[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-267065-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-267065-en":131},{"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":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","mathematical-problem-solving-by-analogy","Mathematical Problem Solving by Analogy","","Examines how college students solve mathematical word problems by analogical transfer through two experiments and a verbal protocol study. Participants first learn a source problem and solution, then attempt multiple analogous target problems under conditions manipulating key hypothesized processes via hints. Findings distinguish feature mapping from procedural adaptation, show schema induction as a natural consequence, and test how time pressure and mathematical expertise shape transfer accuracy and effectiveness. Implications address models of analogical transfer and instructional guidance.",{"@graph":14,"@context":73},[15,34,56],{"@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/mathematical-problem-solving-by-analogy/267065/",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/mathematical-problem-solving-by-analogy/267065.png","ImageObject",300,407,{"name":42,"@type":43},"Jordan Avery","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-04","2026-09-14",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",12,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What processes are analyzed in solving mathematical word problems by analogy?","Question",{"text":63,"@type":64},"The study focuses on retrieval, mapping, and learning, and it emphasizes a separate adaptation process needed to use the source solution for the target problem.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do mapping and adaptation relate to successful analogical transfer?",{"text":68,"@type":64},"Successful mapping alone is insufficient for transfer, while adaptation is identified as a major source of difficulty in applying the source procedure to the target.",{"name":70,"@type":61,"acceptedAnswer":71},"What factors influence transfer accuracy in the multiple-solution problems?",{"text":72,"@type":64},"For multiple-solution problems, the relation between analogical transfer and solution accuracy is mediated by the degree of time pressure exerted, and mathematical expertise predicts analogical transfer more than general analogical reasoning ability.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},267065,1789414367,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,106,111,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & 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the results of 2 experiments and a verbal protocol study examining the componentprocesses of solving mathematical word problems by analogy.College students first studied aproblem and its solution,which provided a potential source for analogical transfer.Then theyattempted to solve several analogous problems.For some problems,subjects received one of avariety of hints designed to reduce or eliminate the difficulty of some of the major processeshypothesized to be involved in analogical transfer.Our studies yielded 4 major findings.First,the process of mapping the features of the source and target problems and the process of adaptingthe source solution procedure for use in solving the target problem were clearly distinguished:(a)Successful mapping was found to be insufficient for successful transfer and (b)adaptation wasfound to be a major source of transfer difficulty.Second,we obtained direct evidence that schemainduction is a natural consequence of analogical transfer.The schema was found to co-exist withthe problems from which it was induced,and both the schema and the individual problemsfacilitated later transfer.Third,for our multiple-solution problems,the relation between analog-ical transfer and solution accuracy was mediated by the degree of time pressure exerted for thetest problems.Finally,mathematical expertise was a significant predictor of analogical transfer,but general analogical reasoning ability was not.The implications of the results for models ofanalogical transfer and for instruction were considered.  \nThis research was supported by National Science FoundationGrant BNS-8215316 awarded to Keith Holyoak,and by an NIMHIndividual Postdoctoral Fellowship,two Vanderbilt University Re-search Council Grants,and a grant from the dean's office of PeabodyCollege of Vanderbilt University awarded to Laura Novick.We thankPaula Messamer,Livian Perez,and Suzanne Dutka for their help inrunning subjects.Michael Whitlock deserves special thanks for as-sisting us in determining the reliability of our coding schemes.Wealso thank Miriam Bassok and several anonymous reviewers for theirhelpful comments on earlier versions of the manuscript.  \nCorrespondence concerning this article should be addressed toLaura Novick,Department of Psychology and Human Development,Box 512 Peabody,Vanderbilt University,Nashville,Tennessee37203.  \nIn the past decade,there has been a surge of interest in thepsychological study of analogical problem solving.Many stud-ies have shown that solving an initial source problem caninfluence solution of a subsequent analogous target problem,as a result of exploiting systematic correspondences betweenthe problems.At the same time,abundant evidence indicatesthat analogical transfer is highly fallible.Some analogies pro-duce robust transfer(e.g.,Holyoak &Koh,1987),but othersdo not(e.g.,Gick &Holyoak,1980).Moreover,some indi-viduals are reliably more successful than others(Novick,1988a).The sources of variation in the use of analogies tosolve problems are far from understood.The aim of thepresent paper is to investigate such variation in the domainof mathematical word problems.Because of their rigorousstructure,these problems are particularly well suited for ana-lyzing the formal basis of analogical transfer.Moreover,thestudy of mathematical problem solving has direct educationalrelevance.  \nKeith J.HolyoakUniversity of California,Los Angeles  \n## The Role of Adaptation in Analogical ProblemSolving\n\nTask analyses of problem solving by analogy have focusedon three processes:retrieval,mapping,and learning.Whilereading and attempting to understand the target problem,solvers will encode it in terms of various features.Thesefeatures will provide memory retrieval cues that may enablethe solver to access information about relevant problemsencountered previously.To investigate the retrieval process,researchers have often used a hint/n","cbCaid2M8RoOZnJy","https://ap.wps.com/l/cbCaid2M8RoOZnJy","pdf",1989558,18,"English","# Mathematical Problem Solving by Analogy\n## The Role of Adaptation in Analogical ProblemSolving\n## Analogical Transfer and Schema Induction","[{\"question\":\"What processes are analyzed in solving mathematical word problems by analogy?\",\"answer\":\"The study focuses on retrieval, mapping, and learning, and it emphasizes a separate adaptation process needed to use the source solution for the target problem.\"},{\"question\":\"How do mapping and adaptation relate to successful analogical transfer?\",\"answer\":\"Successful mapping alone is insufficient for transfer, while adaptation is identified as a major source of difficulty in applying the source procedure to the target.\"},{\"question\":\"What factors influence transfer accuracy in the multiple-solution problems?\",\"answer\":\"For multiple-solution problems, the relation between analogical transfer and solution accuracy is mediated by the degree of time pressure exerted, and mathematical expertise predicts analogical transfer more than general analogical reasoning ability.\"}]","Mathematical Problem Solving by Analogy | PDF",45]