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Results show participants more often attended to correct versus incorrect solution reasoning, and they struggled to interpret students’ algebraic thinking overall, especially when reasoning was incorrect.",{"@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/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/prospective-teachers-noticing-of-students-algebraic-thinking-the-case-of-pattern-generalization/577752/",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/prospective-teachers-noticing-of-students-algebraic-thinking-the-case-of-pattern-generalization/577752.png","ImageObject",300,407,{"name":42,"@type":43},"Olivia Brown","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-27","2026-10-15",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},"What was the study’s main aim?","Question",{"text":62,"@type":63},"To investigate how prospective middle school mathematics teachers notice students’ algebraic thinking when students provide both correct and incorrect solutions in a pattern generalization context.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"How was the study conducted?",{"text":67,"@type":63},"It used a qualitative case study. 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Designed as a qualitative case study, three noticing prompts were asked of thirty-two prospective middle school mathematics teachers. Along with it, a semi-structured interview was conducted with eight prospective teachers out of thirty-two prospective teachers. The findings of this study demonstrated that while most prospective teachers could attend to the students’ correct and incorrect solutions, they had difficulty interpreting the students’ algebraic thinking. The prospective teachers even provided less evidence to interpret the algebraic thinking of the student with the incorrect solution than with the correct solution. Finally, although a vast majority of the prospective teachers could support the algebraic thinking of the student having an incorrect solution, they could not extend the algebraic thinking of the student having a correct solution.  \nKeywords: correct and incorrect solution; pattern generalization; professional noticing of children’s mathematical thinking; students’ algebraic thinking; teacher noticing  \nIntroduction  \nRather than being a haphazard act, noticing is an intentional act performed consistently within various contexts (Mason, 2011) . For more than two decades, many researchers have paid greater attention to how people notice their environment and have approached noticing from a professional point of view (Goodwin, 1994; Stevens & Hall, 1998) . For instance, Goodwin (1994) used the term“professional vision” to explain how members of a profession revealed and developed a perceptual framework that allowed them to recognize complicated situations in certain ways. If it is adapted to the context of teaching, professional vision refers to the ability to interconnect theoretical knowledge and practice by noticing the noteworthy events in complex classroom environments (Blömeke et al., 2015; Goodwin, 1994) . Professional vision helps teachers notice the classroom environment and,  \nspecifically, students’ thinking, and it is considered an indispensable skill and a prerequisite for effective teaching (Grossman et al., 2009) .  \nTeacher noticing is an active process rather than a static category of knowledge. It includes the skills of analyzing remarkable events in a classroom setting in which everything simultaneously occurs and the ability to tackle these complex events (Jacobs et al., 2010; Star & Strickland, 2008; van Es & Sherin, 2002, 2021) . Teacher noticing also requires teachers to be knowledgeable about the ways students’ solutions are not meaningful, as well as to be alert to the correctness of their answers (Holt et al., 2013; Jacobs et al., 2010; van Es, 2011). Thus, teacher noticing, as a skill, is an important dynamic competency required for all teachers, and mathematical teaching could be enriched further by paying more attention to these skills (Franke et al., 2001; Goodwin, 1994; Kaiser et al., 2015) .  \nThe significance of teacher noticing skills is not a matter of dispute among scholars, but previous research has explored teacher noticing by confining it to either teachers’ correct mathematical thinking (Tyminski et al., 2021) or incorrect mathematical thinking (Copur-Genckturk & Rodrigues, 2021; Girit-Yıldız et al., 2022) . Investigating teachers’ noticing by focusing on students’ both correct and incorrect solutions gives more detailed implications about teachers’ expertise. More specifically, as mentioned by Chick et al. (2006), students’ correct solutions provided a more significant opportunity to attend to the steps","cbCaifR8zl38kANk","https://ap.wps.com/l/cbCaifR8zl38kANk","pdf",508517,26,"English","# Introduction\n## Teacher noticing and professional vision\n## Domain-specific nature of teacher noticing\n## Motivation for focusing on correct and incorrect solutions\n## Focus on algebra and pattern generalization","[{\"question\":\"What was the study’s main aim?\",\"answer\":\"To investigate how prospective middle school mathematics teachers notice students’ algebraic thinking when students provide both correct and incorrect solutions in a pattern generalization context.\"},{\"question\":\"How was the study conducted?\",\"answer\":\"It used a qualitative case study. Three noticing prompts were administered to thirty-two prospective teachers, and a semi-structured interview was conducted with eight of them.\"},{\"question\":\"What did the findings show about teachers’ noticing?\",\"answer\":\"Most prospective teachers could attend to both correct and incorrect solutions, but they had difficulty interpreting students’ algebraic thinking, and they provided less evidence for interpreting the incorrect solution than the correct one.\"}]","Prospective Teachers’ Noticing of Students’ Algebraic Thinking - The Case of Pattern Generalization | PDF",1792032344,66]