LEADER 05569nam 22006375 450 001 9910299551503321 005 20200705005010.0 010 $a3-319-59204-1 024 7 $a10.1007/978-3-319-59204-6 035 $a(CKB)4100000000882729 035 $a(DE-He213)978-3-319-59204-6 035 $a(MiAaPQ)EBC5116613 035 $a(EXLCZ)994100000000882729 100 $a20171028d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aUsing Design Research and History to Tackle a Fundamental Problem with School Algebra /$fby Sinan Kanbir, M. A. (Ken) Clements, Nerida F. Ellerton 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (XXIV, 327 p. 55 illus., 14 illus. in color.) 225 1 $aHistory of Mathematics Education,$x2509-9736 311 $a3-319-59203-3 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aIdentifying a Problem with School Algebra -- Historical Reflections on How Algebra Became a Vital Component of Middle- and Secondary-School Curricula -- Framing a Classroom Intervention Study in a Middle-School Algebra Environment -- Document Analysis: The Intended CCSSM Elementary- and Middle-School Algebra Curriculum -- Review of Pertinent Literature -- Research Design and Methodology -- Quantitative Analyses of Data -- Qualitative Analyses of Data -- Answers to Research Questions, and Discussion -- Postscript: Framing Research Aimed at Improving School Algebra. 330 $aIn this well-illustrated book the authors, Sinan Kanbir, Ken Clements, and Nerida Ellerton, tackle a persistent, and universal, problem in school mathematics?why do so many middle-school and secondary-school students find it difficult to learn algebra well? What makes the book important are the unique features which comprise the design-research approach that the authors adopted in seeking a solution to the problem.  The first unique feature is that the authors offer an overview of the history of school algebra. Despite the fact that algebra has been an important component of secondary-school mathematics for more than three centuries, there has never been a comprehensive historical analysis of factors influencing the teaching and learning of that component. The authors identify, through historical analysis, six purposes of school algebra: (a) algebra as a body of knowledge essential to higher mathematical and scientific studies, (b) algebra as generalized arithmetic, (c) algebra as a prerequisite for entry to higher studies, (d) algebra as offering a language and set of procedures for modeling real-life problems, (e) algebra as an aid to describing structural properties in elementary mathematics, and (f) algebra as a study of variables. They also raise the question whether school algebra represents a unidimensional trait. Kanbir, Clements and Ellerton offer an unusual hybrid theoretical framework for their intervention study (by which seventh-grade students signifi cantly improved their elementary algebra knowledge and skills). Their theoretical frame combined Charles Sanders Peirce?s triadic signifier-interpretant-signified theory, which is in the realm of semiotics, with Johann Friedrich Herbart?s theory of apperception, and Ken Clements? and Gina Del Campo?s theory relating to the need to expand modes of communications in mathematics classrooms so that students engage in receptive and expressive modes. Practicing classroom teachers formed part of the research team. This book appears in Springer?s series on the ?History of Mathematics Education.? Not only does it include an important analysis of the history of school algebra, but it also adopts a theoretical frame which relies more on ?theories from the past,? than on contemporary theories in the field of mathematics education. The results of the well-designed classroom intervention are sufficiently impressive that the study might have created and illuminated a pathway for future researchers to take. 410 0$aHistory of Mathematics Education,$x2509-9736 606 $aMathematics?Study and teaching  606 $aLearning 606 $aInstruction 606 $aMathematics 606 $aHistory 606 $aMathematics Education$3https://scigraph.springernature.com/ontologies/product-market-codes/O25000 606 $aLearning & Instruction$3https://scigraph.springernature.com/ontologies/product-market-codes/O22000 606 $aHistory of Mathematical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M23009 615 0$aMathematics?Study and teaching . 615 0$aLearning. 615 0$aInstruction. 615 0$aMathematics. 615 0$aHistory. 615 14$aMathematics Education. 615 24$aLearning & Instruction. 615 24$aHistory of Mathematical Sciences. 676 $a512.0712 700 $aKanbir$b Sinan$4aut$4http://id.loc.gov/vocabulary/relators/aut$01064139 702 $aClements$b M. A. (Ken)$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aEllerton$b Nerida F$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299551503321 996 $aUsing Design Research and History to Tackle a Fundamental Problem with School Algebra$92536610 997 $aUNINA