__The Problem of Persistence__," just because a student needs further mathematics for the intended career and has done well in the last mathematics course is no guarantee that he or she will decide to continue the study of mathematics. This loss between courses is a significant contributor to the disappearance from STEM fields of at least half of the students who enter college with the intention of pursuing a degree in science, technology, engineering, or mathematics. Chris Rasmussen and Jess Ellis, drawing on data from MAA’s Calculus Study, have now shed further light on this problem. This column draws on some of the results they have gleaned from our data.

For the MAA Calculus Study, students
were surveyed both at the start and end of the fall term in
mainstream Calculus I. A student was classified as a

*persister*if she or he indicated at the start of the term an intention to continue on to Calculus II and still held that intention at the end of the term. A student was classified as a*switcher*if she or he intended at the start of the term to continue on to Calculus II, but changed his or her mind by the end of the term.
Not all students completed both the
start and end of term surveys. While 50% of all Calculus I students
received an A or B in the course, A or B students accounted for 80%
of those who completed both surveys. Almost all of the remainder
received a C. This implies that our data reflect what happened to the
students who were doing well in the class. Of the students who
started the term with the intention of taking Calculus II (74% of the
students who answered both surveys), 15% turned out to be switchers.
Less than 2% of all Calculus I students started with the expectation
that they would not continue on to Calculus II but changed their
minds by the end of the course.

The rates of switchers varied
considerably. Women were far more likely to switch (20%) than men
(11%). Those at large research universities were also more likely to
switch (16%), particularly if they were taught by a graduate teaching
assistant (19%). Rates varied by intended major, from a low of 6%
switchers for those headed into engineering to 23% for pre-med majors
and 27% for business majors taking mainstream calculus.

Classroom instruction had a significant
effect on switcher rates (see Figure 1). "Good Teaching" reflects
the collection of highly correlated observations described in this
column in March 2013, "

__MAA Calculus Study: Good Teaching__." "Progressive Teaching" refers to those practices described in the following column from April, "__MAA Calculus Study: Progressive Teaching__." Good Teaching is most important. In combination, Good and Progressive Teaching can significantly lower switcher rates.Figure 1. |

Our study offered students who had
chosen to switch out a variety of reasons from which they could
select any with which they agreed. Just over half reported that they
had changed their major to a field that did not require Calculus II.
A third of these students, as well as a third of all switchers,
identified their experience in Calculus I as responsible for their
decision. It also was a third of all switchers who reported that the
reason for switching was that they found calculus to require too much
time and effort.

This observation was supported by other
data from our study that showed that switchers visit their
instructors and tutors more often than persisters and spend more time
studying calculus. As stated before, these are students who are doing
well, but have decided that continuing would require more effort than
they can afford.

I am concerned by these good students
who find calculus simply too hard. As I documented in my column from
May 2011, "

__The Calculus I Student__," these students experienced success in high school, and an overwhelming majority had studied calculus in high school. They entered college with high levels of confidence and strong motivation. Their experience of Calculus I in college has had a profound effect on both confidence and motivation.
The solution should not be to make
college calculus easier. However, we do need to find ways of
mitigating the shock that hits so many students when they transition
from high school to college. We need to do a better job of preparing
students for the demands of college, working on both sides of the
transition to equip them with the skills they need to make effective
use of their time and effort.

Twenty years ago, I surveyed Calculus I
students at Penn State and learned that most had no idea what it
means to study mathematics. Their efforts seldom extended beyond
trying to match the problems at the back of the section to the
templates in the book or the examples that had been explained that
day. The result was that studying mathematics had been reduced to the
memorization of a large body of specific and seemingly unrelated
techniques for solving a vast assortment of problems. No wonder
students found it so difficult. I fear that this has not changed.

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