[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-detail-173904-en":53,"doc-seo-173904-105":76},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":5,"data":54},{"doc_id":55,"user_id":56,"nickname":57,"user_avatar":58,"doc_module":9,"category_id":50,"category_name":51,"doc_title":59,"doc_description":60,"doc_content":61,"file_id":62,"file_url":63,"file_type":64,"file_size":65,"view_count":66,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":67,"language":68,"language_code":69,"site_id":70,"html_lang":69,"table_of_contents":71,"faqs":72,"seo_title":73,"seo_description":60,"update_tm":74,"read_time":75},173904,962084925502,"Emma Mercer","https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Social Activity Method - A Fractal Language for Mathematics","Social Activity Method (SAM) presents an organisational language developed by Paul Dowling to analyse how one activity recontextualises the practices of another, with applications to school mathematics examination papers and the esoteric domain. The argument situates understanding as localised and transient within continuously developing individual semiotic systems, with curriculum sequencing becoming increasingly individualised. It further claims that nothing lies beyond semiosis, implying that education must prioritise the pragmatic acquisition and deployment of mathematical technologies over treating understanding as a stable goal. SAM is positioned as usable in many contexts.","SOCIAL ACTIVITY METHOD: A FRACTAL LANGUAGE FOR MATHEMATICS\nPaul Dowling\nUCL Institute of Education, University College London\n\u0013 HYPERLINK \"mailto:p.dowling@ioe.ac.uk\" \u0014p.dowling @ ioe.ac.uk\u0015\nAbstract\nIn this paper I shall present and develop my organisational language, social activity method (SAM) and illustrate some of its applications. I shall introduce a new scheme for modes of recontextualisation that enables the analysis of the ways in which one activity—which might be school mathematics or social research or any empirically observed regularity of practice—recontextualises the practice of another and I shall also present, deploy and develop an existing scheme—domains of action—in an analysis of school mathematics examination papers and in the structuring of what I refer to as the esoteric domain. This domain is here conceived as a hybrid domain of, firstly, linguistic and extralinguistic resources that are unambiguously mathematical in terms of both expression and content and, secondly, pedagogic theory—often tacit—that enables the mathematical gaze onto other practices and so recontextualises them.\nA second and more general theme that runs through the paper is the claim that there is nothing that is beyond semiosis, that there is nothing to which we have direct access, unmediated by interpretation. This state of affairs has implications for mathematics education. Specifically, insofar as an individual’s mathematical semiotic system is under continuous development—the curriculum never being graspable all at once—understanding—as a stable semiotic moment—of any aspect or object of mathematics is always localised to the individual and is at best transient and the sequencing of such moments may well also be more individualised than consistent in some correspondence with the sequencing of the curriculum. This being the case, a concentration on understanding as a goal may well serve to inhibit the pragmatic acquisition and deployment of mathematical technologies, which should be the principal aim of mathematics teaching and learning.\nThe paper is primarily concerned with mathematics education. SAM, however, is a language that is available for recruiting and deploying in potentially any context as I have attempted to illustrate with some of the secondary illustrations in the text.\nKey Words: sociology, social activity method, discursive saturation, esoteric domain, recontextualisation.\nForensics and the myth of reference\nThere is a marked tendency in social and educational research to promote what I have called the myth of reference (Dowling, 1998), which is to say, to present itself as if it were about something other than itself, as if the language of the research represents objects and activities that the research has uncovered, but that, in principle, are accessible to all of us. Having represented the world, the mechanisms articulating the representation are pushed into the represented world and represented as causal structures. I call this forensics (Dowling, 2009). The research game proceeds as a wrestle over which language constitutes the best representation, which structures the most deserving causes. I want to take a different tack. This paper presents an organisational language—SAM—that is about itself. This is achieved within a general approach that I refer to as constructive description (Dowling, 1998, 2009) on which a little more later. Having announced this, I need to address two urgent issues. Firstly, I do not mean to claim (or even aspire to) solipsism. I must establish an exteriority, which I shall refer to as the empirical setting (Dowling & Brown, 2010). I will name the setting ‘knowledge’, for the time being. This minimal detail is sufficient to give me a bearing on what lies beyond my constructions. The outcome of my engagement with the setting, however, is not a representation, but a recontextualisation so that, ultimately, ‘knowledge’ becomes incorporated into my language.