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Appendix C Two-Year College Mathematics and Student Progression in STEM Programs of Study Debra D. Bragg Professor and Director, Office of Community College Research and Leadership University of Illinois at Urbana-Champaign EXECUTIVE SUMMARY In spite of the strident pursuit of standards-based reform of two- year college mathematics, implementation of reform has been slow and uneven. National studies show student enrollment in two-year college mathematics is growing in proportion to overall enrollment growth in higher education, but a substantial portion of these students are taking pre-college mathematics courses. Research suggests many of these stu - dents never reach college-level mathematics. Improvements need to be made to two-year college mathematics to prepare more students for sci - ence, technology, engineering, and mathematics (STEM)-related careers. Specific recommendations to support this goal are Take a P-20 approach to reforming the entire mathematics curricu- lum. Without a strategic, collaborative endeavor, it will be difficult for two-year colleges that are caught between K-12 education and higher education to implement and sustain meaningful change. Conduct more research on the teaching and learning of two-year college mathematics. Finding ways to support two-year college faculty to engage in professional development that reinforces innovative peda- gogies is important. Included in this list are topics linked to quantitative literacy, accelerated and contextualized instruction, and college placement and related assessments that need to be better linked closely to student learning. Investigate more fully the characteristics, experiences, and aspira - 81
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82 COMMUNITY COLLEGES IN THE EVOLVING STEM EDUCATION LANDSCAPE tions of students who enroll in two-year college mathematics. More information is needed about how diverse learners, especially women and minorities, experience their two-year mathematics courses (pre-college and college level) and how these experiences influence their subsequent enrollment, completion, and career decisions related to STEM. Engage practitioners in action research on mathematics education to facilitate the adoption and scale-up of innovation. Two-year faculty would benefit from opportunities to engage in action research that helps them to understand how various pedagogical and assessment strategies impact the learning of diverse students, and then employ these strategies in their classrooms. INTRODUCTION There is wide consensus that mastery of mathematics is essential to progressing into and through STEM programs of study, yet many stu- dents are unsuccessful at navigating the normative mathematics course sequence (Cullinane and Treisman, 2010) that is fundamental to their advancement into STEM-related careers. Recent concerns about inter- national competition and the struggling economy have focused atten - tion on this important issue and renewed concerns about the challenges that many students, particularly women and minorities, face succeeding in mathematics coursework (National Academy of Sciences, National Academy of Engineering, and Institute of Medicine, 2010). Resolving this problem is an urgent priority if the nation is to see growth in student enrollment and success in STEM programs of study, placement of gradu - ates in STEM-related careers, and rejuvenation of the nation’s economy. This paper examines the influence of the two-year mathematics cur- riculum on students’ progression into and through STEM programs by drawing upon extant literature, materials on the Internet, and personal communication with two-year college mathematics experts and practitio - ners. It acknowledges the expansive developmental mathematics curricu- lum offered by two-year colleges, but even more importantly, provides insights into college-level mathematics that has been overshadowed by a preoccupation with developmental education. The paper begins with a brief historical perspective and then proceeds to address such ques - tions as: what is the status of two-year mathematics courses, who teaches them, and how are they taught? What standards-based reforms are associ- ated with two-year college mathematics, what curricular and pedagogical innovations are capturing the attention of mathematics reformers, and what do we know about the impact of these reforms on student success? This paper concludes with recommendations for future research, policy, and practice on two-year college mathematics that is intended to enhance
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83 APPENDIX C student progression through STEM programs of study and into STEM- related careers. PERSPECTIVES ON MATHEMATICS CURRICULUM IN THE TWO-YEAR COLLEGE A useful framework for understanding two-year mathematics cur- riculum comes from Cullinane and Treisman (2010), who label the math- ematics curriculum in the United States the “normative mathematics course sequence” (pp. 7-8), which they claim is ubiquitous to the P-20 (primary through grade 20) education system. The normative mathemat - ics course sequence extends from basic arithmetic, to pre-algebra, algebra, and intermediate algebra on to trigonometry, pre-calculus, calculus, and other calculus-based courses, with a fuzzy demarcation between pre- college and college-level mathematics that starts with college algebra. Geometry may be part of the sequential mathematics continuum, or it may be omitted, to the detriment of students’ advancement into calculus and calculus-based sciences such as physics. Because this framework represents the dominant schema for which mathematics is taught and for which student competence is assessed at the secondary and postsecond - ary levels, I use this framework as the basis for discussing the literature. Later, in my discussion of reforms of the two-year college mathematics curriculum, I again cite Cullinane and Treisman (2010) who are studying alternatives to the normative mathematics course sequence. First, how - ever, I provide a brief historical foundation and then move to contempo - rary developments in two-year college mathematics. Liberal arts and sciences courses, including mathematics courses, have been part of the two-year college curriculum since creation of junior colleges in the early 1900s. Cohen and Brawer (1982) observed that, by the time two-year colleges arrived on the U.S. higher education scene, the academic disciplines were already “codified” (p. 284) by the rest of the educational system. Junior colleges that emerged to fill the void between high schools and universities adopted the prevailing curriculum structure advocated by the mathematics discipline and were therefore caught in between the K-12 sector and the four-year college sector from the start. To this end, Cohen and Brawer observed that, “the liberal arts [courses of two-year colleges] were captives of the disciplines; the disciplines dictated the structure of the courses; [and] the courses encompassed the collegiate function” (1982, p. 285). To facilitate the acceptance of college credits at the university level, two-year colleges reproduced the curriculum as well as the pedagogical methods used by universities to which their students sought entry. Transfer was born from these early replication efforts. A landmark
