Difference between pages "Confrey & Smith (1994)" and "Schoenfeld (2007)"

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imported>Raymond Johnson
(Created page with "{{Title|Exponential Functions, Rates of Change, and the Multiplicative Unit}} __NOTOC__ * Authors: Jere Confrey and Erick Smith * Journal: Educational Studies in Mat...")
 
imported>Raymond Johnson
(→‎Outline of Headings: added headings)
 
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{{Title|Exponential Functions, Rates of Change, and the Multiplicative Unit}}
{{Title|Method}}
__NOTOC__
* Authors: [[Jere Confrey]] and [[Erick Smith]]
* Journal: [[Educational Studies in Mathematics]]
* Year: 1994
* Source: http://link.springer.com/article/10.1007/BF01273661


==Abstract==
* Author: [[Alan Schoenfeld|Alan H. Schoenfeld]]
Conventional treatments of functions start by building a rule of correspondence between ''x''-values and ''y''-values, typically by creating an equation of the form ''y=f(x)''. We call this a ''correspondence'' approach to functions. However, in our work with students we have found that a ''covariational'' approach is often more powerful, where students working in a problem situation first fill down a table column with ''x''-values, typically by adding 1, then fill down a ''y''-column through an operation they construct within the problem context. Such an approach has the benefit of emphasizing rate-of-change. It also raises the question of what it is that we want to cal 'rate' across different functional situations. We make two initial conjectures, first that a rate can be initially understood as a ''unit per unit'' comparison and second that a unit is the ''invariant relationship between a successor and its predecessor''. Based on these conjectures we describe a variety of multiplicative units, then propose three ways of understanding rate of change in relation to exponential functions. Finally we argue that rate is different than ratio and that an integrated understanding of rate is built from multiple concepts.
* 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
: Confrey, J., & Smith, E. (1994). Exponential functions, rates of change, and the multiplicative unit. ''Educational Studies in Mathematics'', 26(2-3), 135–164. http://doi.org/10.1007/BF01273661
: 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{Confrey1994,
@incollection{Schoenfeld2007,
author = {Confrey, Jere and Smith, Erick},
address = {Charlotte, NC},
doi = {10.1007/BF01273661},
author = {Schoenfeld, Alan H.},
journal = {Educational Studies in Mathematics},
booktitle = {Second handbook of research on mathematics teaching and learning},
number = {2-3},
chapter = {3},
pages = {135--164},
editor = {Lester, Frank K.},
title = {{Exponential functions, rates of change, and the multiplicative unit}},
pages = {69--107},
url = {http://link.springer.com/article/10.1007/BF01273661},
publisher = {Information Age},
volume = {26},
title = {{Method}},
year = {1994}
year = {2007}
}
}
</pre>
</pre>


[[Category:Journal Articles]]
[[Category:Book Chapters]]
[[Category:Educational Studies in Mathematics]]
[[Category:2007]]
[[Category:1994]]
[[Category:Research Methods]]
[[Category:Covariation]]
[[Category:Exponential Functions]]
[[Category:Rate]]
[[Category:Ratio]]

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}
}