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10:15 – 10:45 am |
Session 10 – Preliminary
Reports |
Marquis A |
Does it converge? A look at second semester calculus
students' struggles determining convergence of series David Earls and Eyob
Demeke Despite
the multitude of research that exists on student difficulty in first semester
calculus courses, little is known about student difficulty determining
convergence of sequences and series in second semester calculus courses. In
our preliminary report, we attempt to address this gap specifically by
analyzing student work from an exam question that asks students to determine
the convergence of a series. We develop a framework that can be used to help
analyze the mistakes students make when determining the convergence of
series. In addition, we analyze how student errors relate to prerequisites
they are expected to have entering the course, and how these errors are
unique to knowledge about series. 108 |
Marquis B |
An example of a linguistic obstacle to proof construction:
Dori and the hidden double negative Annie Selden and John
Selden This
paper considers the difficulty that university studentsÕ may have when
unpacking an informally worded theorem statement into its formal equivalent
in order to understand its logical structure, and hence, construct a proof.
This situation is illustrated with the case of Dori who encountered just such
a difficulty with a hidden double negative. She was taking a
transition-to-proof course that began by having students first prove formally
worded Òif-thenÓ theorem statements that enabled them to construct proof
frameworks, and thereby, make initial progress on constructing proofs. But
later, students were presented with some informally worded theorem statements
to prove. We go on to consider the question of when, and how, to enculturate
students into the often informal way that theorem statements are normally
written, while still enabling them to progress in their proof construction
abilities. 63 |
Marquis C |
Student characteristics and online retention: Preliminary
investigation of factors relevant to mathematics course outcomes Claire Wladis, Alyse
Hachey and Katherine Conway There
is evidence that students drop out at higher rates from online than
face-to-face courses, yet it is not well understood which students are
particularly at risk online. In particular, online mathematics (and other
STEM) courses have not been well-studied in the context of larger-scale
analyses of online dropout. This study surveyed online and face-to-face
students from a large U.S. university system. Results suggest that for online
courses generally, grades are significant predictors of differential online
versus face-to-face performance and that student parents may be particularly
vulnerable to poor online course outcomes. Native-born students were also
vulnerable online. The next stage of this research will be to analyze the
factors that are relevant to online versus face-to-face retention in
mathematics (and other STEM) courses specifically. 69 |
Grand Ballroom 5 |
Student interpretation and justification of ÒbackwardÓ
definite integrals Vicki Sealey and John
Thompson The
definite integral is an important concept in calculus, with applications
throughout mathematics and science. Studies of student understanding of
definite integrals reveal several student difficulties, some of which are
related to determining the sign of an integral. Clinical interviews of 5
students gleaned their understanding of ÒbackwardÓ definite integrals, i.e.,
integrals for which the lower limit is greater than the upper limit and the
differential is negative. Students initially invoked the Fundamental Theorem
of Calculus to justify the negative sign. Some students eventually accessed
the Riemann sum appropriately but could not determine how to obtain a
negative quantity this way. We see the primary obstacle here as interpreting
the differential as a width, and thus an unsigned quantity, rather than a
difference between two values. 80 |
City Center A |
Divergent definitions of inquiry-based learning in
undergraduate mathematics Samuel Cook, Sarah Murphy
and Tim Fukawa-Connelly Inquiry-based
learning is becoming more important and widely practiced in undergraduate
mathematics education. As a result, research about inquiry-based learning is
similarly becoming more common, including questions of the efficacy of such
methods. Yet, thus far, there has been little effort on the part of
practitioners or researchers to come to a description of the range(s) of
practice that can or should be understood as inquiry-based learning. As a
result, studies, comparisons and critiques can be dismissed as not using the
appropriate definition, without adjudicating the quality of the evidence or
implications for research and teaching. Through a large-scale literature
review and surveying of experts in the community, this study begins the
conversation about possible areas of agreement that would allow for a
constituent definition of inquiry-based learning and allow for
differentiation with non-inquiry pedagogical practices. 88 |
City Center B |
IVT as a starting point for multiple real analysis topics Steve Strand The
proof of the Intermediate Value Theorem (IVT) provides a rich and
approachable context for motivating many concepts central to real analysis,
such as: sequence and function convergence, completeness of the real numbers,
and continuity. As a part of the development of local instructional theory,
an RME-based design experiment was conducted in which two post-calculus
undergraduate students developed techniques to approximate the root of a
polynomial. They then adapted those techniques into a (rough) proof of the
IVT. 118 |