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Peer Review, Summer 2004
Multiple Approaches to Improving Quantitative
Skills at James Madison University
By David F. Brakke, dean of the College of
Science and Mathematics, and David C. Carothers, head
of the Department of Mathematics and Statistics, both
at James Madison University |
Improving the quantitative skills of all students and enhancing
the development of quantitative skills within major programs
require looking and working well beyond the boundaries of
individual departments. At James Madison University (JMU),
the Department of Mathematics and Statistics has been reaching
out and connecting with general education and through departments
and programs across campus with a comprehensive approach.
Careful thought and planning is required to achieve a balanced
and comprehensive approach to improving quantitative skills
and reasoning in response to multiple demands. These sometimes
competing demands include the need to establish effective
and measurable liberal education goals for all students, the
need for specific skills for students in traditionally quantitatively-oriented
disciplines, the evolving need for quantitative skills in
areas not previously thought of as "mathematical,"
and very special needs for teacher preparation. One guiding
principle is to encourage more students to learn more mathematics
and statistics and to provide more opportunities for them
to apply this knowledge within major programs.
Freshman Advising
All entering freshmen at JMU take an algebra-based placement
exam. We have carefully examined the mathematics placement
scores and the eventual performance of students in basic mathematics
and statistics courses, using the information to develop a
matrix for freshmen advisors in collaboration with the general
education program. Our intent is to improve placement and,
therefore, success in mathematics and statistics courses.
Standards are not changed, but we try to avoid advising students
into courses where they have little chance of succeeding.
We also try to avoid "math-phobic" advising--the
kind of advice that would suggest a student go take that one
required math course and get it over with--or advising
that suggests that freshmen in certain majors must take a
certain set of courses immediately, even if they are not fully
prepared.
We have extended the attention to advising to combine mathematics
placement scores in other areas. For example, mathematics
placement and math SAT scores are reliable predictors of passing
general chemistry. Student effort is obviously an important
factor, but below certain placement scores the probability
of passing is essentially zero due to the extensive use of
algebraic manipulations. As a result, some entering biology
majors may be advised to delay general chemistry until they
have completed a particular mathematics course. Similarly,
we have found that students who might have mathematics placement
scores adequate to enroll in statistics do not perform well
if they have lower SAT verbal scores. However, after taking
a course in writing, their chances of succeeding in statistics
improve because of increased proficiency in working through
written problems.
Support
Recognizing that nearly all students can run into a mental
block in a mathematics course and may benefit from additional
support, we have developed the Science and Mathematics Learning
Center to provide professional assistance in working through
problems in basic mathematics, statistics, and science courses.
The center has two full-time professional faculty members
who, assisted by trained students, work with approximately
10,000 student visitors each year. Assessment of grades for
students using the center indicates improved performance.
Similarly, we provide supplemental instruction by student
mentors for a number of key classes in which students often
struggle. This too produces positive results.
Paying careful attention to hiring, staffing, and delivery
of courses is essential. We search for faculty who are balanced
teachers and scholars--and who are genuinely interested
in working with undergraduate students. Departments match
faculty strength and pedagogical approaches to the levels
of the course. For example, peer mentoring has produced benefits
in general chemistry and in entry-level computer information
system courses, both of which emphasize problem solving.
Assessment
All entering students take assessment exams during orientation
for the fall semester. In the spring semester of the sophomore
year, the students are reexamined during a day devoted to
assessment university-wide. Thus, we can examine their performance
and compare it with the courses they have taken to satisfy
general education requirements. The exams were developed by
our Center for Assessment and Research Studies in conjunction
with faculty members who have written questions related to
the learning objectives for general education. One of these
exams covers quantitative literacy. In addition to the testing
of all students, the Department of Mathematics and Statistics
is in the process of assessing outcomes across a series of
mathematics courses as part of a project with the Mathematical
Association of America.
Curricular Changes
Within the Department of Mathematics and Statistics, there
have been many curricular changes designed to improve the
preparation of students. For example, a new calculus sequence
was developed for students who might have gaps in their preparation
and not be fully prepared for science-oriented Calculus I.
The two-semester course combines calculus and precalculus,
is very rigorous, and fully prepares students to be successful
in Calculus II. This route has become very popular for many
majors in chemistry and biology. Previously, many of these
students would have enrolled in a softer "terminal"
calculus course, making it difficult for them to continue
on to the advanced mathematics courses that are becoming increasingly
important to these disciplines.
