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Increasing Student Success in Developmental Mathematics: Proceedings of a Workshop (2019)

Chapter: 2 The Current Landscape of Developmental Mathematics Education

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Suggested Citation:"2 The Current Landscape of Developmental Mathematics Education." National Academies of Sciences, Engineering, and Medicine. 2019. Increasing Student Success in Developmental Mathematics: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/25547.
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Suggested Citation:"2 The Current Landscape of Developmental Mathematics Education." National Academies of Sciences, Engineering, and Medicine. 2019. Increasing Student Success in Developmental Mathematics: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/25547.
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Suggested Citation:"2 The Current Landscape of Developmental Mathematics Education." National Academies of Sciences, Engineering, and Medicine. 2019. Increasing Student Success in Developmental Mathematics: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/25547.
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Suggested Citation:"2 The Current Landscape of Developmental Mathematics Education." National Academies of Sciences, Engineering, and Medicine. 2019. Increasing Student Success in Developmental Mathematics: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/25547.
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Suggested Citation:"2 The Current Landscape of Developmental Mathematics Education." National Academies of Sciences, Engineering, and Medicine. 2019. Increasing Student Success in Developmental Mathematics: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/25547.
×
Page 11
Suggested Citation:"2 The Current Landscape of Developmental Mathematics Education." National Academies of Sciences, Engineering, and Medicine. 2019. Increasing Student Success in Developmental Mathematics: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/25547.
×
Page 12
Suggested Citation:"2 The Current Landscape of Developmental Mathematics Education." National Academies of Sciences, Engineering, and Medicine. 2019. Increasing Student Success in Developmental Mathematics: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/25547.
×
Page 13
Suggested Citation:"2 The Current Landscape of Developmental Mathematics Education." National Academies of Sciences, Engineering, and Medicine. 2019. Increasing Student Success in Developmental Mathematics: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/25547.
×
Page 14
Suggested Citation:"2 The Current Landscape of Developmental Mathematics Education." National Academies of Sciences, Engineering, and Medicine. 2019. Increasing Student Success in Developmental Mathematics: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/25547.
×
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Suggested Citation:"2 The Current Landscape of Developmental Mathematics Education." National Academies of Sciences, Engineering, and Medicine. 2019. Increasing Student Success in Developmental Mathematics: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/25547.
×
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Suggested Citation:"2 The Current Landscape of Developmental Mathematics Education." National Academies of Sciences, Engineering, and Medicine. 2019. Increasing Student Success in Developmental Mathematics: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/25547.
×
Page 17
Suggested Citation:"2 The Current Landscape of Developmental Mathematics Education." National Academies of Sciences, Engineering, and Medicine. 2019. Increasing Student Success in Developmental Mathematics: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/25547.
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PREPUBLICATION COPY: UNCORRECTED PROOFS 2 The Current Landscape of Developmental Mathematics Education Rapid change is occurring in the developmental mathematics education reform space, as institutional leaders, faculty members, researchers, and policy makers work to create learning environments that enable more students to be successful in mathematics (U.S. Department of Education, 2017). During the second and third sessions of the workshop, participants exchanged insights on the current research on and implementation of developmental mathematics education reforms that could help institutions determine what data, support, and infrastructure they need to best meet the needs of their students, especially those from underrepresented populations. Additionally, the current strategies for creating equitable opportunities for all students were discussed. STRATEGIES TO IMPROVE DEVELOPMENTAL MATHEMATICS EDUCATION Elizabeth Zachry Rutschow, a senior research associate at MDRC, who has led numerous research projects on developmental education, provided an overview of “Developmental Mathematics Reforms,” 7 a paper commissioned by the workshop planning committee on the range of developmental mathematics reforms being implemented and evaluated at 2- and 4-year institutions across the United States. She highlighted the most common reform models and discussed the students they target, their relative scale, and current research documenting their positive or negative effects on student outcomes. Zachry Rutschow opened her presentation by describing developmental education as coursework that students complete to build their skills prior to enrolling in college-level courses. Typically, these semester-long and often multi-course sequences are offered in mathematics, English, and reading; they are generally non-credit bearing and nontransferable (i.e., they do not count toward a college degree); and they are a costly undertaking for students, who, on average, take two to three successive courses. Approximately 59 percent of students from 2-year institutions and 33 percent of students from 4-year institutions take developmental mathematics courses. Yet, no common standards exist across institutions for how these courses should be taught, structured, or sequenced, and there are varying philosophies as to how students should be evaluated for appropriate course placement. In addition to the above information, Zachry Rutschow shared recent research that revealed that less than 58 percent of students who start developmental mathematics sequences finish them, and only 20 percent of those students successfully complete a college-level mathematics course. Low-income students and students from underrepresented groups are overrepresented in developmental education, and a significant number of students have been incorrectly placed in developmental courses (i.e., students who might have been successful in college- level courses are actually being placed in developmental education courses). To this end, she continued, policy makers, practitioners, and researchers have been motivated to consider new approaches to developmental education in order to improve student success. Of the new approaches, Zachry Rutschow described five sets of reforms that are currently being offered to students in developmental mathematics education: assessment and placement, structure and sequence, instruction and content, student support, and comprehensive (see Box 2-1). Some overlap exists among these reform categories, some reforms are implemented together, and similar reforms are being implemented in English and reading curricula to serve students in need of multiple developmental 7 To read Zachry Rutschow’s commissioned paper, see http://sites.nationalacademies.org/cs/groups/dbassesite/documents/webpage/dbasse_191791.pdf. 7