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84 COMMUNITY COLLEGES IN THE EVOLVING STEM EDUCATION LANDSCAPE study of junior colleges conducted at mid-20th century by Medsker (1960) confirmed the lengths to which two-year colleges mimicked university curriculum to enhance students’ ability to transfer. He noted, “the junior college forfeits its identity and its opportunity to experiment in the devel - opment of a program most appropriate for it” (p. 53). Looking back to the start of the comprehensive curriculum of the two-year college, Cohen and Brawer (1982) cited findings from a very early study of 58 junior colleges conducted in 1921 and 1922 by Koos (1924, p. 29) that showed liberal arts, sciences, and humanities courses dominated the early junior college cur- riculum, with three-fourths of all courses representing these disciplines. Across a broad array of the liberal arts and sciences, mathematics repre - sented about 8% of all course offerings. Whereas mathematics was not as dominant as English, communications, and the sciences, it was nearly universally offered in the two-year college. By the late-1950s, a national survey conducted by Medsker (1960) of 230 two-year colleges in 15 states confirmed mathematics courses were ubiquitous to the two-year college curriculum, but still, only a relatively modest proportion of students enrolled in them. In fact, only about one-quarter of two-year colleges required their students to take at least one mathematics course to meet general education requirements. Medsker’s study was also important because it was one of the first to document the prevalence of pre-college courses in reading, writing, and mathematics, foreshadowing a phenom- enon that would continue to grow to the present day. Several decades subsequent to Medsker’s study, Cohen and Brawer (1987) studied the two-year college curriculum and found remarkably similar findings about mathematics course-taking. Their analysis showed 9 percent of total course enrollments in the liberal arts, sciences, and humanities curriculum were in mathematics, and again reflective of Medsker’s results, the survey revealed a high proportion of mathematics courses were at the pre-college1 level. Subsequent studies conducted by Cohen, Brawer, and colleagues included a curriculum mapping study conducted by Cohen and Ignash (1992) about two decades ago. This study examined courses offered by a national sample of two-year colleges by scouring the spring 1991 catalogs and course schedules of 164 commu - nity colleges, balanced by small (less than 1,500 students), medium, and large (over 6,000 students) institution size. Cohen and Ignash mapped the liberal arts and nonliberal arts curriculum into broad subject areas of which mathematics and computer science were combined into one area. Their study showed the preponderance of mathematics enrollments were 1Consistent with other literature on two-year college mathematics (see, for example, Blair, 2006), I use the term pre-college to refer to mathematics courses offered below the college level, including courses often referred to as developmental and remedial education courses.
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85 APPENDIX C in classes offered at the introductory and intermediate course levels, with enrollments at the introductory or intermediate level being nearly 9 times larger than enrollments at the advanced level (about 766,000 enrollments in the former and approximately 87,000 enrollments in the latter). Though enrollments were substantially lower in advanced mathematics courses, this study confirmed that two-year colleges offered a substantial array of mathematics courses, including courses extending from the develop- mental level to calculus, as well as statistics. The number of sections of mathematics accounted for 10.7 percent of the total liberal arts curricu - lum, which ranked mathematics just behind humanities at 13.4 percent and English at 12.8 percent. Another important aspect of two-year college mathematics curricu - lum that is evident in the curriculum mapping study of Cohen and Ignash (1992), and that also has relevance to this discussion, pertains to the rise of nonliberal arts curriculum, a trend that began in the 1970s (Cohen and Brawer, 1987). Since much of mathematics course-taking in the two-year colleges relates to the majors that students choose in nonmathematics subjects, it is important to understand the ways mathematics is used to fulfill general education requirements. Cohen and Ignash (1994) identi- fied the emergence of occupational-technical fields of study (many hav - ing a technical focus and having some STEM-related content) beginning in the 1970s, and they documented the growth of technical education, trades and industrial education, and other programs of study offered by two-year colleges that require various levels and forms of mathemat - ics. Whereas the offering of liberal arts and sciences courses has been relatively robust over the years, by the 1990s nonliberal arts and sciences courses accounted for about 45 percent of the two-year college curricu - lum and occupational-technical education course were prominent among them. Technical mathematics and courses tailored for other majors such as elementary education were apparent in the curriculum as well. One impli- cation of this trend is that the teaching of mathematics, which had been the purview of the mathematics discipline, spread to other instructional units and efforts to integrate mathematics with other subjects emerged as a strategy to increase learners’ abilities to apply mathematics in diverse occupational settings (Grubb, 1999). Concerns about students’ lack of preparation for college-level math- ematics were also growing during the latter decades of the 20th century, as noted by an American Mathematical Association of Two-Year Col- leges (AMATYC) report that showed developmental mathematics courses were offered by 91 percent of two-year colleges (Baldwin and the Devel- opmental Mathematics Committee, 1975). Literature documenting the growth in remedial enrollments in two-year colleges observed pre-college mathematics courses were necessary for “marginally literate students
