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020 _a9789400727120
_9978-94-007-2712-0
024 7 _a10.1007/978-94-007-2712-0
_2doi
050 4 _aLC8-6691
072 7 _aJNU
_2bicssc
072 7 _aPB
_2bicssc
072 7 _aEDU029010
_2bisacsh
082 0 4 _a370
_223
100 1 _aRivera, Ferdinand.
_eauthor.
245 1 0 _aTeaching and Learning Patterns in School Mathematics
_h[electronic resource] :
_bPsychological and Pedagogical Considerations /
_cby Ferdinand Rivera.
264 1 _aDordrecht :
_bSpringer Netherlands :
_bImprint: Springer,
_c2013.
300 _aIX, 216 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
520 _aThis book draws on research findings on patterns in the last twenty years or so in order to argue for a theory of graded representations in pattern generalization. Pattern generalization encompasses the construction and justification of structures that give meanings to sequences of numerical and figural objects. While empirical studies conducted with different age-level groups have sufficiently demonstrated varying shifts in structural awareness and competence, which influence the eventual shape of an intended generalization, such shifts, however, are not necessarily permanent but parallel and graded, adaptive, and fundamentally distributed among a variety of cognitive and noncognitive sources that mutually influence each other. Thus, the emergence and complexity of the pattern generalization process cannot be reduced to a simple narrative of cognitive shifts from the arithmetic to the algebraic, from the recursive to the functional, from discerning details to perceiving properties, and so on and so forth. In this book, we pursue an alternative view of pattern generalization processing, that is, one that is not about permanent shifts or transition phases but graded and multimodal depending on individual learners’ experiences with patterns and, especially, the manner in which they perceive, think about, and act on them.     A nonlinear graded perspective offers a much more robust and dynamic understanding of the similarities and differences in patterning competence since it is sensitive to, and acknowledges, the varying learning conditions and opportunities that shape generalization processing and representational conversion. Empirical evidence from a variety of sources will be provided to demonstrate this emergent perspective. Further, instructional implications commingle with research knowledge throughout the book, providing researchers and teachers with usable information that will help them cope with issues they may encounter when they use patterns to engage learners in generalization activity, which involves various aspects of abstract, quantitative, model-driven, structural, and regularity thinking.  .
650 0 _aEducation.
650 0 _aCurriculums (Courses of study).
650 0 _aEducation
_xCurricula.
650 0 _aMathematics
_xStudy and teaching.
650 0 _aTeaching.
650 0 _aEducational psychology.
650 1 4 _aEducation.
650 2 4 _aMathematics Education.
650 2 4 _aPedagogic Psychology.
650 2 4 _aLearning & Instruction.
650 2 4 _aCurriculum Studies.
650 2 4 _aTeaching and Teacher Education.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9789400727113
856 4 0 _uhttp://dx.doi.org/10.1007/978-94-007-2712-0
912 _aZDB-2-SHU
942 _2Dewey Decimal Classification
_ceBooks
999 _c48331
_d48331