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The model identifies two main classes: action on/change of an initial quantity, and coordination/comparison of two quantities. It unifies basic operations of quantities while offering greater comprehensiveness and differentiation than existing CCSSM and related classifications by emphasizing students’ conceptual demands, coherence across learning progressions, and alignment with thinking modes.",{"@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-new-classification-of-semantic-structures-of-one-step-word-problem-situations/585946/",{"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-new-classification-of-semantic-structures-of-one-step-word-problem-situations/585946.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":14},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What are the two main classes in the proposed classification?","Question",{"text":112,"@type":113},"The classification identifies action on/change of an initial quantity and coordination/comparison of two quantities.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Which sources and theories inform the proposed classification?",{"text":117,"@type":113},"It draws on CCSSM (2010) illustrations, related historical studies, and conceptual elaborations of embodied and grounded nature.",{"name":119,"@type":110,"acceptedAnswer":120},"Why does the paper argue that a new classification is needed?",{"text":121,"@type":113},"Because existing categorizations are less comprehensive and differentiated, and the proposal aims to emphasize conceptual demands, coherence of progressions, and consistency with children’s thinking modes and strategies.","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},585946,1792488391,{"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":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","A NEW CLASSIFICATION OF SEMANTIC STRUCTURES OF ONE-STEP WORD  \nPROBLEM SITUATIONS  \nOh Hoon Kwon  \nDepartment of Mathematics  \nUniversity of Wisconsin – Madison  \n[kwon@math.wisc.edu](kwon@math.wisc.edu)  \nA new classification for semantic structures of one-step word problems is proposed in this paper. The classification is based on illustrations of word problem situations in Common Core State Standards (CCSSM, 2010) and related historical studies (e.g. Weaver, 1973, 1979, 1982), as well as conceptual elaborations of embodied and grounded nature in Lakoff et al. (2000). The classification identifies two main classes: action on/change of an initial quantity and coordination/comparison of two quantities, providing a unifying characteristic of basic operations of quantities. This classification is more comprehensive and differentiated than the classification of CCSSM (2010) and Polotskaia et al. (2021), as it emphasizes conceptual demands of children's mathematics, coherence and continuity of progressions, and consistency with thinking modes and/or problem-solving strategies.  \nKeywords: Number Concepts and Operations, Mathematical Representations, Cognition, Learning Trajectories and Progressions  \nIntroduction  \nCommon Core State standards describe the situation types or the categories of word problems using two tables (CCSSM, 2010) . The first table shows the distinct types of addition and subtraction situations: add to, take from, put together/take apart, and compare. The second table shows the distinct types of multiplication and division situations: equal groups of objects, arrays of objects, and comparison.  \nHaving a thorough grasp of various problem types is of utmost importance for teachers as it enables them to discern the different approaches and methods employed by students when tackling problems. On occasion, the positioning of the unknown element within a problem significantly influences the strategies utilized and the level of complexity experienced. Moreover, there is a widely held belief that students should comprehend problems and devise solutions that align with their own understanding, rather than strictly adhering to a predetermined approach based on problem types. However, an alternative viewpoint can also suggest that if feasible, aligning problem types with thinking modes and strategies could enhance comprehension and empower students to effectively employ appropriate representations and modeling techniques.  \nThere is an expected progression in comprehending different types of situations. Initially, students learn and solve problems related to situations involving whole numbers, which later advances to word problems incorporating fractions, integers, and eventually all rational and real numbers. Additionally, teachers typically introduce addition and subtraction situations in earlier grades, while multiplication and division situations are introduced in later grades. Despite research studies, such as Carpenter et al. (1999) and others, confirming that young children are capable of solving multiplication, division, and multistep problems by directly modeling the action or structure, some teachers and researchers still tend to believe that additive reasoning always precedes multiplicative reasoning. Our argument revolves around the notion that in order  \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.  \n769  \nArticles published in the Proceedings are copyrighted by the authors.  \nto gain a comprehensive understanding of how the situation types in word problems contribute to students' comprehension, problem-solving methods, and thinking strategies associated with these situation types, it is imperative to illuminate the continuity in progressions and the shared characteristics of operations involving quantities grounded in human activity. Th","cbCaijtkm1UIm46f","https://ap.wps.com/l/cbCaijtkm1UIm46f","pdf",1241891,"English","# Introduction\n## Word problem situation types in CCSSM\n## Role of unknown placement and thinking-aligned strategies\n## Expected progression across number domains\n## Motivation for continuity in progressions\n# The necessity of a new classification\n## Semantic structures of quantity operations","[{\"question\":\"What are the two main classes in the proposed classification?\",\"answer\":\"The classification identifies action on/change of an initial quantity and coordination/comparison of two quantities.\"},{\"question\":\"Which sources and theories inform the proposed classification?\",\"answer\":\"It draws on CCSSM (2010) illustrations, related historical studies, and conceptual elaborations of embodied and grounded nature.\"},{\"question\":\"Why does the paper argue that a new classification is needed?\",\"answer\":\"Because existing categorizations are less comprehensive and differentiated, and the proposal aims to emphasize conceptual demands, coherence of progressions, and consistency with children’s thinking modes and strategies.\"}]","A NEW CLASSIFICATION OF SEMANTIC STRUCTURES OF ONE-STEP WORD PROBLEM SITUATIONS | PDF",1792056406,25]