TY - JOUR
T1 - The precalculus concept assessment
T2 - A tool for assessing students' reasoning abilities and understandings
AU - Carlson, Marilyn
AU - Oehrtman, Michael
AU - Engelke, Nicole
N1 - Funding Information:
Thanks to our many graduate students and colleagues who have contributed to the development of the PCA instrument. Thanks to Sean Larsen, Trey Cox, Nicole Thompson, Millie Trotter, Edward Coe, Phil Clark, Kacie Joyner, Kevin Moore, Stacey Bowling, Sharon Lima, Carlos Castillo-Chavez, Karen Platt, Vicki Sealey, and Jennifer Wilken for their assistance in conducting clinical interviews, analyzing student interviews, and building the PCA database. Thanks to Christine Baum for assisting with formatting and edits, and also to Sally Jacobs and Patrick Thompson for their reviews and discussions. We also want to thank Jack Smith for his very helpful editorial assistance in processing this article. This research was supported by Grants 0412537 and 9876127 from the National Science Foundation (NSF). Any opinions expressed in the article are those of the authors and do not necessarily reflect the views of NSF.
PY - 2010/1
Y1 - 2010/1
N2 - 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.
AB - 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.
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U2 - 10.1080/07370001003676587
DO - 10.1080/07370001003676587
M3 - Article
AN - SCOPUS:77951271521
SN - 0737-0008
VL - 28
SP - 113
EP - 145
JO - Cognition and Instruction
JF - Cognition and Instruction
IS - 1
ER -