5**The Two-Year Curriculum in Mathematics**

**Important Points Made by the Speaker**

• Many more students are taking mathematics at community colleges than has been the case in the past, but the majority of students enroll at the precollege, noncredit level.

• Reform of the mathematics curriculum needs to encompass the entire educational system.

• Much more research is needed on teaching and learning in two-year college mathematics and on the characteristics, experiences, and aspirations of students.

• Practitioners need to be engaged in research on mathematics education to facilitate adoption and scale-up.

Mathematics is seen by many as the backbone of the STEM pipeline, said Debra Bragg, professor of higher education at the University of Illinois, and author of one of the three papers commissioned for the summit. The complete paper is available in Appendix C. Yet very few students in community colleges ever progress beyond arithmetic or algebra. Though reforming mathematics education in the United States is an “enormous” job, said Bragg, changes at the community college level can help set the process in motion.

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5
The Two-Year Curriculum
in Mathematics
Important Points Made by the Speaker
• any more students are taking mathematics at community colleges than
M
has been the case in the past, but the majority of students enroll at the
precollege, noncredit level.
• eform of the mathematics curriculum needs to encompass the entire edu-
R
cational system.
• uch more research is needed on teaching and learning in two-year col-
M
lege mathematics and on the characteristics, experiences, and aspirations
of students.
• ractitioners need to be engaged in research on mathematics education to
P
facilitate adoption and scale-up.
Mathematics is seen by many as the backbone of the STEM pipeline,
said Debra Bragg, professor of higher education at the University of Illi -
nois, and author of one of the three papers commissioned for the summit.
The complete paper is available in Appendix C. Yet very few students in
community colleges ever progress beyond arithmetic or algebra. Though
reforming mathematics education in the United States is an “enormous”
job, said Bragg, changes at the community college level can help set the
process in motion.
29

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30 COMMUNITY COLLEGES IN THE EVOLVING STEM EDUCATION LANDSCAPE
RISING ENROLLMENTS
The normative mathematics sequence in U.S. education progresses
from arithmetic to algebra to geometry to trigonometry to calculus. Over
the past three decades, many more students have at least embarked upon
this progression in two-year institutions—from about one million stu -
dents enrolled in two-year mathematics and statistics programs in the
early 1980s to more than two million today, according to data provided
to Bragg from the Conference Board of Mathematical Sciences. Further-
more, about 47 percent of mathematics enrollments in higher education
are at the two-year level. “That is a lot of enrollments and clearly a very
important part of the pipeline,” said Bragg.
However, 57 percent of the students enrolled in two-year college
mathematics are enrolled at the pre-college, noncredit level. The course
with the largest enrollment is elementary algebra, which is usually one to
two levels below college-level algebra. Over the past five years, the great -
est growth in enrollments has been in arithmetic and pre-college algebra.
“We are seeing growth at the lower end, not where we were hoping to
see it,” she said.
The preponderance of enrollments in college-level mathematics is
in college algebra, and most students do not move beyond that level.
Only about 7 percent of enrollments are in calculus, and only about 7
percent are in statistics, with most students never moving beyond the
introductory courses in these subjects. Other significant enrollments are
pre-calculus (18%) and other mathematics classes (11%) such as linear
algebra, mathematics for elementary teachers, or non-calculus mathemat-
ics for technical careers.
INSTRUCTIONAL APPROACHES
The Conference Board of Mathematical Sciences also has conducted a
survey about instructional approaches in two-year mathematics courses.1
Relatively few two-year courses offer special mathematics programs that
provide support for minorities or women (11% and 6%, respectively).
About 14 percent offer undergraduate research opportunities, and 20
percent offer honors sections to mathematics students.
In contrast to these sparse offerings, 90 percent of two-year col-
lege mathematics programs require diagnostic or placement testing. An
increasing number of researchers are raising questions about the use of
1The survey is available at http://www.ams.org/profession/data/cbms-survey/
cbms2005.

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31
THE TWO-YEAR CURRICULUM IN MATHEMATICS
these tests, said Bragg, and about alternative educational approaches that
could reduce the number of students needing developmental mathematics.
MATHEMATICS REFORM
The American Mathematical Association of Two-Year Colleges
(AMATYC) has made an extended commitment to reform in mathemat-
ics education. The AMATYC Crossroads in Mathematics Program2 led
to follow-up programs called Beyond Crossroads3 and College Renewal
Across the First Two Years, under the aegis of the Mathematical Asso-
ciation of America,4 which have tackled the implementation challenges
inherent in reform. In addition, work by Lynn Steen, Uri Treisman, and
others have contributed to careful thinking about what and how math-
ematics is taught, Bragg said (references are in Appendix C).
SPEAKER AND PARTICIPANT SUGGESTIONS
FOR FUTURE ACTION
Bragg made four suggestions for future action on the basis of her
observations.
First, reform of the mathematics curriculum needs to encompass the
entire educational system. Without a strategic, collaborative endeavor, it
will be difficult for two-year colleges, caught as they are between K-12
education and universities, to implement and sustain reform, except in
isolated ways. Today, reform at different levels is largely separate, Bragg
said; it needs to be combined and integrated.
Second, much more research is needed on teaching and learning
in two-year college mathematics, especially in college-level mathemat -
ics. Numerous pedagogical strategies are emerging that have promise to
change the way two-year college mathematics is taught, said Bragg, but
today lecture-led, teacher-centered instruction predominates.
Third, the characteristics, experiences, and aspirations of students
who enroll in two-year college mathematics need to be investigated in
greater depth. More research is needed to understand how students
develop the “habits of the mathematical mind” that are required to be
successful in all STEM fields.
Finally, practitioners need to be engaged in research on mathematics
education to facilitate adoption and scale-up. Two-year faculty would
2Additional information is available at http://www.amatyc.org/Crossroads/CrsrdsXS.
pdf.
3Additional information is available at http://beyondcrossroads.amatyc.org/.
4Additional information is available at http://www.maa.org/cupm/crafty/.

