home - login - register

Journal Article Detail Page

Cognition and Instruction
written by Marilyn Carlson, Michael Oehrtman, and Nicole Engelke
This article describes the development of the Precalculus Concept Assessment (PCA) instrument, a 25-item multiple-choice exam. The reasoning abilities and understandings central to precalculus and foundational for beginning calculus were identified and characterized in a series of research studies and are articulated in the PCA Taxonomy. These include a strong understanding of ideas of rate of change and function, a process view of function, and the ability to use covariational reasoning to examine and represent how two covarying quantities change together. This taxonomy guided the PCA development and now provides the theoretical basis for interpreting and reporting PCA results. A critical element of PCA's design was to identify the constructs essential for learning calculus and to employ methods to assure that PCA items are effective in assessing these constructs. We illustrate the role that cognitive research played during both the design and validation phases of the PCA instrument. We also describe our Four-Phase Instrument Development Framework that articulates the methods used to create and validate PCA. This framework should also be useful for others interested in developing similar instruments in other content areas. The uses of PCA are described and include (a) assessing student learning in college algebra and precalculus, (b) comparing the effectiveness of various curricular treatments, and (c) determining student readiness for calculus.
Cognition and Instruction: Volume 28, Issue 2, Pages 113-145
Subjects Levels Resource Types
Education - Basic Research
- Assessment
= Conceptual Assessment
= Instruments
- Research Design & Methodology
= Validity
Mathematical Tools
- Trig and Pre-cal
- Lower Undergraduate
- High School
- Reference Material
= Research study
PER-Central Type Intended Users Ratings
- PER Literature
- Researchers
  • Currently 0.0/5

Want to rate this material?
Login here!


Formats:
application/pdf
non-digital
Access Rights:
Available by subscription and
Available for purchase
Restriction:
© 2010 Cognition and Instruction
DOI:
10.1080/07370001003676587
Record Creator:
Metadata instance created October 10, 2019 by Lyle Barbato
Record Updated:
October 24, 2019 by Sam McKagan
Last Update
when Cataloged:
April 15, 2010
ComPADRE is beta testing Citation Styles!

Record Link
AIP Format
M. Carlson, M. Oehrtman, and N. Engelke, Cog. Instr. 28 (2), 113 (2010), WWW Document, (https://doi.org/10.1080/07370001003676587).
AJP/PRST-PER
M. Carlson, M. Oehrtman, and N. Engelke, The Precalculus Concept Assessment: A Tool for Assessing Students’ Reasoning Abilities and Understandings, Cog. Instr. 28 (2), 113 (2010), <https://doi.org/10.1080/07370001003676587>.
APA Format
Carlson, M., Oehrtman, M., & Engelke, N. (2010, April 15). The Precalculus Concept Assessment: A Tool for Assessing Students’ Reasoning Abilities and Understandings. Cog. Instr., 28(2), 113-145. Retrieved November 13, 2019, from https://doi.org/10.1080/07370001003676587
Chicago Format
Carlson, M, M. Oehrtman, and N. Engelke. "The Precalculus Concept Assessment: A Tool for Assessing Students’ Reasoning Abilities and Understandings." Cog. Instr. 28, no. 2, (April 15, 2010): 113-145, https://doi.org/10.1080/07370001003676587 (accessed 13 November 2019).
MLA Format
Carlson, Marilyn, Michael Oehrtman, and Nicole Engelke. "The Precalculus Concept Assessment: A Tool for Assessing Students’ Reasoning Abilities and Understandings." Cog. Instr. 28.2 (2010): 113-145. 13 Nov. 2019 <https://doi.org/10.1080/07370001003676587>.
BibTeX Export Format
@article{ Author = "Marilyn Carlson and Michael Oehrtman and Nicole Engelke", Title = {The Precalculus Concept Assessment: A Tool for Assessing Students’ Reasoning Abilities and Understandings}, Journal = {Cog. Instr.}, Volume = {28}, Number = {2}, Pages = {113-145}, Month = {April}, Year = {2010} }
Refer Export Format

%A Marilyn Carlson
%A Michael Oehrtman
%A Nicole Engelke
%T The Precalculus Concept Assessment: A Tool for Assessing Students' Reasoning Abilities and Understandings
%J Cog. Instr.
%V 28
%N 2
%D April 15, 2010
%P 113-145
%U https://doi.org/10.1080/07370001003676587
%O application/pdf

EndNote Export Format

%0 Journal Article
%A Carlson, Marilyn
%A Oehrtman, Michael
%A Engelke, Nicole
%D April 15, 2010
%T The Precalculus Concept Assessment: A Tool for Assessing Students' Reasoning Abilities and Understandings
%J Cog. Instr.
%V 28
%N 2
%P 113-145
%8 April 15, 2010
%U https://doi.org/10.1080/07370001003676587


Disclaimer: ComPADRE offers citation styles as a guide only. We cannot offer interpretations about citations as this is an automated procedure. Please refer to the style manuals in the Citation Source Information area for clarifications.

Citation Source Information

The AIP Style presented is based on information from the AIP Style Manual.

The AJP/PRST-PER presented is based on the AIP Style with the addition of journal article titles and conference proceeding article titles.

The APA Style presented is based on information from APA Style.org: Electronic References.

The Chicago Style presented is based on information from Examples of Chicago-Style Documentation.

The MLA Style presented is based on information from the MLA FAQ.

Save to my folders

Contribute

Similar Materials