer också spelar stor roll, medan ingenjörsstudenter främst uttrycker en algoritmisk kontext med procedurkunskap. Vid prövande frågor tycks ingenjörsstudenterna skifta mot en mer acontextualiserande ton som synliggör begreppsliga dimensioner av kalkyl.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},455655,1791433737,{"code":4,"msg":81,"data":82},"success",[83,87,91,95,100,105,110,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":92,"show_sort_weight":93,"slug":94},"Exam",70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":112,"slug":113},8,30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":111,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":30,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":139,"language":140,"language_code":8,"site_id":7,"html_lang":141,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":12,"update_tm":145,"read_time":146},962085564807,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","AKADEMISK AVHANDLING FÖR FILOSOFIE DOKTORSEXAMEN  \nAlgoritmiska, intuitiva och formella aspekter av matematikeni dynamiskt samspel  \nEn studie av hur studenter nyttjar sina begreppsuppfattningarinom matematisk analys  \nKerstin Pettersson  \nMatematiska vetenskaper  \nChalmers Tekniska Högskola och Göteborgs Universitet Göteborg 2008  \nAlgoritmiska, intuitiva och formella aspekter av matematikeni dynamiskt samspel  \nEn studie av hur studenter nyttjar sina begreppsuppfattningarinom matematisk analys  \nKERSTIN PETTERSSON  \n©Kerstin Pettersson, Göteborg, 2008  \nISBN 978-91-628-7379-0  \nMatematiska vetenskaper  \nChalmers Tekniska Högskola och Göteborgs Universitet 412 96 Göteborg  \nTelefon 031-772 10 00  \nTryck: Matematiska vetenskaper, Göteborg 2008  \nAbstract  \nAlgorithmic, intuitive and formal aspects of mathematics in dynamic interplay: A study of students’ use of their conceptions in calculus  \nFocusing on the potentiality of students’ ways of treating a mathematical material this thesis aims to investigate how students use their conceptual understanding when working with mathematical tasks in calculus. Two case studies were carried out to explore students’ understanding of threshold concepts. The first study, an interview study, explored engineering students’understanding of limit and integral. The second study, a problem solving study, involved students within a mathematics programme, working on a challenging task including the concepts function and derivative, requiring proof by induction. Drawing on a theory of contextualisation data were analysed within a constructivist research framework following the principles of intentional analysis. The results reveal that the students in the mathematics programme expressed their understanding in a formal context in which also intuitive ideas played an important role. They used intuitive ideas and formal reasoning in a dynamic interplay with several functions: to control intuitive ideas, to offer a new basis of reasoning, to reduce the complexity of the problem and to push the problem solving process forward. The engineering students expressed their conceptions in an algorithmic context, in which procedural knowledge was predominant and the operations of the concepts were seen as defining features and a basis for understanding. However, faced with probing questions, the students appeared to shift to acontextualisation foregrounding ideas relating to conceptual dimensions of calculus. These contextual shifts display the transformative aspect of threshold concepts allowing the development of conceptions and students’awareness of ways of thinking and practising in mathematics.  \nKeywords: Algorithmic context; Calculus; Conceptual understanding; Contextualisation; Higher education; Intentional analysis; Learning potentiality; Procedural knowledge.  \nFörteckning över artiklar  \nDenna avhandling baseras på studier presenterade i följande artiklar:  \nArtikel 1  \nPettersson, K., & Scheja, M. (2007) . Algorithmic contexts and learning potentiality: A case study of students’ understanding of calculus. Manuscript submitted for publication.  \nArtikel 2  \nScheja, M., & Pettersson, K. (2007) . Transformation and contextualisation: Exploring students’ conceptual understandings of threshold concepts in calculus. Manuscript submitted for publication.  \nArtikel 3  \nPettersson, K. (under tryckning) . Växelverkan mellan intuitiva idéer och formella resonemang-En fallstudie av universitetsstudenters arbete med en analysuppgift. Nordisk Matematikdidaktik (NOMAD).  \nFörord  \nEfter några spännande och innehållsrika år med kurser i matematik och pedagogik, artikelläsning och andra litteraturstudier, praktiskt arbete medempiriska studier, möten med internationella forskare inom matematikdidaktik, konferenser, diskussioner och många egna funderingar kan en avhandling nu gå i tryck. Jag vill med detta förord tacka alla dem som bidragit till den process som lett fram till denna avhandling.  \nFörst och främst vill ","cbCaiqbQ2TPqU9qk","https://ap.wps.com/l/cbCaiqbQ2TPqU9qk","pdf",1322708,166,"Swedish","en","# Abstract\n# Keywords\n# Förteckning över artiklar\n## Artikel 1\n## Artikel 2\n## Artikel 3\n# Förord","[{\"question\":\"Vilket område och vilken typ av uppgifter undersöker avhandlingen?\",\"answer\":\"Avhandlingen undersöker begreppsuppfattning i matematisk analys och hur studenter använder sin förståelse när de arbetar med kalkyluppgifter, inklusive utmanande uppgifter med funktion, derivata och induktionsbevis.\"},{\"question\":\"Hur är de två fallstudierna upplagda?\",\"answer\":\"Den första studien är en intervjustudie om ingenjörsstudenters förståelse av gräns- och integralbegrepp. Den andra är en problemlösningsstudie där studenter inom matematikprogrammet arbetar med en uppgift som kräver proof by induction.\"},{\"question\":\"Vilka skillnader i kontextualisering framträder mellan studentgrupperna?\",\"answer\":\"Resultaten visar att matematikprogrammets studenter uttrycker förståelse i en formell kontext där intuitiva idéer också spelar stor roll, medan ingenjörsstudenter främst uttrycker en algoritmisk kontext med procedurkunskap. Vid prövande frågor tycks ingenjörsstudenterna skifta mot en mer acontextualiserande ton som synliggör begreppsliga dimensioner av kalkyl.\"}]","AKADEMISK AVHANDLING FÖR FILOSOFIE DOKTORSEXAMEN - Algoritmiska, intuitiva och formella aspekter av matematik i dynamiskt samspel | PDF",1790743783,418]