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Qualitative analysis compares teacher goals for students’ focusing and noticing with students’ actual attention and noticed features. Findings show partial alignment alongside clear cases of mismatch, informing understanding of learning mechanisms for quadratic functions and suggesting implications for focusing and noticing in other mathematics topics.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/a-study-of-what-students-focus-on-and-notice-about-quadratic-functions-representations-during-instruction/585945/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/a-study-of-what-students-focus-on-and-notice-about-quadratic-functions-representations-during-instruction/585945.png","ImageObject",300,407,{"name":92,"@type":93},"Jordan Avery","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":14},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the study trying to understand about quadratic functions instruction?","Question",{"text":112,"@type":113},"It investigates what students focus on and notice while learning quadratic functions representations, and how these outcomes relate to teacher goals.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How did the researchers analyze student focusing and noticing?",{"text":117,"@type":113},"They conducted a qualitative comparison between what teachers aimed for students to focus on and notice and what students actually focused on and noticed.",{"name":119,"@type":110,"acceptedAnswer":120},"What did the study find about alignment between teacher goals and student outcomes?",{"text":121,"@type":113},"Results indicated some alignment, but also informative ways in which teacher goals and student outcomes for focusing and noticing were misaligned.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},585945,1792056402,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":14,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":44,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":143,"preview_page_count":4},1099523882367,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","A STUDY OF WHAT STUDENTS FOCUS ON AND NOTICE ABOUT QUADRATIC FUNCTIONS REPRESENTATIONS DURING INSTRUCTION  \nCharles Hohensee University of Delaware [hohensee@udel.edu](hohensee@udel.edu)  \nYue Ma University of Delaware  \n[yuemajoy@udel.edu](yuemajoy@udel.edu)  \nSara Gartland  \nNational University of Ireland Galway [sara.gartland@nuigalway.ie](sara.gartland@nuigalway.ie)  \nSrujana Acharya University of Delaware [srujana@udel.edu](srujana@udel.edu)  \nStudent focusing and noticing, which drive reasoning, are important but under researched aspects of student learning. Quadratic functions representations are perceptually and conceptually complex and thus, offer much for students to focus on and notice. Our study compared a teacher’s goals for student focusing and noticing during quadratic functions instruction with what students actually focused on and noticed. Qualitative analysis revealed some alignment but also informative ways that the teacher’s goals and student outcomes for focusing and noticing were misaligned. These results will further the field’s understanding of how students learn about quadratic functions and may have implications for student focusing and noticing of other mathematics topics as well.  \nKeywords: Algebra and Algebraic Thinking, Cognition, Learning Theory.  \nThis study is about what students focus on and notice during quadratic functions instruction. The topic of student focusing and noticing is a vitally important consideration for the field of mathematics education because (a) focusing and noticing are crucial processes for any and all reasoning (i.e., what remains unnoticed cannot be reasoned with or about; Bransford & Schwartz, 1999), and (b) what students focus on and notice might not always align with what their teachers want students to focus on and notice (Mason, 1999). Although teacher noticing has become a thriving area of research among teacher education researchers, student focusing and noticing has yet to garner the same kind of attention among student learning researchers. Our research sets out to help address that imbalance. Foremost, our research sets out to produce insights about how students learn about quadratic functions. However, we also view our findings as having potential relevance for the learning of other topics as well.  \nTheoretical Orientation Towards Student Noticing and the Learning of Quadratic Functions  \nIn this section, we first present our theoretical orientation toward student focusing and noticing. We then present our theoretical orientation toward the learning of quadratic functions.  \nStudent Focusing and Noticing  \nWe conceive of student focusing and noticing as the last two parts of a three-part process involving attending, focusing, and noticing. All three are needed for student noticing to occur (i.e., attending and focusing are precursors to noticing) . To conceptualize these processes, we turn to von Glasersfeld (1995). We conceptualize attending as “pick[ing] a chunk of experience, isolate[ing] it from what came before and from what follows, and treat[ing] it as a closed entity,”(p. 91). In other words, to attend to an object in a complex perceptual or conceptual context requires that the object be mentally isolated or foregrounded. While driving, for example, someone could foreground traffic signals against a background of other aspects of the  \nLamberg, T., & Moss, D. (2023). Proceedings of the forty-fifth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2). University of Nevada, Reno.  \n15  \nArticles published in the Proceedings are copyrighted by the authors.  \nenvironment.  \nNext, we conceptualize focusing on an object as “the mind, then,‘to posit it as object against itself’. . . to re-present it,”(von Glasersfeld, 1995, p. 91). In other words, focusing on an object ina complex perceptual and/or conceptual field goes beyond simply attending to the object, and requires the creation ","cbCaiqNOtlCG2LFB","https://ap.wps.com/l/cbCaiqNOtlCG2LFB","pdf",524820,"English","# Theoretical orientation toward student focusing and noticing\n## Student focusing and noticing\n# Theoretical orientation toward learning of quadratic functions\n## Quadratic functions","[{\"question\":\"What is the study trying to understand about quadratic functions instruction?\",\"answer\":\"It investigates what students focus on and notice while learning quadratic functions representations, and how these outcomes relate to teacher goals.\"},{\"question\":\"How did the researchers analyze student focusing and noticing?\",\"answer\":\"They conducted a qualitative comparison between what teachers aimed for students to focus on and notice and what students actually focused on and noticed.\"},{\"question\":\"What did the study find about alignment between teacher goals and student outcomes?\",\"answer\":\"Results indicated some alignment, but also informative ways in which teacher goals and student outcomes for focusing and noticing were misaligned.\"}]","A STUDY OF WHAT STUDENTS FOCUS ON AND NOTICE ABOUT QUADRATIC FUNCTIONS REPRESENTATIONS DURING INSTRUCTION | PDF",23]