This column continues my report on results of the MAA National Study of Calculus I,

*Characteristics of Successful Programs in College Calculus**.*This month I am sharing what we learned about the use of graphing calculators (with or without computer algebra systems) and computer software such as

*Maple*or

*Mathematica*. Our results draw on three of the surveys:

- Student survey at start of term: We asked students how calculators and/or computer algebra systems (CAS) were used in their last high school mathematics class and how comfortable they are in using these technologies.
- Student survey at end of term: We asked students how calculators or CAS had been used both in class and for out of class assignments.
- Instructor survey at start of term: We asked instructors what technologies would be allowed on examinations and which would be required on examinations.

Our
first question asked students how calculators were used on exams in
their last high school mathematics class (see Figure 1). As in
previous columns, “research” refers to the responses of students
taking Calculus I at research universities (highest degree in
mathematics is doctorate), “undergrad” refers to undergraduate
colleges (highest degree is bachelor’s), “masters” to masters
universities (highest degree is masters), and “two-year” to
two-year colleges (highest degree is associate’s).

Figure
1. GC = graphing calculator. CAS = graphing calculator with computer
algebra system capabilities (e.g.
TI-89 or TI-92). |

There
are several interesting observations to be made from this graph.
First, not surprisingly, almost all Calculus I students reported
having used graphing calculators on their exams at least some of the
time (“always” and “sometimes” were mutually exclusive
options). Second, there is a difference by type of institution.
Students at undergraduate colleges were most likely to have used
graphing calculators on high school exams (94%), then those at
research universities (91%), then masters universities (86%), and
finally two-year colleges (77%). The differences are small but
statistically significant. My best guess is that these are
reflections of the economic background of these students. A second
observation is that for most students, access to a graphing
calculator was not always allowed. However, it is still common
practice in high schools (roughly one-third of all students) to
always allow students to use graphing calculators on mathematics
exams.

Another
striking observation from Figure 1 is that the percentage of students
who were always allowed to use graphing calculators on exams is
almost identical to the percentage of students who were always
allowed to use graphing calculators with CAS capabilities on exams.
For all categories of students, over half of them were allowed to use
graphing calculators with CAS capabilities at least some of the time,
which suggests that over half of the students in college Calculus I
own or have had access to such calculators.

The
next graph (Figure 2) shows how students at the start of the term
reported their comfort level with using graphing calculators or
computer algebra systems (

*Maple*and*Mathematica*were provided as examples of what we meant). The most interesting feature of this graph is that students at two-year colleges are much more likely to be comfortable with*Maple*or*Mathematica*than those at four-year programs. I suspect that the reason behind this is that most Calculus I students at two-year colleges are sophomores who took pre-calculus at that college the year before. This gave them more opportunity to experience these computer algebra systems.Figure 2. Student attitude toward use of graphing calculator or CAS on a computer such as Maple or Mathematica. |

The
graphs in Figures 3–5 show what students reported at the end of the
term about use of technology. For the graph in Figure 3, students
were asked how frequently each of these occurred in class. Percentage
shows the fraction of students who responded “about half the class
sessions,” “most class sessions,” or “every class session.”
We note large differences in instructor use of technology generally
(for this question, “technology” was not defined), and especially
sharp differences for instructor use of graphing calculators or CAS
(with

*Maple*and*Mathematica*given as examples). It is interesting that students are most likely to encounter computer algebra systems in undergraduate and two-year colleges, much less likely in masters and research universities. Figure
3. End of term student reports on frequency of use of technology (at
least once/month). For this question, CAS refers to a computer
algebra system on a computer, such as Maple
or Mathematica. |

The
first two sets of bars in Figure 4 show student responses to “Does
your calculator find the symbolic derivative of a function?” The
first set gives the percentage responding “N/A, I do not use a
calculator.” The second set displays the percentage responding
“yes.” Looking at the complement of these two responses, we see
that across all types of institutions, roughly 50% of students taking
Calculus I own a graphing calculator without CAS capabilities. The
third set records the percentage responding “yes” to the
question, “Were you allowed to use a graphing calculator during
your exams?” Note that there are some discrepancies between what
students and instructors report about allowing graphing calculators
on exams (Figures 4 and 6), but the basic pattern that graphing
calculators are allowed far less frequently at research universities
than at other types of institutions is consistently demonstrated.

We
also asked how often “The assignments completed outside of class
time required that I use technology to understand ideas.” Again, we
see much less use of technology at research universities, the
greatest use at undergraduate and two-year colleges.

The
last two graphs (Figures 6 and 7) are taken from the instructor
responses at the start of the term: what technology they would allow
on their exams and what technology they would require on their exams.
Again, we see a clear indication that technology, especially the use
of graphing calculators without CAS capabilities, is much less common
at research universities than other types of institutions.

It
is interesting to observe that there are large numbers of instructors
who allow but do not require technology on the exams. At research
universities, 26% require the use of some kind of technology, and a
further 25% allow but do not require the use of some sort of
technology. For undergraduate colleges, 38% of instructors require
technology, an additional 42% allow it. At masters universities, 42%
require, and a further 33% allow. At two-year colleges, 52% require,
and an additional 36% allow.

We
see a pattern of very heavy use of graphing calculators in high
schools, driven, no doubt, by the fact that students are expected to
use them for certain sections of the Advanced Placement Calculus
exams. They are still the dominant technology at colleges and
universities, but there the use is as likely to be voluntary as
required. This implies that in many colleges and universities
questions and assignments are posed in such a way that graphing
calculators confer little or no advantage. The use of graphing
calculators at the post-secondary level varies tremendously by type
of institution. Yet even at the research universities, over half the
instructors allow the use of graphing calculators for at least some
portions of their exams.

*The MAA national study of calculus, Characteristics of Successful Programs in College Calculus, is funded by NSF grant no. 0910240. The opinions expressed in this column do not necessarily reflect those of the National Science Foundation.*