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86 COMMUNITY COLLEGES IN THE EVOLVING STEM EDUCATION LANDSCAPE emanating from the secondary schools” (Cohen, 1984, p. 1). In a national survey conducted in the early 2000s, Greene and Forster (2003) found only 32 percent of all high school graduates demonstrated the level of competence needed to enter college mathematics coursework. Among all learners, Greene and Forster identified Hispanics and African Americans as “seriously underrepresented in the pool of minimally qualified col - lege applicants” (p. 3), and they attributed their lack of preparation to inadequate K-12 education rather than “financial aid or affirmative action policies” (p. 3). Their research points to the uniquely important role that community colleges play in transferring underserved students to the uni - versity level in STEM-related careers (Arbona and Nora, 2009). However, transfer is not possible if students are unable to navigate the mathematics curriculum that begins at the pre-college level. Attewell et al. (2006) found 60 percent of community college entrants are required to take one or more developmental courses, usually mathematics, and numerous studies by Bailey and colleagues at the Community College Research Center (CCRC) (see, for example, Bailey, Jeong, and Cho, 2010) reveal the dismal success rates of students whose placement test scores prescribe multiple devel - opmental mathematics courses. Beyond the developmental level, Adel - man (2004) noted failure and withdrawal rates of 50 percent or higher in college algebra and pre-calculus courses, demonstrating problems with student success extend beyond to the gatekeeper course level. This trend and other critical aspects of the two-year mathematics curriculum, includ- ing documenting enrollment in mathematics course sequences extending from pre-college to college level, are examined in the next section. CONTEMPORARY TWO-YEAR COLLEGE MATHEMATICS Most of what we know about two-year college mathematics in the United States comes from a few large-scale national surveys. The fullest depiction of the curricular landscape about two-year college mathematics is the national inventory of the mathematics curriculum in U.S. higher education that has been conducted every five years starting in 1965 by the Conference Board of Mathematical Sciences (CBMS) with support from the National Science Foundation (NSF). The CBMS2005: Fall 2005 Statistical Abstract of Undergraduate Programs in the Mathematical Sciences in the United States is the last published installment of the national survey results on the two-year college mathematics curriculum (Lutzer et al., 2007). However, preliminary results of the 2010 CBMS national inventory on two-year college mathematics were shared with me by Ellen Kirkman and Rikki Blair (personal communication, December 4, 2011) to update
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87 APPENDIX C this paper.2 Taken together, the 2005 and 2010 reports (as well as selective use of earlier CBMS surveys) provide the most detailed description of two-year college mathematics curriculum offered by public community colleges in the United States, including trends in student enrollments, courses, faculty, and instructional practices. The CBMS survey used a stratified, simple random sampling design, with strata based on the three variables of curriculum, highest degree level offered, and total institutional enrollments to address three distinct universes: two-year college mathematics programs, mathematics depart - ments in four-year colleges and universities, and statistics departments in four-year colleges and universities. The stratum specifications used in the 2005 CBMS administration exactly replicated the ones used in the CBMS 2000, and closely emulates the specifications of previous CBMS surveys that were adjusted over time to improve national estimates. With respect to the 2005 CBMS administration, the most recent date for which a full report of methodology is available, a total of 600 public two- and four-year colleges and universities were surveyed during the period of September 2005 to May 2006. Minor adjustments are made to the CBMS at each administration, but the core of items included on the survey remains constant to address enrollments, instructional strategies, faculty demographics, and so forth. Figure C-1 reveals fall enrollments in mathematics and statistics at a 5-year interval from 1975 to 2005 (Lutzer et al., 2007), compared to total enrollments in public four-year and two-year colleges obtained from the Community Colleges, Special Supplement to the Condition of Education, 2008 report (Provasnik and Planty, 2008). Results suggest the enrollments in mathematics and statistics are growing commensurate with the increase in enrollments in public four-year and two-year colleges over the last 25-year period. Total enrollment growth in public two-year college is highly correlated (r = .96) with mathematics and statistics enrollment over this time span. More recent enrollment figures for Fall 2010 for mathematics and statistics show enrollment climbed to an all-time high of 2,096,000 (E. Kirkman and R. Blair, personal communication), mirroring the enrollment growth in public two-year colleges to an unprecedented high of 7,101,000 for 2009, the latest year statistics are available from the U.S. Census Bureau (2012). With respect to the growth in mathematics enrollment, the CBMS 2010 survey showed a 26 percent increase from 2005, which is about the same percentage increase that was observed between 2000 and 2005. 2Iwant to express my sincere appreciation to Ellen Kirkman and Rikki Blair for their gen - erosity in sharing preliminary tables from the forthcoming CBMS2010: Fall 2010 Statistical Abstract of Undergraduate Programs in the Mathematical Sciences in the United States .
