Difference between pages "Lehrer, Strom, & Confrey (2002)" and "Schoenfeld (2007)"

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imported>Raymond Johnson
(Created page with "{{Title|Grounding Metaphors and Inscriptional Resonance: Children's Emerging Understanding of Mathematical Similarity}} __NOTOC__ * Authors: Richard Lehrer, Dolores Stro...")
 
imported>Raymond Johnson
(→‎Outline of Headings: added headings)
 
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{{Title|Grounding Metaphors and Inscriptional Resonance: Children's Emerging Understanding of Mathematical Similarity}}
{{Title|Method}}
__NOTOC__
* Authors: [[Richard Lehrer]], [[Dolores Strom]], and [[Jere Confrey]]
* Journal: [[Cognition and Instruction]]
* Year: 2002
* Source: http://www.tandfonline.com/doi/abs/10.1207/S1532690XCI2003\_3


==Abstract==
* Author: [[Alan Schoenfeld|Alan H. Schoenfeld]]
The goal of this classroom study of third-grade students was to support and document the emergence of multiple senses of mathematical similarity. Beginning with grounding metaphors of scale, magnification, and classification, the classroom teacher helped students redescribe their perceptions of these everyday experiences with the mathematics of similarity. Each sense of similarity was mediated by a distinct form of mathematical inscription: a ratio, an algebraic "rule," and a line in a Cartesian system. These forms of inscription were tools for externalizing and structuring children's perceptions of magnification and scale ("growing") and of classification ("same shape"). Children's interpretations of the mathematical meanings of the notational systems employed were supported by successive forms of signification, which Peirce (1898/1992) described as iconic, indexical, and symbolic. We tracked student sense making through 2 sequences of lessons, first involving 2- and then 3-dimensional forms. The shift in dimension supported students' integration of multiple senses of similarity as ratio and as scale. The process of integration was assisted by resonances among diverse forms of inscription. Students' explorations of similarity served later in the year as a resource for modeling nature (e.g., by conducting explorations of density and growth). This shift toward modeling introduced a troublesome, yet ultimately rewarding, epistemological dissonance between mathematics and science. Postinstructional interviews suggested that most children came to appreciate the mathematical generalizations afforded by the algebraic and graphical forms of notation used to inscribe similar forms. A follow-up design experiment conducted in the fifth grade included some revisions to instruction that proved fruitful. Our concluding comments about design experiments and developmental corridors are motivated by a need to rethink these ideas in light of the contingent and historical nature of student thinking as it unfolded in these classrooms.
* Book: [[Second Handbook of Research on Mathematics Teaching and Learning]]
* Year: 2007
* Source: http://www.infoagepub.com/products/Second-Handbook-Research-Mathematics-Teaching-Learning
 
==Outline of Headings==
*Part 1 On the Relationship Between Theory and Method; On Qualitative and Quantitative Methods; And a Framework for Examining Fundamental Issues Related to Empirical Inquiry
** On Framing Questions, Data Gathering, and Questions of Values
** On the Relationship Between Theory and Data
** A Framework for Conducting and Examining Empirical Research
*** Caveat
*** A First Example
*** A Second Example
** Discussion
* Part 2 Aspects of Research—Issues of Trustworthiness, Generality, and Importance
** Trustworthiness
*** Descriptive and Explanatory Power
*** Prediction and Falsification
*** Rigor and Specificity
*** Replicability
*** Multiple Sources of Evidence (Triangulation)
*** Generality and Importance
** Studies of Limited Warranted Generality
*** Studies Where Some Degree of Generality is Claimed and/or Warranted
*** Studies Where Significant Generality, if Not Universality, is Claimed or Warranted
** Discussions
* Part 3 From Ideas to Implementation: A Reconsideration of the Concept of "Clinical Trials" in Educational Research and Development
** Preliminary and Phase 1 Studies in Educational R&D
** Phase 2 Studies in Educational R&D
** Phase 3 Studies in Educational R&D
* Coda


==Corrolary==
==Corrolary==
;APA
;APA
: Lehrer, R., Strom, D., & Confrey, J. (2002). Grounding metaphors and inscriptional resonance: Children’s emerging understanding of mathematical similarity. ''Cognition and Instruction'', 20(3), 359–398. http://doi.org/10.1207/S1532690XCI2003_3
: Schoenfeld, A. H. (2007). Method. In F. K. Lester (Ed.), ''Second handbook of research on mathematics teaching and learning'' (pp. 69–107). Charlotte, NC: Information Age.
;BibTeX
;BibTeX
<pre>
<pre>
@article{Lehrer2002,
@incollection{Schoenfeld2007,
author = {Lehrer, Richard and Strom, Dolores and Confrey, Jere},
address = {Charlotte, NC},
doi = {10.1207/S1532690XCI2003\_3},
author = {Schoenfeld, Alan H.},
journal = {Cognition and Instruction},
booktitle = {Second handbook of research on mathematics teaching and learning},
number = {3},
chapter = {3},
pages = {359--398},
editor = {Lester, Frank K.},
title = {{Grounding metaphors and inscriptional resonance: Children's emerging understanding of mathematical similarity}},
pages = {69--107},
url = {http://www.tandfonline.com/doi/abs/10.1207/S1532690XCI2003\_3},
publisher = {Information Age},
volume = {20},
title = {{Method}},
year = {2002}
year = {2007}
}
}
</pre>
</pre>


[[Category:Journal Articles]]
[[Category:Book Chapters]]
[[Category:Cognition and Instruction]]
[[Category:2007]]
[[Category:2002]]
[[Category:Research Methods]]
[[Category:Similarity]]
[[Category:Design Research]]

Latest revision as of 19:38, 27 May 2015

Method

Outline of Headings

  • Part 1 On the Relationship Between Theory and Method; On Qualitative and Quantitative Methods; And a Framework for Examining Fundamental Issues Related to Empirical Inquiry
    • On Framing Questions, Data Gathering, and Questions of Values
    • On the Relationship Between Theory and Data
    • A Framework for Conducting and Examining Empirical Research
      • Caveat
      • A First Example
      • A Second Example
    • Discussion
  • Part 2 Aspects of Research—Issues of Trustworthiness, Generality, and Importance
    • Trustworthiness
      • Descriptive and Explanatory Power
      • Prediction and Falsification
      • Rigor and Specificity
      • Replicability
      • Multiple Sources of Evidence (Triangulation)
      • Generality and Importance
    • Studies of Limited Warranted Generality
      • Studies Where Some Degree of Generality is Claimed and/or Warranted
      • Studies Where Significant Generality, if Not Universality, is Claimed or Warranted
    • Discussions
  • Part 3 From Ideas to Implementation: A Reconsideration of the Concept of "Clinical Trials" in Educational Research and Development
    • Preliminary and Phase 1 Studies in Educational R&D
    • Phase 2 Studies in Educational R&D
    • Phase 3 Studies in Educational R&D
  • Coda

Corrolary

APA
Schoenfeld, A. H. (2007). Method. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 69–107). Charlotte, NC: Information Age.
BibTeX
@incollection{Schoenfeld2007,
address = {Charlotte, NC},
author = {Schoenfeld, Alan H.},
booktitle = {Second handbook of research on mathematics teaching and learning},
chapter = {3},
editor = {Lester, Frank K.},
pages = {69--107},
publisher = {Information Age},
title = {{Method}},
year = {2007}
}
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