[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-173988-en":3,"doc-seo-173988-105":29,"detail-sidebar-cat-1-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":11,"category_id":12,"category_name":13,"doc_title":14,"doc_description":15,"doc_content":16,"file_id":17,"file_url":18,"file_type":19,"file_size":20,"view_count":11,"is_deleted":4,"is_public":11,"is_downloadable":11,"audit_status":11,"page_count":12,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":26,"seo_description":15,"update_tm":27,"read_time":28},173988,2336464648746,"Skyler","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",1,11,"Presentations","THEORETICAL INCOMPLETENESS - a driving mechanism of evolution in mathematics education Research","The study examines how four centuries of philosophical thought shaped the growth of theoretical perspectives in mathematics learning and teaching. Using the AQAL model of integral theory as a heuristic, it argues for the need to employ multiple theories in mathematics education research by tracing sequential historical moments: late seventeenth-century hermeneutics, eighteenth-century transcendental idealism, nineteenth-century pragmatic theory, and twentieth-century postmodernist theory. It identifies weaknesses or blind spots in each philosophical precursor and concludes with implications for twenty-first century research.","THEORETICAL INCOMPLETENESS: a driving mechanism of evolution in mathematics education Research\nIskra Nunez\niskra.nunez @ googlemail.com\nABSTRACT\nThe current study considers four centuries of philosophical thought in influencing the expansion of theoretical perspectives brought to bear on mathematics learning and teaching. Drawing upon the AQAL model of integral theory as a heuristic, it inquires into the necessity to use multiple theories in mathematics education research (thereafter MER) through four moments in history, from the late seventeenth-century hermeneutics, to eighteenth-century transcendental idealism, to nineteenth-century pragmatic theory, to the twenty-century postmodernist theory. Each moment in the analysis of theoretical perspectives in use within MER proceeds sequentially by identifying weaknesses (or blind spots) in its philosophical precursor. This research concludes with a discussion of some of the possible contributions of this approach for twenty-first century MER.\nKeywords Critical Realism, Evolution, Integral Theory, Mathematics Education Research, Mechanism, Philosophical Methods, Plurality, Theoretical Incompleteness.\nINTRODUCTION\nWhat drives the evolution of theoretical perspectives currently employed in MER? What mechanism must be at work for such a theoretical plurality to occur? Or what must be at work in a particular theoretical perspective for the next breakthrough in the history of philosophical thought to occur? We suppose that there must be a mechanism at work driving such a movement of evolution derived in philosophical thought from the late seventeenth-century hermeneutics, to eighteenth-century transcendental idealism, to nineteenth-century pragmatic theory, to the twenty-century postmodernist theory in order to transition historically from one century to the next. This assumption is thus an impetus for the present study. In fact, mathematics education researchers have been concerned for a long time with new attempts to harmonize, connect, synthetize, or integrate MER’s plurality of theoretical perspectives (see e.g. Sriraman & English, 2010). As a way to contribute to this discussion, we begin by introducing integral theory, as a heuristic framework to organize four centuries of philosophical thought constituting MER’s theoretical precursors. Then, in the methodology section, we introduce the idea of Achilles’ heel critique, drawn from the philosophy of critical realism to formalize this study’s argument for a mechanism of evolution capable of explaining MER’s theoretical plurality in temporal terms, and in terms of a real, natural necessity for the existing expansion in philosophical thought. To our knowledge, no research has yet considered integral theory to study the internal workings of the evolution and current expansion of theoretical perspectives brought to bear on mathematics learning and teaching.\nHeuristic Framework\nIntegral theory’s characterizing feature is its all-quadrants, all-levels, all-lines, all-states, and all-types framework involving a four-dimensional (or quadrivium) perspective of the world (see Figure 1). We draw upon we idea of quadrivium as a heuristic based on integral theory. This quadrivium represents AQAL, a graphical model by which integral theorists understand reality as constituted of the all-encompassing relationship between its four dimensions: intensions (or experiences), individual (or group) behaviors, cultures, and social systems (or structures). In brief, AQAL provides a framework by which to assess, deal with, and potentially interrelate multi-theoretical insights from these four primary dimensions of knowledge into a binding resolution of problems. The all-quadrant element of the AQAL model of integral theory, for instance, has been used within the mathematics educational community in studies of inclusive pedagogy, as we shall see next.\nFigure 1: AQAL adopted from Esbjörn-Hargens’ (2015) comparative introduction of integral theory\nAQAL’s all-qu","cbCaidmnj3dQleMh","https://ap.wps.com/l/cbCaidmnj3dQleMh","docx",875375,"English","en",105,"# Abstract\n# Introduction\n## Heuristic Framework\n## AQAL all-quadrants and living mathematics education","[{\"question\":\"What question motivates the study on theoretical plurality in mathematics education research?\",\"answer\":\"The study asks what drives the evolution of theoretical perspectives used in mathematics education research and what mechanism enables the transition between philosophical epochs.\"},{\"question\":\"How does the AQAL model function as a framework in this research?\",\"answer\":\"AQAL provides an all-quadrants perspective to assess, connect, and potentially interrelate multi-theoretical insights across four knowledge dimensions for resolving research problems.\"},{\"question\":\"What is the role of “Achilles’ heel critique” in the argument?\",\"answer\":\"It is introduced from the philosophy of critical realism to formalize the claim of a mechanism that explains how theoretical perspectives evolve and expand over time.\"}]","THEORETICAL INCOMPLETENESS - 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