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88 COMMUNITY COLLEGES IN THE EVOLVING STEM EDUCATION LANDSCAPE 8,000 7,000 6,000 5,000 Thousands 4,000 3,000 2,000 1,000 0 Fall 1975 Fall 1980 Fall 1985 Fall 1990 Fall 1995 Fall 2000 Fall 2005 Public Four-Year College Enrollment Public Two-Year College Enrollment Two-Year Math and Stats Enrollment FIGURE C-1 Total public enrollment in two-year and four-year colleges and two- year mathematics and statistics enrollment (Fall 1975–Fall 2005). Figure C-2 shows two-year college mathematics enrollments are criti- cal to the overall U.S. postsecondary education system. Whereas two-year mathematics enrollment has seen some fluctuation over the 15-year period from 1990 to 2005, the 2005 mathematics enrollment figure confirms sub- stantial growth from earlier years to the point where there were only mod- estly fewer enrollments in mathematics at the public two-year colleges ( n = 1,580,000) than four-year public and private colleges (n = 1,607,000) by Fall 2005, based on 2005 CBMS results (Lutzer et al., 2007). These totals take into account dual enrollment, which has grown substantially over the last decade (Waits, Setzer, and Lewis, 2005); however, they do not take into account mathematics courses taught outside of mathematics disciplinary units, including centralized pre-college education units that are responsible for teaching pre-college mathematics classes. Therefore, these figures almost certainly underestimate enrollments in pre-college mathematics (arithmetic, pre-algebra, elementary algebra, intermediate algebra, and geometry) and possibly other mathematics-related courses taught on two-year college campuses, suggesting the actual enrollment in two-year college mathematics may be higher still. Figure C-3 shows the percentage enrollment in two-year college mathematics courses by type of course and by the year the survey data were collected, based on the most recent CBMS 2010 data supplied by Kirkman and Blair (personal communication). Looking at the overall cur- riculum delivered by two-year college mathematics units, the preponder-
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89 APPENDIX C 2,000 1,500 Thousands 1,000 500 - Fall 1990 Fall 1995 Fall 2000 Fall 2005 Four-Year Math Enrollment Two-Year Math Enrollment FIGURE C-2 Total enrollment in four-year college mathematics and two-year col - lege mathematics (Fall 1990–Fall 2005). 2,500 2,016 2,000 1,696 1,425 Thousands 1,500 1,347 1,271 57.0% 56.8% 1,000 56.1% 56.6% 57% 500 - Fall 1990 Fall 1995 Fall 2000 Fall 2005 Fall 2010 Pre-College Math Enrollment College Math Enrollment FIGURE C-3 Total two-year college enrollment in mathematics and percentage of total enrollment at the pre-college level (Fall 1990–Fall 2010).
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90 COMMUNITY COLLEGES IN THE EVOLVING STEM EDUCATION LANDSCAPE ance of enrollment is at the pre-college level, with a persistent percentage of about 57 percent of all enrollments in mathematics units over the last two decades. Other survey results reveal only modest changes in the distribution of enrollment across the mathematics curriculum since 1990 (not shown in tabular form), with a small but persistent decline in enroll - ment in pre-calculus (college algebra and trigonometry) courses since 1995, a slight drop but also fluctuation in calculus enrollment from 1990 to 2010, and a modest increase in enrollment in statistics courses since 1990 and in other mathematics courses since 1995, including classes for non- mathematics majors (e.g., mathematics for liberal arts and mathematics for elementary school teachers). The CBMS also examined faculty and instruction, which is an impor- tant issue for two-year colleges where part-time faculty are well docu- mented and an important part of the teaching workforce (Townsend and Twombly, 2008). The Fall 2005 survey reveals the extent to which part-time faculty are engaged in mathematics instruction (Lutzer et al., 2007), with the percentage of two-year college mathematics sections taught by part- time faculty being 44 percent. (Although a percentage was not apparent in preliminary results from the Fall 2010 survey, it is clear that part-time faculty numbers remain high in the 2010 CBMS survey.) Part-time faculty members are most evident at the pre-college level, with 56 percent of these sections being taught by part-time faculty, and part-time faculty are least involved in teaching of mainstream calculus and advanced mathematics compared to other courses in the two-year mathematics curriculum, with only 12 percent and 9 percent, respectively. These results suggest students taking the advanced college-level mathematics curriculum are most likely to be taught by a full-time fac - ulty, a finding that seems to recognize the importance of advanced math - ematics curriculum being taught by professionally trained mathematics specialists as well as the need to align standards with disciplinary require- ments that support student progression (transfer) to the university. Not - ing this advantage, there is little evidence to suggest students who take even the most advanced two-year college mathematics courses intend to continue their study of mathematics at the university level as math - ematics or STEM majors. Looking at all the CBMS data for 2005, Lutzer et al. (2007) suggested relatively few two-year college students intend to transfer to the university and major in mathematics at the four-year col- lege level, although community college science and engineering (S&E) students do transfer to the baccalaureate level to pursue S&E and engi - neering technology baccalaureate degrees. Indeed, associates’ degrees in S&E and engineering technology constitute about 11 percent of all associate’s degrees awarded in 2007 (National Science Board, 2010), and presumably most of these students are interested in transferring. Looking
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91 APPENDIX C retrospectively, about 44 percent of S&E graduates attended community colleges (Tsapogas, 2004). The proportion of associate’s degree holders who are racial-ethnic minorities is higher among associate’s degree than bachelor’s degree holders in S&E fields, making these programs a rich ground for recruiting of STEM majors at the baccalaureate level (Handel, 2011). From 1995 to 2007, the number of S&E associate’s degrees earned by racial-ethnic minority students more than doubled from 7,836 to 19,435. The Fall 2005 CBMS survey data report on instructional approaches that provide insights into how two-year mathematics curriculum courses are taught (Lutzer et al., 2007). These data show over three-quarters of on-campus sections of college algebra and trigonometry, two courses core to the mathematics curriculum for many transfer students, are taught using the standard lecture method. The standard lecture method was less evident in pre-college course sections such as arithmetic (64%) and more evident in mainstream and nonmainstream calculus, elementary statis- tics, differential equations and technical mathematics (calculus), ranging from 81 percent to 93 percent. Given that calls for reform of mathematical pedagogy have been made for many years (see, for example, Wubbels and Girgus, 1997, and the authors of two-year college standards-based reform mentioned in the next section), it is perplexing that so little change has occurred in the teaching of such important two-year college mathematics courses. Looking at both instructional and outreach methods in the Fall 2005 and Fall 2010 CBMS surveys (E. Kirkman and R. Blair, personal com- munication, December 4, 2011; Lutzer et al., 2007), results show college placement testing in mathematics is nearly universal in two-year colleges, although the preliminary finding from CBMS 2010 shows a 7 percent drop from 2005 to 2010 that deserves further study. Blair indicated she and her colleagues are still exploring the reason for this drop, but point out that all of the 90 percent of two-year colleges that report diagnostic testing report requiring mathematics placement testing for all incoming students. These results also show an increase in K-12 outreach opportunities and undergraduate research, but a decline in honors sections and special programs to encourage women and minorities to enroll in two-year col- lege mathematics. In terms of the use of distance and online learning, the CBMS 2010 surveys show relatively modest use of online instruction, with most courses showing less than 10 percent of the sections using online learning systems. These results are consistent with previous results from CBMS 2000 and CBMS 2005. Given the dearth of information about student enrollments and out- comes in two-year college mathematics, results of a national study by Horn and Li (2009) on postsecondary awards (credentials) below the baccalaureate level provide some insights into the scope and status of
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96 COMMUNITY COLLEGES IN THE EVOLVING STEM EDUCATION LANDSCAPE mathematics courses have been immensely important to understanding student success (or lack thereof) in mathematics courses and the larger STEM pipeline. Researchers such as Bailey, Jeong, and Cho (2009); Perry et al. (2010); and many others have laid a foundation for understanding complex issues associated with pre-college mathematics. Despite a grow - ing body of research, more rigorous research is needed on pre-college as well as college-level mathematics curriculum at the two-year college level. Research on mathematics teaching and learning at the classroom level is needed to provide a fuller and more nuanced understanding of content-based and pedagogically oriented reforms that may promote mathematics competency and positive student outcomes at the two-year level, including mastery of pre-college competencies, matriculating to and mastering advanced competencies, and advancing to and through the STEM pipeline. An important recommendation that emerged from the AMATYC standards-based reform reports, particularly the 2006 Beyond Crossroads report, is consistent with the wider national and international conversa - tions to emphasize quantitative literacy and quantitative reasoning as an element of or, in some cases, alternative to the normative mathematics course sequence. A leader in the dialogue about quantitative literacy, Steen (2001) argues that enabling students to use mathematics to solve real-world problems that are complex, ambiguous, and incomplete is the most important thing that college mathematics courses can do. She notes that “rarely will high school graduates be faced with problems that pres- ent themselves in the language of algebra” (Steen, 1992, n.p.), but just because students don’t appreciate algebra in its traditional forms does not mean that it is not applicable or useful to them. Steen notes that quantita - tive literacy is rooted in real data that are part of life’s diverse contexts and situations. She believes pedagogy should change to encourage quan - titative thought that can help learners “to understand the meaning of numbers, to see the benefits (and risks) of thinking quantitatively about commonplace issues, and to approach complex problems with confidence in the value of careful reasoning” (Steen, 2001, p. 58). Students who experience quantitative literacy are empowered to think independently, to ask smart questions, and to confront complexities and challenges with confidence, and, as Steen concludes, “these are the skills required to thrive in the modern world” (p. 58). Given the importance of this topic, it is unfortunate that the litera - ture on quantitative literacy and quantitative reasoning is disconnected from literature on contextualized teaching and learning, integrated aca - demic and technical curriculum, and problem-based learning. Referring to this collection of curricular and instructional approaches, Perin (2011) described contextualization as the “practice of systematically connect -
