id: 06581375
dt: j
an: 2016c.00527
au: Tallman, Michael A.; Carlson, Marilyn P.; Bressoud, David M.; Pearson,
Michael
ti: A characterization of Calculus I final exams in U.S. colleges and
universities.
so: Int. J. Res. Undergrad. Math. Educ. 2, No. 1, 105-133 (2016).
py: 2016
pu: Springer US, New York, NY
la: EN
cc: D65 I15
ut: calculus; assessment; mathematical reasoning; university level mathematics
ci:
li: doi:10.1007/s40753-015-0023-9
ab: Summary: In this study, we developed a three-dimensional framework to
characterize post-secondary Calculus I final exams. Our {\it Exam
Characterization Framework} (ECF) classifies individual exam items
according to the cognitive demand required to answer the item, the
representation of both the task statement and the solution, and the
item’s format. Our results from using the ECF to code 150
post-secondary Calculus I final exams from across the United States
revealed that the exams generally require low levels of cognitive
demand, seldom contain problems stated in a real-world context, rarely
elicit explanation, and do not require students to demonstrate or apply
their understanding of the course’s central ideas. We compared the
results from analyzing individual instructor’s exams with survey data
of their beliefs about the conceptual orientation of their exams. Our
analysis revealed inconsistencies between our characterization of
Calculus I final exams and instructors’ perceptions of their final
exams relative to their conceptual focus and the extent to which the
exam items ask students to explain their thinking. We also compared the
characteristics of our sample of final exams with post-secondary
Calculus I final exams administered in 1986/87. We found that Calculus
I final exams in U.S. colleges and universities have changed very
little in the past 25 years with respect to the percentage of exam
items that require students to apply their understanding of
foundational concepts, which suggest that the calculus reform movement
of the late 1980s has had little effect on what is being assessed in
current Calculus I courses in U.S. postsecondary institutions.
rv: