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A Calculus II instructor conducted a teaching experiment in which 11 students reinvented a formal definition of a limit over five class periods using instructor guidance. Teaching practices during the experiment were grounded in principles from the literature on defining discourse. Analysis of the instructor’s practices and students’ follow-up work identifies methods that support students’ development toward formal, definition-oriented narratives.",{"@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/guided-reinvention-teaching-practices-that-promote-student-learning-to-define-an-analytical-object/585953/",{"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/guided-reinvention-teaching-practices-that-promote-student-learning-to-define-an-analytical-object/585953.png","ImageObject",300,407,{"name":92,"@type":93},"Jordan Avery","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What learning process does the study focus on?","Question",{"text":112,"@type":113},"The study focuses on students’ learning to define an analytical object, framed as meta-level learning in commognition.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How was the guided reinvention teaching experiment conducted?",{"text":117,"@type":113},"A Calculus II instructor guided 11 students to reinvent a formal definition of a limit across five class periods.",{"name":119,"@type":110,"acceptedAnswer":120},"Which teaching practices were found to promote students’ progress toward formal definitions?",{"text":121,"@type":113},"Providing testing methods for whether student narratives complete the defining task, having students map definition components onto graphs with related quantities, and asking students to reflect how their illustrations appear in their written definitions.","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},585953,1792190983,{"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":29,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":52,"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":143,"read_time":144,"preview_page_count":4},1099523882367,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","GUIDED REINVENTION AS TEACHING PRACTICES THAT AIM TO PROMOTE  \nSTUDENT LEARNING TO DEFINE  \nJungeun Park University of Delaware [jungeun@udel.edu](jungeun@udel.edu)  \nMichael Oehrtman Oklahoma State University [michael.oehrtman@okstate.edu](michael.oehrtman@okstate.edu)  \nJason Martin University of Central Arkansas  \n[jasonm@uca.edu](jasonm@uca.edu)  \nDouglas Rizzolo University of Delaware [drizzolo@udel.edu](drizzolo@udel.edu)  \nOur study explores teaching practices that aim to promote students’ learning to define an analytical object. A Calculus II instructor conducted a teaching experiment (TE) in which 11 students reinvented a formal definition of a limit over five class periods with the instructor’s guidance. During the TE, the instructor’s teaching practices were based on what principles of definitions from the literature inform about defining discourse. Our analysis of the instructor’s teaching practices and students’follow-up work revealed several teaching practices that seem to promote development of students’ narratives towards a formal definition of an analytical object: Providing testing methods to check if students’ narratives can be considered as a completion of the defining task, asking students to place components of their definitions on graphs with related quantities, and asking them to reflect their illustration of the definition in their written definition.  \nKeywords: Calculus, Classroom Discourse, Undergraduate Education  \nRecently, there has been growing interest in students’ learning at times when the rules of mathematical discourse change and the teaching practices promoting such learning. The Commognition approach (Sfard, 2008) defines such learning as meta-level learning because it involves students learning about new rules of discourses as well as expanding and changing properties of mathematical objects that the students are already familiar with (Valenta & Enge, 2022). The instructor’s role in meta-level learning is particularly important because those new discursive rules are historically established and thus difficult for learners to discover on their own or appreciate their value in contrast to the ones that are familiar to them (Nachlieli & Elbaum-Cohen, 2021; Valenta & Enge, 2022) . There have been recent studies about the teaching practices that aim to promote meta-level learning and calls for more studies (Cooper & Lavie, 2021; Nachlieli & Elbaum-Cohen, 2021; Schüler-Meyer, 2020; Valenta & Enge, 2022) .  \nIn this study, we consider students’ learning to define as meta-level learning because this learning involves students learning about the rules of defining discourse, which impacts both their defining procedure and the end product, i.e., their definitions as well as expanding their narratives about mathematical objects. Studies about students’ engagement with definitions have examined their difficulties with formal definitions and how they come to agreement on how to use mathematical words according to their formal definitions (e.g., Tabach & Nachlieli, 2015) and how students develop their own definition based on iterative refinements oftheir intuitive thinking about a mathematical object (Oehrtman et al., 2014; Swinyard, 2011; Schuler-Meyer, 2018 & 2020; Swinyard & Larsen, 2012) . This study aims to expand our understanding of students learning to define by examining teaching practices that aim to promote students’  \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.  \n875  \nArticles published in the Proceedings are copyrighted by the authors.  \ndevelopment of a definition of an analytic object in a guided reinvention setting with the research question:  \nWhat teaching practices can promote students’ reinvention of a formal definition of an analytic object?  \nTheoretical Background  \nWe adopted commognition as our theoretical ","cbCaiqy6ogYFioHr","https://ap.wps.com/l/cbCaiqy6ogYFioHr","pdf",477485,"English","# Theoretical Background\n## Commognition as Framework\n## Learning and Teaching in Commognition\n# Research Question and Study Aim\n## Teaching Practices for Reinvention","[{\"question\":\"What learning process does the study focus on?\",\"answer\":\"The study focuses on students’ learning to define an analytical object, framed as meta-level learning in commognition.\"},{\"question\":\"How was the guided reinvention teaching experiment conducted?\",\"answer\":\"A Calculus II instructor guided 11 students to reinvent a formal definition of a limit across five class periods.\"},{\"question\":\"Which teaching practices were found to promote students’ progress toward formal definitions?\",\"answer\":\"Providing testing methods for whether student narratives complete the defining task, having students map definition components onto graphs with related quantities, and asking students to reflect how their illustrations appear in their written definitions.\"}]","Guided Reinvention - Teaching Practices that Promote Student Learning to Define an Analytical Object | PDF",1792056426,25]