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97 APPENDIX C ing basic skills instruction [in fields of study such as mathematics] to a specific content that is meaningful and useful to students” (p. 3). Her recent review of the literature includes findings of various types of con- textualization employed in postsecondary settings, especially pre-college mathematics courses. Baker, Hope, and Karandjeff (2009) have explored the wide range of definitions that are used for contextualized instruction, and, to their credit, they link practices associated with contextualization to theories of learning and pedagogical strategies. Among the recommen - dations made by Baker et al. is the importance of exploring alternative formats for delivering the normative mathematics curriculum. Whereas rigorous research has not been performed on contextualized math at the two-year college level, an experimental study that examined the effect of training of high school math and career and technical education (CTE) teachers to work cooperatively to make math explicit in CTE classrooms produced statistically significant outcomes, including higher scores on standardized and college placement tests without negatively impacting technical skill attainment (Stone, Alfeld, and Pearson, 2008). This study has not been replicated in the two-year college context, but it would be very helpful to do so. Examples of other innovative mathematics curriculum formats that are being studied include modularization, which involves delivering instruc - tion in manageable segments or “chunks” (Rutschow and Schneider, 2011, p. 25), rather than traditional, semester-long courses. Mostly applied to pre-college mathematics, this strategy of chunking the curriculum could be extended to college-level mathematics. When implemented properly, students can achieve success in shorter time periods than traditional courses, which also motivates them to persist to the next shortened seg - ment. Bailey et al. (2003) evaluated modularization in six NSF Advanced Technological Education (ATE) projects and four centers, and they noted that instructors praised the method for its flexibility and adaptability. The National Center for Academic Transformation Mathematics Empo - rium model, which Twigg (2011) described as a “silver bullet,” combines modularization with technology-supported instruction (G. Reese and C. Kirby, personal communication, October 18, 2011). Another innovation that is being attempted in mathematics, particu- larly pre-college mathematics, involves compression of the curriculum, meaning compressing the amount of time it takes for students to complete mathematics course sequences, and accelerating them toward their next course or completion. Compression often requires scheduling courses more hours a day for shorter amounts of time, and pairing courses that complement one another, including pairing mathematics and science courses or pairing multiple mathematics courses (including pre-college and college level) to create an intensive learning experience. Though
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98 COMMUNITY COLLEGES IN THE EVOLVING STEM EDUCATION LANDSCAPE most of the research on compression and acceleration is focused on the pre-college level curriculum, this strategy may be useful to attempt with college-level mathematics courses (e.g., college algebra and statistics). For example, two forms of acceleration were used by the FastStart Program at the Community College of Denver, wherein FastStart accelerated stu- dents through the mathematics course sequence by allowing students to enroll in a developmental course concurrently with a college-level course. Results from 11 student cohorts who began developmental mathematics at various levels revealed encouraging outcomes on retention and credit accumulation (Bragg, Baker, and Puryear, 2010). Synthesizing the litera - ture on acceleration, Edgecombe (2011) noted evidence of the impact of acceleration on developmental education is limited but promising based on evaluations of FastStart and other similar programs. Change of not only how mathematics is taught but also what is taught is also important for mathematics reformers. One of the most notable efforts in this regard are the Carnegie Foundation for Learning and the Dana Center’s Quantway™ and Statway™ projects (Carnegie Foundation for the Advancement of Teaching, 2011a, 2001b) that are attempting to replace the normative pre-college mathematics courses with mathematics courses focused on quantitative literacy and statistics. Using an acceler- ated timeframe, the Quantway and Statway projects seek to prepare stu- dents for college level mathematics instruction. Quantway and Statway “enable developmental mathematics students in community colleges to complete a[n accelerated] credit-bearing, transferable mathematics course in one academic year while simultaneously building skills for long-term college success” (Cullinane and Treisman, 2010, p. 4). The Statway course sequence assists students to develop statistical literacy and engages them in mathematical reasoning using data, and it provides them with college credit in statistics. Cullinane and Treisman hypothesize that the adoption of a statistics sequence such as Statway will support many more students to engage in mathematical reasoning, especially when the curriculum is institutionalized from K-12 education and extended to the postsecond - ary level. Quantway is similarly focused on increasing the mathematical literacy of students who need to take pre-college mathematics by replac- ing traditional textbook-based, procedural instruction with numerical reasoning that is necessary to solve real-world problems. The Quantway pathway promotes an accelerated format, allowing students who place into elementary algebra to gain access to and move through a college-level quantitative reasoning course in one year. Reform of instructional materials such as those associated with Stat - way and Quantway address a disconcerting problem that Kays (2004), Mesa (2010), and others have noted in the literature: the reliance on textbooks to structure and guide classroom instruction of mathematics.