\nSecondly, I must explain the s","cbCaiddZBDYSAe7u","https://ap.wps.com/l/cbCaiddZBDYSAe7u","docx",395067,3,23,"English","en",105,"# Abstract\n# Forensics and the Myth of Reference\n## The myth of reference\n## Constructive description and empirical setting\n## The significance of “for”\n## Strong and weak grammars","[{\"question\":\"What is the Social Activity Method (SAM) intended to do in the paper?\",\"answer\":\"SAM is presented as an organisational language that develops schemes for recontextualisation, analysing how one activity reshapes another and applying this to mathematics education contexts.\"},{\"question\":\"How does the paper describe understanding in mathematics education?\",\"answer\":\"Understanding is treated as a localised and transient semiotic moment because individuals’ mathematical semiotic systems continuously develop, and curriculum knowledge cannot be grasped all at once.\"},{\"question\":\"What does “nothing is beyond semiosis” imply for mathematics teaching and learning?\",\"answer\":\"Since all access is mediated by interpretation, focusing on understanding alone may inhibit students’ pragmatic acquisition and deployment of mathematical technologies, which the paper argues should be the principal aim.\"}]","Social Activity Method - A Fractal Language for Mathematics | DOCX",1788308474,8,{"code":4,"msg":77,"data":78},"ok",{"site_id":70,"language":69,"slug":79,"title":59,"keywords":80,"description":60,"schema_data":81,"social_meta":136,"head_meta":138,"extra_data":140,"updated_unix":74},"social-activity-method-a-fractal-language-for-mathematics","",{"@graph":82,"@context":135},[83,98,118],{"@type":84,"itemListElement":85},"BreadcrumbList",[86,90,93,95],{"item":87,"name":88,"@type":89,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":91,"name":10,"@type":89,"position":92},"https://docshare.wps.com/template/",2,{"item":94,"name":51,"@type":89,"position":66},"https://docshare.wps.com/template/general/",{"item":96,"name":59,"@type":89,"position":97},"https://docshare.wps.com/template/social-activity-method-a-fractal-language-for-mathematics/173904/",4,{"url":96,"name":59,"@type":99,"image":100,"author":105,"headline":59,"publisher":107,"fileFormat":110,"inLanguage":69,"description":60,"dateModified":111,"datePublished":112,"encodingFormat":110,"isAccessibleForFree":113,"interactionStatistic":114},"DigitalDocument",{"url":101,"@type":102,"width":103,"height":104},"https://docshare.wps.com/thumbnails/social-activity-method-a-fractal-language-for-mathematics/173904.png","ImageObject",442,249,{"name":57,"@type":106},"Person",{"url":87,"name":108,"@type":109},"DocShare","Organization","application/vnd.openxmlformats-officedocument.wordprocessingml.document","2026-10-03","2026-09-02",true,{"@type":115,"interactionType":116,"userInteractionCount":97},"InteractionCounter",{"@type":117},"ViewAction",{"@type":119,"mainEntity":120},"FAQPage",[121,127,131],{"name":122,"@type":123,"acceptedAnswer":124},"What is the Social Activity Method (SAM) intended to do in the paper?","Question",{"text":125,"@type":126},"SAM is presented as an organisational language that develops schemes for recontextualisation, analysing how one activity reshapes another and applying this to mathematics education contexts.","Answer",{"name":128,"@type":123,"acceptedAnswer":129},"How does the paper describe understanding in mathematics education?",{"text":130,"@type":126},"Understanding is treated as a localised and transient semiotic moment because individuals’ mathematical semiotic systems continuously develop, and curriculum knowledge cannot be grasped all at once.",{"name":132,"@type":123,"acceptedAnswer":133},"What does “nothing is beyond semiosis” imply for mathematics teaching and learning?",{"text":134,"@type":126},"Since all access is mediated by interpretation, focusing on understanding alone may inhibit students’ pragmatic acquisition and deployment of mathematical technologies, which the paper argues should be the principal aim.","https://schema.org",{"og:url":96,"og:type":137,"og:title":59,"og:site_name":108,"og:description":60},"article",{"robots":139,"canonical":96},"index,follow",{"doc_id":55,"site_id":70}]