Difference between pages "Sztajn, Confrey, Wilson, & Edgington (2012)" and "Lehrer, Strom, & Confrey (2002)"

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imported>Raymond Johnson
(Created page with "{{Title|Learning Trajectory Based Instruction: Toward a Theory of Teaching}} __NOTOC__ * Authors: Paola Sztajn, Jere Confrey, P. Holt Wilson, and Cyn...")
 
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...")
 
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{{Title|Learning Trajectory Based Instruction: Toward a Theory of Teaching}}
{{Title|Grounding Metaphors and Inscriptional Resonance: Children's Emerging Understanding of Mathematical Similarity}}
__NOTOC__
__NOTOC__
* Authors: [[Paola Sztajn]], [[Jere Confrey]], [[Holt Wilson|P. Holt Wilson]], and [[Cynthia Edgington]]
* Authors: [[Richard Lehrer]], [[Dolores Strom]], and [[Jere Confrey]]
* Journal: [[Educational Researcher]]
* Journal: [[Cognition and Instruction]]
* Year: 2012
* Year: 2002
* Source: http://edr.sagepub.com/cgi/doi/10.3102/0013189X12442801
* Source: http://www.tandfonline.com/doi/abs/10.1207/S1532690XCI2003\_3


==Abstract==
==Abstract==
In this article, we propose a theoretical connection between research on learning and research on teaching through recent research on students' learning trajectories (LTs). We define learning trajectory based instruction (LTBI) as teaching that uses students' LTs as the basis for instructional decisions. We use mathematics as the context for our argument, first examining current research on LTs and then examining emerging research on how mathematics teachers use LTs to support their teaching. We consider how LTs provide specificity to four highly used frameworks for examining mathematics teaching, namely mathematical knowledge for teaching, task analysis, discourse facilitation practices, and formative assessment. We contend that by unifying various teaching frameworks around the science of LTs, LTBI begins to define a theory of teaching organized around and grounded in research on student learning. Thus, moving from the accumulation of various frameworks into a reorganization of the frameworks, LTBI provides an integrated explanatory framework for teaching.
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.


==Corrolary==
==Corrolary==
;APA
;APA
: Sztajn, P., Confrey, J., Wilson, P. H., & Edgington, C. (2012). Learning trajectory based instruction: Toward a theory of teaching. ''Educational Researcher'', 41(5), 147–156. http://doi.org/10.3102/0013189X12442801
: 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
;BibTeX
;BibTeX
<pre>
<pre>
@article{Sztajn2012,
@article{Lehrer2002,
author = {Sztajn, Paola and Confrey, Jere and Wilson, P. Holt and Edgington, Cynthia},
author = {Lehrer, Richard and Strom, Dolores and Confrey, Jere},
doi = {10.3102/0013189X12442801},
doi = {10.1207/S1532690XCI2003\_3},
journal = {Educational Researcher},
journal = {Cognition and Instruction},
number = {5},
number = {3},
pages = {147--156},
pages = {359--398},
title = {{Learning trajectory based instruction: Toward a theory of teaching}},
title = {{Grounding metaphors and inscriptional resonance: Children's emerging understanding of mathematical similarity}},
url = {http://edr.sagepub.com/cgi/doi/10.3102/0013189X12442801},
url = {http://www.tandfonline.com/doi/abs/10.1207/S1532690XCI2003\_3},
volume = {41},
volume = {20},
year = {2012}
year = {2002}
}
}
</pre>
</pre>


[[Category:Journal Articles]]
[[Category:Journal Articles]]
[[Category:Educational Researcher]]
[[Category:Cognition and Instruction]]
[[Category:2012]]
[[Category:2002]]
[[Category:Learning Trajectories]]
[[Category:Similarity]]
[[Category:Teacher Knowledge]]
[[Category:Design Research]]
[[Category:Mathematical Tasks]]
[[Category:Classroom Discourse]]
[[Category:Formative Assessment]]

Latest revision as of 05:22, 23 May 2015

Grounding Metaphors and Inscriptional Resonance: Children's Emerging Understanding of Mathematical Similarity

Abstract

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.

Corrolary

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
BibTeX
@article{Lehrer2002,
author = {Lehrer, Richard and Strom, Dolores and Confrey, Jere},
doi = {10.1207/S1532690XCI2003\_3},
journal = {Cognition and Instruction},
number = {3},
pages = {359--398},
title = {{Grounding metaphors and inscriptional resonance: Children's emerging understanding of mathematical similarity}},
url = {http://www.tandfonline.com/doi/abs/10.1207/S1532690XCI2003\_3},
volume = {20},
year = {2002}
}