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99 APPENDIX C These studies demonstrate the ways classroom teaching that relies on procedural-based textbooks reinforce the memorization of procedural knowledge at the expense of quantitative reasoning. Many mathemat - ics texts are also tied to the normative math course sequence, and tra - ditional pedagogies associated with teaching the mainstay courses in that sequence (e.g., algebra, geometry, trigonometry, and calculus) pro - vide a valuable backdrop for a discussion of the critical needs that lay ahead as two-year college mathematics educators delve more deeply into reform. These studies suggest that systemic reforms, including cur- riculum, instruction, and instructional materials, are need to be pursued if mathematics education is to be responsive to the diversity of learners who seek the opportunity to pursue STEM-related programs of study in the two-year college. RECOMMENDATIONS FOR FURTHER RESEARCH, POLICY, AND PRACTICE In spite of strident pursuit of standards-based reform of two-year college mathematics, implementation of reform of the mathematics cur- riculum has been slow and uneven. National studies show more students are enrolling in two-year college mathematics, but a substantial portion of these enrollments are at the pre-college level, and many of these students never reach college-level mathematics. Thus, the STEM pipeline appears to be widening at the start, which is encouraging, but it also seems to nar- row rapidly as students attempt to advance to college-level mathematics, a prerequisite to pursuing STEM programs of study and STEM-related careers. To facilitate the role that two-year mathematics can play in providing access to the STEM pipeline and preparing larger numbers of postsecond- ary students, mathematics instruction needs to be sufficiently engaging and useful to support their interests and to assist them to make the com- mitment necessary to pursue a STEM program of study. A whole host of issues need to be addressed with respect to two-year college mathematics and the preparation of students who seek subbaccalaureate credentials and who desire to transfer to universities in STEM fields. Specific rec - ommendations for research, policy, and practice to support this goal are described below. A systemic, P-20 approach is needed to reform mathematics cur- riculum. Recommendations offered by a plethora of professional groups, including AMATYC and the Mathematics Association of American (MAA), and at different levels of the educational system are logical, rea- sonable, and substantive, and equally importantly, they consistently argue
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100 COMMUNITY COLLEGES IN THE EVOLVING STEM EDUCATION LANDSCAPE for a multi-level yet coordinated P-20 approach. Without such a strategic, collaborative endeavor, it will be difficult for two-year colleges that are caught between K-12 education and higher education to engage in reform, except in isolated ways. Given the national imperative to enhance the STEM pipeline, and the critical role that mathematics needs to play in that work, this recommendation may be the most important of all to emerge from the Summit on Realizing the Potential of Community Colleges as Pathways to STEM Education and Careers. More research is needed to improve two-year college mathemat- ics instruction. Although numerous pedagogical strategies are emerging that offer promise to change the way mathematics is taught at the two- year college level, CBMS survey data confirm the prevalence of lecture- led, teacher-centered instruction rather than the sorts of contextualized, problem- and project-based approaches that support quantitative literacy. Finding ways to support two-year college faculty to engage in profes- sional development that reinforces innovative instructional reforms is important. Included in this list is the importance of helping faculty to adopt curriculum and instruction that draws upon students’ everyday life experiences in the workforce, their communities, and other aspects of their lives. Mathematics instructors also need to understand how to integrate technologies to deliver instruction in the classroom or from a distance. Moreover, mathematics instructors need to understand how col- lege placement tests can either impede or advance students through the mathematics curriculum. Involving faculty in decisions about assessment may help them to understand how college placement testing impacts stu - dent learning and ultimately, improves student outcomes. More research is needed on the students who enroll in two-year col- lege mathematics, especially college-level mathematics (college algebra and beyond), and how their experiences and performance in college-level mathematics courses influences subsequent enrollment, completion, and career decisions. Because two-year colleges are the gateway to postsecond- ary education for diverse learners, these schools have an important role to creating pathways that prepare students to advance to higher levels of postsecondary education. More research is needed to support the study of mathematics pathways, other than the normative mathematics sequence, and to understand how students “develop the ‘habits of the mathematical mind’ that are required to be successful in mathematics and science and engineering and technology courses” (R. Blair, personal communication, December 8, 2011). Students need to know what these new mathematical pathways look like and how they lead to STEM careers, and they can- not be expected to understand or navigate them on their own, without encouragement and support. Systemic change is needed to ensure that all students who have aspirations for STEM careers get the chance to learn