A course in discrete mathematics was expanded into a sequence
in very close collaboration with the computer science program.
A course in quantitative geology has been offered as a result
of collaborations of geologists and mathematicians. Working
with the College of Education, an elementary and middle school
teacher preparation program has been developed, which includes
three core courses for all teachers followed by four upper-division
courses for middle school mathematics teachers and elementary
school mathematics specialists. A computational science minor
has been implemented jointly with physics and a course in
"Mathematical Models in Biology" has been developed
and co-taught. Each of these areas grew from faculty collaborations,
and new faculty have been hired to support the developing
connections across disciplines. We also are seeing evidence
of additional quantitative and analysis courses springing
up within the disciplines.
Minors and Majors
Students can benefit greatly from a minor. We offer minors
in mathematics and in statistics, and both are increasingly
popular. The mathematics minor is often taken by students
in the natural sciences and in business. The statistics minor
is frequently chosen by students in the health professions,
psychology, and sociology. For the students in the biomathematics
course mentioned above, the mathematics majors indicated that
they would take more biology and the biology students that
they would take more mathematics, with some deciding to add
a minor. These impacts suggest that infusing more mathematics
into biology (and other courses) may be successful.
As students become more aware of the practical benefits of
additional mathematics and the interesting and rewarding new
opportunities that result, faculty in mathematics and statistics
are collaborating with those in science, business, and computer
science on plans to make it more convenient for students to
pursue a double major while still meeting the core demands
of the individual disciplines. A new statistics major promises
to be a popular choice as a second major for students in several
other disciplines.
Interdisciplinarity
Many fields have become more quantitative over time, especially
biology, chemistry, and finance. This is also true of professional
programs and a wide range of disciplines. But what quantitative
applications and approaches are being used? Have they changed
over time? What might be the best preparation for students?
These questions are not simple ones and require connections
and conversations among mathematicians, statisticians, and
faculty working in other programs. Our experience suggests
that collaborative course development and research help faculty
appreciate quantitative applications in other fields, which
is especially true in interdisciplinary research questions.
But that is only one piece of the answer to these questions.
Making substantial progress in improving the quantitative
skills and reasoning of students requires careful attention
to the development of a student in a very intentional way--something
most majors rarely consider. For example, if we are interested
in having students engage in a capstone experience that involves
research, possibly as part of an interdisciplinary team, we
should align a curriculum intentionally to prepare students
for such an experience. Sometimes majors have been constructed
and offered as collections of courses, with coherence often
lacking. However, if we are to develop quantitative reasoning
in students, it cannot be accomplished solely by requiring
certain courses in mathematics or statistics; it will require
attention to enhancing quantitative skills within a major
program.
Undergraduate research experiences have brought faculty together
in new ways and have developed further connections between
disciplines. For example, our Materials Science Research Experiences
for Undergraduates program, funded by the National Science
Foundation, includes faculty mentors from several departments,
including mathematicians, and mathematics majors have participated
in research programs in other disciplines. Statisticians frequently
work with students from a range of disciplines as they engage
in senior projects or other research experiences. More recently,
work in visualization emanating from the Center for Computational
Mathematics and Modeling by applied mathematicians and physicists
is sparking interest from faculty from a wide range of areas,
including economics, art, computer science, and geology, among
others.
Conclusion
Rapid developments in many fields, emerging disciplines,
blurring boundaries, and the need for enhanced quantitative
skills challenge us all to provide improved quantitative preparation
for our students. Responding effectively requires careful
reexamination and coordinated design of curricula, which may
in some cases mean changes in cognate requirements, revisions
to existing courses, and more attention to building quantitative
skills within major programs. We suggest that, in order to
be successful, it will be necessary to recognize student backgrounds
and support developmental progress of students in an organized
way, to reach out from mathematics to disciplines to understand
and serve their needs, to build connections with disciplines,
to use multiple approaches and curricula designed for different
purposes, and to assess outcomes related to learning goals.
Clearly we are calling for a comprehensive approach and fully
recognize that many steps are required over a period of years
to produce the kind of transformation required. What we envision
is not the isolated island of mathematics that, unfortunately,
has been in the minds of many faculty (or even within departments
of mathematics), but rather departments at the center of a
university with helpful hands interdigitating across a campus
with vibrancy and excitement in pursuing quantitative solutions
and applications in a wide range of settings.
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