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.
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 students 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. Furthermore, 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 greatest 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 mathematics for technical careers.
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 college 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.
these tests, said Bragg, and about alternative educational approaches that could reduce the number of students needing developmental mathematics.
The American Mathematical Association of Two-Year Colleges (AMATYC) has made an extended commitment to reform in mathematics 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 Association 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 mathematics 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 mathematics. 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
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 college 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 research and identification of pockets of excellence, exist today. However, there are too few documented cases where they are being strategically replicated and expanded.
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 University of New York, directed attention to the 60 percent of the institutionâ€™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
part-time faculty teach an estimated 45 percent of all mathematics twoyear 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, mathematics 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 studentsâ€™ success in the STEM field,” she wrote.
Joan Sabourin from the American Chemical Society posed the challenge of decreasing the number of developmental mathematics and reading 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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