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101 APPENDIX C mathematics in ways that fully and respectfully support their goals. If the nation expects more women and minorities to participate in STEM programs of study, fulfilling this recommendation is essential. More and better data are needed to support practitioner engagement in active research on mathematics education at the local level, where two-year college mathematics faculty and other stakeholders engage in the teaching and learning process. Beyond participating in training, many two-year faculty would appreciate and benefit from opportunities to engage in active research that encourages them to try out new pedagogi- cal strategies in the classroom and determine how they impact student learning. The Equity Scorecard™ and Benchmarking projects of the Center for Urban Education at the University of Southern California provide valuable examples of ways that professional development of two-year college faculty can be integrated with action research to address equity issues for minority students who seek to participate in STEM programs (Baldwin et al., 2011). The Achieving the Dream initiative has established a strong track record of engaging practitioners in using data to improve pre-college mathematics (Rutschow et al., 2011). Lessons learned from this initiative and other newer ones, such as Pathways to Results in Illinois (Bragg and Bennett, 2011), offer the potential to improve two-year college mathematics and support student success in STEM programs of study. SUPPLEMENTAL INFORMATION Methods This paper relies on existing literature available from a number of sources. Most importantly, academic databases were queried to identify peer-refereed articles as well as books, monographs, reports, papers, and conference presentations on two-year college mathematics. Databases included in this review were ERIC, EBSCO, Education Full-Text, JSTOR, Dissertation Abstracts, and Sociological Abstracts. In addition, Google and Google Scholar were queried to identify relevant documents and materi - als that appear outside of the traditional scholarly databases. Searches of websites maintained by organizations known to research and publish on the topic of two-year college mathematics were conducted, including the National Center for Education Statistics, the National Science Foundation, the Community College Research Center at Teachers College, and Charles A. Dana Center at the University of Texas at Austin, the AMATYC web- site, and others. Keywords used in these searches included the following words singularly and in combination with one another: math, mathemat - ics, mathematics education, developmental, remedial, pre-college, alge - bra, calculus, advanced mathematics, statistics, etc.
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102 COMMUNITY COLLEGES IN THE EVOLVING STEM EDUCATION LANDSCAPE Keywords used to understand how the scholarly literature situates two-year mathematics curriculum in the broader liberal arts and sciences context included the following: liberal arts and sciences, liberal arts, sci - ence, STEM, STEM education, technology, technology education, engi- neering, engineering education, technician education, etc. Also, to ensure that the full spectrum of literature on two-year colleges was included in this literature review, I used an extensive set of keywords to capture the institutional context, including the following: two-year college, commu - nity college, technical college, and junior college. I also entered keywords related to four-year college and university, transfer, and articulation to determine whether literature was available to compare the two-year con - text to the four-year context, including transfer. In addition to the above methods, I reached out to several two-year college mathematics experts, including David Lutzer, Ellen Kirkman, and Rikki Blair, all authors of the Fall 2005 and/or Fall 2010 CBMS surveys. Rikki Blair also served as editor of the 2006 Beyond Crossroads report of AMATYC and was an especially thoughtful and gracious con - tributor. I also sought guidance from several two-year college mathemat - ics practitioners and colleagues at the University of Illinois, including George Reese, director of the Office of Mathematics, Science and Tech- nology Education, and Catherine Kirby, assistant director of the Office of Community College Research and Leadership, who collaborated recently on a literature review on this same topic and brought numerous sources on two-year college mathematics to my attention. Finally, I offer my grati- tude to Dr. Julia Makala, research specialist at the Office of Community College Research and Leadership, who offered a critical review that was invaluable to the final draft of this paper. REFERENCES Adelman, C. (2004). Principal indicators of student academic histories in postsecondary educa - tion, 1972-2000. Washington, DC: U.S. Department of Education, Institute of Educa - tion Sciences. Available: http://www2.ed.gov/rschstat/research/pubs/prinindicat/ prinindicat.pdf [June 25, 2012]. Albers, D.J., Loftsgaarden, D., Rung, D., and Watkins, A. (1992). Statistical abstracts of under- graduate programs in the mathematical sciences and computer science in the United States, 1990-1991 CBMS Survey. (MAA Notes Number 23). Washington, DC: Mathematical Association of America. American Mathematics Association for Two-Year Colleges. (n.d.). The right stuff: Appropriate mathematics for all students. Memphis, TN: Author. Available: http://www.therightstuff. amatyc.org/ [June 25, 2012]. Arbona, C., and Nora, A. (2009). The influence of academic and environmental factors on Hispanic college degree attainment. The Review of Higher Education, 30(3), 247-269. Arnold, R. (2010). Contextualization toolkit: A tool for helping low-skilled adults gain postsecondary certificates and degrees. Boston, MA: Jobs for the Future. Available: http://www.jff.org/ sites/default/files/BT_toolkit_June7.pdf [June 25, 2012].
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