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32 COMMUNITY COLLEGES IN THE EVOLVING STEM EDUCATION LANDSCAPE
appreciate and benefit from opportunities to engage in research that
encourages them to try out new pedagogical strategies in the classroom
and determine how they affect student learning. “The math faculty will
be hungry and excited to be part of this kind of research, because they live
this issue every day,” Bragg said.
Report of Collective Observations from a
Breakout Group on Mathematics
Participants in the breakout session on mathematics education at the summit
reported three main observations from their discussions during a plenary session
of all Summit attendees:
First, additional research about mathematics education at the community col-
lege level could lead to more informed policies and decision making.
Second, successful evidence-based instructional systems for mathematics
need to be identified. Research on instruction indicates that effective systems
encompass curriculum, pedagogy, faculty development, and student support
mechanisms.
Third, excellent evidence-based instructional systems, which combine the re-
search and identification of pockets of excellence, exist today. However, there
are too few documented cases where they are being strategically replicated and
expanded.
DISCUSSION
During the discussion sessions at the summit, participants made a
number of comments related to mathematics at the community college
level.
Pamela Brown from the National Science Foundation, on leave from
the New York City College of Technology, a branch of the City Univer-
sity of New York, directed attention to the 60 percent of the institution’s
16,000 incoming students who need to take developmental mathematics.
“I would not describe it as a gatekeeper,” she said. “I would have to say it
is more like a firing squad, because only about 20 percent of the students
pass the lowest levels of developmental math, and a great percentage of
those students withdraw unofficially. They just give up and stop coming
to classes.” Part-time faculty who receive only a few thousand dollars
per course teach half of these classes. These faculty need help to become
good mentors, get involved in educational research, and adopt good
pedagogical practices, said Brown. In her response, Bragg noted that
national statistics point toward something like 60 percent of the sections
of precollege mathematics being taught by part-time faculty, and overall

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33
THE TWO-YEAR CURRICULUM IN MATHEMATICS
part-time faculty teach an estimated 45 percent of all mathematics two-
year college sections.
Sally Johnson from the College of Southern Nevada said that her
school gave 10,000 placement tests in the fall of 2011, and it provided
students with options in taking the test. Nevertheless, 60 percent of those
10,000 students ended up in the lowest levels of mathematics, which are
the equivalent of fifth grade and ninth grade mathematics. As she phrased
it, “That is the reality of what we have on the ground.” Furthermore, a
student who starts in the fifth grade-level developmental mathematics
class has approximately a 3 percent chance of ever taking a college-level
mathematics class, she said.
Why are students enrolled in these classes when so many fail, asked
Packard, commenting that “it is heartbreaking.” If money is going to be
invested in running so many sections of developmental mathematics,
faculty also need development and support.
Carl Wieman, associate director for science in the White House Office
of Science and Technology Policy, questioned the unusually high reliance
on diagnostic tests and sorting in mathematics. In that respect, mathemat-
ics differs dramatically from other disciplines, which tend not to identify
a lack of preparation as a deficiency. Biology, physics, and chemistry
have courses for students who have not taken high-level classes in these
subjects in high school. As an example of an alternative approach, George
Boggs said that some colleges have been giving refresher courses before
students take the assessment exam, and some of these students then do
not have to go through a whole semester of developmental mathematics.
Jeannette Mowery from Madison Area Technical College, who was
listening on the live webcast, e-mailed comments to the summit regarding
developmental mathematics. She pointed out that, with few exceptions,
mathematics is taught in isolation at all educational levels and not in
context as a necessary tool to solve interesting and complex problems in
a variety of industries and STEM application areas. All students would
learn more mathematics if it were taught in context, she contended. She
also pointed out that the level of mathematics needed for the majority
of technical occupations is not higher mathematics such as trigonometry
or calculus. Yet counselors and the standardized test system imply that
students need to master mathematics at this high level to succeed in the
sciences. “It is just not true, and it is a major barrier to students’ success
in the STEM field,” she wrote.
Joan Sabourin from the American Chemical Society posed the chal-
lenge of decreasing the number of developmental mathematics and read -
ing courses taught at two-year colleges by 5 percent each year through
collaborations with K-12 institutions to increase the skills in mathematics
and reading of 5 percent of K-12 students each year.

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