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The study centers on collective mathematical understanding in an ironworking apprenticeship classroom, examining how three apprentices collaborate to solve a workplace problem with significant mathematical content. Using “improvisational coactions,” it explains how individual ideas and contributions combine to create shared meaning, with implications for workplace training beyond this case.",{"@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/some-guys-wouldnt-use-three-eighths-on-anything-improvisational-coaction-in-an-apprenticeship-training-classroom/588603/",{"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/some-guys-wouldnt-use-three-eighths-on-anything-improvisational-coaction-in-an-apprenticeship-training-classroom/588603.png","ImageObject",300,407,{"name":92,"@type":93},"Rizky","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the main focus of the paper?","Question",{"text":112,"@type":113},"The paper focuses on collective mathematical understanding in an ironworking apprenticeship classroom and how apprentices collaboratively solve a workplace problem with strong mathematical elements.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What concept does the paper use to analyze group collaboration?",{"text":117,"@type":113},"It uses the notion of “improvisational coactions” to describe how individual ideas and understandings mesh together and are collectively built into shared understanding.",{"name":119,"@type":110,"acceptedAnswer":120},"How does the paper suggest apprentices learn to handle workplace problems mathematically?",{"text":121,"@type":113},"It suggests that improvisational coactions can be a powerful way for apprentices in workplace-training classrooms to effectively learn to think and work mathematically when tackling workplace problems.","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},588603,1792469813,{"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":19,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":41,"preview_page_count":4},962085564807,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Martin, L., and Towers, J. (2012) .“Some Guys Wouldn’t Use Three-Eighths on Anything...”: Improvisational Coaction in an Apprenticeship Training Classroom. Adults Learning Mathematics: An International Journal, 7(1), 8-19.  \n“Some Guys Wouldn’t Use Three-Eighths on Anything...”: Improvisational Coaction in an Apprenticeship Training Classroom  \nLyndon Martin  \nFaculty of Education, York University  \nToronto, Canada  \n\u003C[lmartin@edu.yorku.ca](lmartin@edu.yorku.ca)>  \nJo Towers  \nFaculty of Education, University of Calgary  \nCalgary, Canada  \nAbstract  \nThis paper presents some ongoing findings from a larger project exploring the growth of mathematical understanding in a variety of construction trades training programs. In this paper we specifically focus on the notion of collective mathematical understanding in an ironworking apprenticeship classroom. We identify the particular ways in which a group of three apprentices work collaboratively together to solve a workplace problem with a substantial mathematical element. Through drawing on the notion of‘improvisational coactions’ (Martin & Towers, 2009) we detail the ways that individual ideas, understandings and contributions mesh together and are collectively built on by the group to allow a shared understanding to emerge. From this analysis we suggest that improvisational coactions can be a powerful means through which apprentices in the workplace-training classroom might effectively learn to tackle workplace problems that involve thinking and working mathematically. Although our conclusions are specific to this case, we would suggest that there are implications that may be relevant to other areas of workplace training.  \nKey words: mathematics; group work ; improvisation; workplace; learning.  \nIntroduction  \nFitzSimons, Micek, Hull, & Wright (2005) note that “current research positions numeracy as asocial and cultural-historical process – to use terms drawn from activity theory” (p. 9) . As a consequence of such a theoretical framing, increased attention is being paid to collaborative actions as an important aspect of both workplace learning and practice. For example, Boyer and Roth (2006), in researching the learning that emerged for participants in an environmental action group, noted “much of their learning occurs informally, simply by participating in the everyday, ongoing collective life of the chosen group” and “changing forms of participation are emergent features of unfolding sociomaterial inter-action, not determinate roles or rules” (p.  \nMartin.“Some Guys Wouldn’t Use Three-Eights on Anything...”: Improvisational Coaction in an Apprenticeship Training Classroom.  \nDrawing on the notion of ‘funds of knowledge’ (Baker & Rhodes, 2007; Gonzalez, Andrade, Civil, & Moll, 2001)—the informal, broader knowledge and experiences that adult learners often possess—Oughton (2009) talks of the need for learners to “admit doubt, challenge each other’s responses, and support each other in group activities”(p. 27) . She further highlights that, in her study into learning in an adult numeracy class,“parts of the data show how the students share and pool metacognitive strategies such as eliminating easy possibilities first, and using different forms of visualisation”(p. 27) .  \nO’Connor (1994) recognises that ethnographic studies also “emphasise that the nature of work itself is collective, and almost always requires the informal collective interaction and action among individuals” (p. 281), a view taken up by FitzSimons, Micek, Hull & Wright (2005) who state that “as an activity, work is a collective process, dependent on interaction and communication, using artefacts, such as tools, written materials, tables and charts, as an integral part of the process”(p. 9) . More specifically, and of significance for learning, they suggest that“the communal model which operates has greater depth than any individual knowledge base; the group develops a communal memory of problems and solutions, a","cbCaittB2YZ4OUp8","https://ap.wps.com/l/cbCaittB2YZ4OUp8","pdf",4802791,12,"English","# Introduction\n## Improvisational coactions and collective understanding","[{\"question\":\"What is the main focus of the paper?\",\"answer\":\"The paper focuses on collective mathematical understanding in an ironworking apprenticeship classroom and how apprentices collaboratively solve a workplace problem with strong mathematical elements.\"},{\"question\":\"What concept does the paper use to analyze group collaboration?\",\"answer\":\"It uses the notion of “improvisational coactions” to describe how individual ideas and understandings mesh together and are collectively built into shared understanding.\"},{\"question\":\"How does the paper suggest apprentices learn to handle workplace problems mathematically?\",\"answer\":\"It suggests that improvisational coactions can be a powerful way for apprentices in workplace-training classrooms to effectively learn to think and work mathematically when tackling workplace problems.\"}]","Some Guys Wouldn’t Use Three-Eighths on Anything... - Improvisational Coaction in an Apprenticeship Training Classroom | PDF",1792065579]