Difference between pages "DiSessa (2004)" and "Jansen, Herbel-Eisenmann, & Smith III (2012)"

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imported>Raymond Johnson
(Created page with "{{Title|Metarepresentation: Native Competence and Targets for Instruction}}{{DISPLAYTITLE:diSessa (2004)}} __NOTOC__ The article ''Metarepresentation: Native Competence and Ta...")
 
imported>Raymond Johnson
(Created page with "{{Title|Detecting Students' Experiences of Discontinuities Between Middle School and High School Mathematics Programs: Learning During Boundary Crossing}} __NOTOC__ The articl...")
 
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{{Title|Metarepresentation: Native Competence and Targets for Instruction}}{{DISPLAYTITLE:diSessa (2004)}}
{{Title|Detecting Students' Experiences of Discontinuities Between Middle School and High School Mathematics Programs: Learning During Boundary Crossing}}
__NOTOC__
__NOTOC__
The article ''Metarepresentation: Native Competence and Targets for Instruction'' was written by [[Andrea diSessa]] and published in ''[[Cognition and Instruction]]'' in 2004. The article is available from Taylor & Francis Online at http://www.tandfonline.com/doi/abs/10.1207/s1532690xci2203_2.
The article ''Detecting Students' Experiences of Discontinuities Between Middle School and High School Mathematics Programs: Learning During Boundary Crossing'' was written by [[Amanda Jansen]], [[Beth Herbel-Eisenmann]], and [[John Smith III]] and published in ''[[Mathematical Thinking and Learning]]'' in 2012. The article is available from Taylor & Francis Online at http://www.tandfonline.com/doi/abs/10.1080/10986065.2012.717379.


== Abstract ==
== Abstract ==


The premise of this article is that the study of representation is valuable and important for mathematics and science students. Learning about representation should go beyond learning specific, sanctioned representations emphasized in standard curricula (graphs, tables, etc.) to include principles and design strategies that apply to any scientific representation, including novel variations and even completely new representations. The article explores what it means to understand representation, what we believe students already know about the topic, and what they can profitably learn about it. The discussion includes learning difficulties-goals for instruction that appear challenging for students and may need particular attention.
Transitions from middle school to high school mathematics programs can be problematic for students due to potential differences between instructional approaches and curriculum materials. Given the minimal research on how students experience such differences, we report on the experiences of two students as they moved out of an integrated, problem-based mathematics program in their middle school into a high school mathematics program that emphasized procedural fluency. We conducted an average of two interviews per year for two and a half years with participants and engaged in participant-observation at their high school. In this study, we illustrate an analytic process for detecting discontinuities between settings from participants' perspectives. We determined that students experienced a discontinuity if they reported meaningful differences between settings (frequent mention, in detail, with emphasis terms) and concurrently reported a change in attitude. Additionally, these students' experiences illustrate two opportunities to learn during boundary-crossing experiences: identification and reflection.


== Outline of Headings ==
== Outline of Headings ==


* Motivating MRC
* Background
** Scientists Are Designers of Representations
** Transition into Secondary School
** Technology Is Changing the Representational Basis of Science
** Students' Experiences in Secondary Mathematics Classrooms
** Students Start With a Rich Pool of Representational Competence
** Boundary Crossing and Discontinuities
** Difficulties in Instruction of Conventional Representations May Be Explained by Gaps and Problems in MRC
** Learning During Boundary-Crossing Experiences
** Metarepresentation May Be an Important Component of "Deeper" Understanding of Any Representation
* Methods
** Some Important Problem-Solving and Learning Skills May Be Metarepresentational
** Context
** Metarepresentational Perspectives May Be Precisely What Make Learning Representations Feel Sensible to Students
*** Curricular shift
** Metarepresentation Has a Different Character Than Many Traditional Scientific Curricular Goals, and It May Appeal to Different Segments of the Student Population
*** Instructional shift
* Situating MRC in the Literature
*** Building shift: Introduction of tracking
** Learning of Specific Representations
** Participants
** Developmental Studies of Representational Competence
** Collection
** Designed Representations for Enhancing Conceptual Development
** Data Analysis
** Joint Development of Representational and Conceptual Competence
*** Meaningful differences
** Student Design of Representations
*** Changes in attitudes
** Professional MRC
*** Discontinuity
* Preface to the Thematic Review
* Two Cases: Illustrations of Boundary Crossing
** An Ecological View: Recalibrating Our Sense of "Good" Representations
** Bethany: Pursuit of Opportunities to Develop and Use Her Own Solution Strategies
** Empirical Context
*** Boundary crossing as a process of identification
* Invention and Critique: Rich Resources, Obvious Sources
** Ethan: Reflections About the Nature of Mathematics Content and Instruction
** Constructive Resources
*** Boundary crossing as a process of reflection
** Critical Resources
* Discussion
*** Sensitivity to psychology
** Limitations
* Natural Developmental Sequences
** Conclusions and Implications
** Figural Effects
** Assumptions About What to Represent and in What Detail
** The Role of Realism
** Abstractness
** Systematicity
** Reflective and Critical Consideration of Representation
** Metric Relations
* Summary


