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Using Grundvorstellungen (GVs), the analysis of student interviews across multiple algebra courses identifies descriptive categories of conceptions that emerged from the data. A property is treated as a mathematical statement enabling transformation to an equivalent object with a different form. Findings aim to support a first step toward improving teaching of symbolic properties and syntactic reasoning.",{"@graph":69,"@context":114},[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/college-students-conceptions-of-symbolic-properties-in-algebra/585955/",{"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/college-students-conceptions-of-symbolic-properties-in-algebra/585955.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":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108],{"name":109,"@type":110,"acceptedAnswer":111},"What role do Grundvorstellungen (GVs) play in the analysis?","Question",{"text":112,"@type":113},"The paper uses prescriptive and descriptive GVs to compare intended instructional mental models with students’ actual conceptions. Descriptive GVs are derived from interview data, while prescriptive GVs reflect aspirational goals for learners.","Answer","https://schema.org",{"og:url":83,"og:type":116,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":118,"canonical":83},"index,follow",{"doc_id":120,"site_id":62},585955,1792210962,{"code":4,"msg":5,"data":123},{"doc_id":120,"user_id":124,"nickname":92,"user_avatar":125,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":126,"file_id":127,"file_url":128,"file_type":129,"file_size":130,"view_count":19,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":52,"language":131,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":132,"faqs":133,"seo_title":134,"seo_description":67,"update_tm":135,"read_time":136,"preview_page_count":4},1099523882367,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","COLLEGE STUDENTS’ CONCEPTIONS OF SYMBOLIC PROPERTIES IN ALGEBRA  \nClaire Wladis BMCC/CUNY CUNY Graduate Center [cwladis@bmcc.cuny.edu](cwladis@bmcc.cuny.edu)  \nBenjamin Sencindiver CUNY Graduate Center [bsencindiver@gc.cuny.edu](bsencindiver@gc.cuny.edu)  \nKathleen Offenholley BMCC/CUNY  \n[koffenholley@bmcc.cuny.edu](koffenholley@bmcc.cuny.edu)  \nHere we investigate how college students may conceptualize symbolic algebraic properties. This work uses the theory of Grundvorstellungen (GVs) to analyze how learners’ conceptions may or may not align with some desired goals of instruction. Through the analysis of interviews with students across a variety of courses, we describe several categories of conceptions, or descriptive GVs, that emerged in the data. We expect these categorizations to be a helpful first step in understanding learners’ thinking and improving instruction on algebraic properties.  \nKeywords: algebraic properties; syntactic reasoning; equivalence; algebraic transformation  \nMathematical properties justify transformation across mathematical domains, especially those that rely on symbolic representation such as algebra. Despite the central role that algebraic properties play in mathematical transformation, learners often do not use them in mathematically valid ways (e.g., Hoch & Dreyfus, 2004; Mok, 2010) and instruction may not support students in learning about properties explicitly enough (e.g., Barnett & Ding, 2019; Eaves et al., 2021; Larsen, 2010) . In this paper we focus on how learners identify parallel syntactic structure between symbolic properties and mathematical objects such as expressions, and we explore how this may relate to their conceptions of symbolic properties in algebra.  \nForms and Symbolic Properties  \nThe framework of student conceptions of symbolic properties presented here is part of a larger structure sense model, which has been presented in more detail in other work (Wladis, 2019; Wladis [et. al. 2022a](et. al. 2022a), 2023a); here we focus in more detail on conceptions of symbolic properties specifically. As part of this framework, we view a property as any mathematical statement that may be used to transform a mathematical object into an equivalent object with a different form. Using this definition, both axiomatic and derived statements are properties. Consider the examples: 1) a definition of rational exponents, written for example as: 8 \\#$ = $√8 for all positive integers 0; and 2) the statement about two equivalent equations: . ∙ 2 = d ↔. = & for all nonzero B. Under our model, both examples are considered to be mathematical  \n'  \nproperties. The key characteristic is that the definition of negative exponents is a valid justification for replacing an expression of the form 8 ~~ ~~\\#$ with one of the form $√8 (or vice versa), and similarly, the statement about equivalent equations is a valid justification for replacing equations with other equivalent equations that have a particular form. Here we are interested in how properties can be used to transform symbolic representations, so we use the term symbolic properties to denote symbolic representations of properties. Properties are made up of smaller sub-structures (e.g., each side of a formal property statement can be viewed as a separate object), which are often referred to colloquially during mathematics instruction asforms (e.g., the “form” 8 ~~ ~~\\#$ , $√8~~ ~~ , . ∙ 2 = d , and . = &  , in the properties above) . Here with the term “form” we are  \n'  \ngeneralizing a common practice that is often used to refer to particularly common forms used in  \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.  \n594  \nArticles published in the Proceedings are copyrighted by the authors.  \ncomputation. For example, it is very common for instructors to ask students if a particula","cbCaieNgHj1pNN1L","https://ap.wps.com/l/cbCaieNgHj1pNN1L","pdf",371385,"English","# Forms and Symbolic Properties\n## Framework for student conceptions of symbolic properties\n# Theoretical Framework\n## Prescriptive vs descriptive Grundvorstellungen\n## Prescriptive GVs for symbolic properties","[{\"question\":\"What role do Grundvorstellungen (GVs) play in the analysis?\",\"answer\":\"The paper uses prescriptive and descriptive GVs to compare intended instructional mental models with students’ actual conceptions. Descriptive GVs are derived from interview data, while prescriptive GVs reflect aspirational goals for learners.\"}]","COLLEGE STUDENTS’ CONCEPTIONS OF SYMBOLIC PROPERTIES IN ALGEBRA | PDF",1792056435,25]