== Also ==
== Also ==


;APA
;APA
: diSessa, A. A. (2004). Metarepresentation: Native competence and targets for instruction. ''Cognition and Instruction'', 22(3), 293–331. doi:10.1207/s1532690xci2203_2
: Jansen, A., Herbel-Eisenmann, B., & Smith III, J. P. (2012). Detecting students' experiences of discontinuities between middle school and high school mathematics programs: Learning during boundary crossing. ''Mathematical Thinking and Learning'', 14(4), 285–309. doi:10.1080/10986065.2012.717379
;BibTeX
;BibTeX
<pre>
<pre>
@article{diSessa2004,
@article{Jansen2012,
author = {diSessa, Andrea A.},
author = {Jansen, Amanda and Herbel-Eisenmann, Beth and {Smith III}, John P.},
doi = {10.1207/s1532690xci2203\_2},
doi = {10.1080/10986065.2012.717379},
journal = {Cognition and Instruction},
journal = {Mathematical Thinking and Learning},
number = {3},
number = {4},
pages = {293--331},
pages = {285--309},
title = {{Metarepresentation: Native competence and targets for instruction}},
title = {{Detecting students' experiences of discontinuities between middle school and high school mathematics programs: Learning during boundary crossing}},
url = {http://www.tandfonline.com/doi/abs/10.1207/s1532690xci2203\_2},
url = {http://www.tandfonline.com/doi/abs/10.1080/10986065.2012.717379},
volume = {22},
volume = {14},
year = {2004}
year = {2012}
}
}
</pre>
</pre>


[[Category:Journal Articles]]
[[Category:Journal Articles]]
[[Category:Cognition and Instruction]]
[[Category:Mathematical Thinking and Learning]]
[[Category:2004]]
[[Category:2012]]
[[Category:Modeling and Representation]]
[[Category:Middle School Mathematics]]
[[Category:High School Mathematics]]
[[Category:Learning Sciences]]

Latest revision as of 05:29, 15 November 2013

Detecting Students' Experiences of Discontinuities Between Middle School and High School Mathematics Programs: Learning During Boundary Crossing

The article Detecting Students' Experiences of Discontinuities Between Middle School and High School Mathematics Programs: Learning During Boundary Crossing was written by Amanda Jansen, Beth Herbel-Eisenmann, and John Smith III and published in Mathematical Thinking and Learning in 2012. The article is available from Taylor & Francis Online at http://www.tandfonline.com/doi/abs/10.1080/10986065.2012.717379.

Abstract

Transitions from middle school to high school mathematics programs can be problematic for students due to potential differences between instructional approaches and curriculum materials. Given the minimal research on how students experience such differences, we report on the experiences of two students as they moved out of an integrated, problem-based mathematics program in their middle school into a high school mathematics program that emphasized procedural fluency. We conducted an average of two interviews per year for two and a half years with participants and engaged in participant-observation at their high school. In this study, we illustrate an analytic process for detecting discontinuities between settings from participants' perspectives. We determined that students experienced a discontinuity if they reported meaningful differences between settings (frequent mention, in detail, with emphasis terms) and concurrently reported a change in attitude. Additionally, these students' experiences illustrate two opportunities to learn during boundary-crossing experiences: identification and reflection.

Outline of Headings

  • Background
    • Transition into Secondary School
    • Students' Experiences in Secondary Mathematics Classrooms
    • Boundary Crossing and Discontinuities
    • Learning During Boundary-Crossing Experiences
  • Methods
    • Context
      • Curricular shift
      • Instructional shift
      • Building shift: Introduction of tracking
    • Participants
    • Collection
    • Data Analysis
      • Meaningful differences
      • Changes in attitudes
      • Discontinuity
  • Two Cases: Illustrations of Boundary Crossing
    • Bethany: Pursuit of Opportunities to Develop and Use Her Own Solution Strategies
      • Boundary crossing as a process of identification
    • Ethan: Reflections About the Nature of Mathematics Content and Instruction
      • Boundary crossing as a process of reflection
  • Discussion
    • Limitations
    • Conclusions and Implications

Also

APA
Jansen, A., Herbel-Eisenmann, B., & Smith III, J. P. (2012). Detecting students' experiences of discontinuities between middle school and high school mathematics programs: Learning during boundary crossing. Mathematical Thinking and Learning, 14(4), 285–309. doi:10.1080/10986065.2012.717379
BibTeX
@article{Jansen2012,
author = {Jansen, Amanda and Herbel-Eisenmann, Beth and {Smith III}, John P.},
doi = {10.1080/10986065.2012.717379},
journal = {Mathematical Thinking and Learning},
number = {4},
pages = {285--309},
title = {{Detecting students' experiences of discontinuities between middle school and high school mathematics programs: Learning during boundary crossing}},
url = {http://www.tandfonline.com/doi/abs/10.1080/10986065.2012.717379},
volume = {14},
year = {2012}
}
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