PREPUBLICATION COPY: UNCORRECTED PROOFS education courses. To examine the impact of these reforms on student outcomes, Zachry Rutschow synthesized data from descriptive, quasi-experimental (QE), and randomized control trial (RCT) studies. 8 BOX 2-1 Developmental Mathematics Education Reform At-A-Glance Assessment and Placement Reforms • Diagnostic assessment • Early assessment • Multiple measures assessment Structure and Sequence Reforms • Intensive non-course-based alternatives • Compression models • Co-requisite models Instruction and Content Reforms • High-quality instruction • Cohort models and learning communities • Self-paced instruction • Multiple mathematics pathways Student Support Reforms • Success courses • Supplemental instruction • Tutoring Comprehensive Reforms • Guided pathways • Wrap-around support models SOURCE: Adapted from Zachry Rutschow (2019). Assessment and Placement Reforms Given that students are often incorrectly placed into developmental courses and often fail to progress to credit-bearing courses, Zachry Rutschow shared that various types of assessment and placement reforms are being implemented to mitigate these outcomes. One reform approach to the assessment and placement process is the use of diagnostic assessments (e.g., the ALEKS or ASSET exams) to identify student-specific strengths and weaknesses and to place students appropriately in modular or self-paced courses to strengthen particular skills. According to the research reviewed by Zachry Rutschow, the target group for diagnostic assessments varies. While all students could benefit from this approach, she explained that it may prove particularly useful for students with high scores on general placement exams and students in need of support across multiple disciplines. QE studies indicated that diagnostic assessments placed students more accurately than computer adaptive tests, but little research exists on the impacts of diagnostic assessments on students’ overall academic progress. Because 8 Descriptive studies offer simple comparisons without controls for preexisting differences; QE studies rely on statistical methods to control for some preexisting differences but cannot account for all preexisting differences (e.g., student motivation); and RCT studies give a random assignment to treatment and control groups. RCT studies are typically the most rigorous of the three because causality can be attributed to intervention. 8

PREPUBLICATION COPY: UNCORRECTED PROOFS diagnostic assessments are often grouped with other assessments used to evaluate students’ levels of college readiness, Zachry Rutschow explained that it can be difficult to discern the exact scale at which diagnostic assessments are being implemented. Despite this, she continued, it is known that academic institutions in Florida, Kentucky, North Carolina, North Dakota, Texas, and Virginia currently use diagnostic assessments. Another type of assessment and placement reform is early assessment, which is targeted to high school students who may not be ready for college—for example, students who score below a 19 on the ACT. These students then have the opportunity to develop needed skills during their junior and senior years of high school, typically through an online tutorial course or in a more traditional classroom. As of 2017, this reform was being implemented at the programmatic level in high schools in 39 states (e.g., the Tennessee Seamless Alignment and Integrated Learning Support [SAILS] program 9 and the California Early Assessment Program10), according to Zachry Rutschow. Descriptive studies in Arkansas and Mississippi found that early assessment increased students’ skills and the likelihood of placement into college-level mathematics courses, but QE studies in California, Florida, and Tennessee suggested that this intervention might not lead to completion of higher college-level mathematics courses, Zachry Rutschow explained. As evidenced in Zachry Rutschow’s examination of the research, traditional standardized tests have not been shown to be good indicators of college readiness or success. Multiple measures assessment is a third type of assessment and placement reform that evaluates college readiness by bringing in additional measures of students’ skills to consider alongside standardized test results. Often these include a student’s high school performance—for example, grade point average, highest level of a course taken, number of courses taken per subject area, and, in some cases, non-cognitive indicators, such as a student’s motivation, academic commitment, and/or awareness of his/her own skills. Zachry Rutschow’s synthesis illustrated that multiple measures assessments could be valuable for all students entering postsecondary institutions but could be particularly useful for recent high school graduates, students who earn high scores on standardized tests, and adult learners. A total of 19 states permit and promote the use of multiple measures assessments for incoming students. 11 A national survey in 2016 12 indicated that multiple measures assessments were used in 57 percent of public 2-year institutions across the United States. Zachry Rutschow shared early results from an RCT study conducted at the State University of New York by the Center for the Analysis of Postsecondary Readiness, which showed that students are more likely to be placed into and complete a college-level mathematics course as a result of the multiple measures assessment reform. Additionally, she shared that a QE study in Florida—a state in which using students’ high school grades to evaluate college readiness is mandatory—showed that students with higher levels of high school preparation succeeded more often in college-level courses, which, she stated, could make a compelling case for offering the multiple measures assessment. Structure and Sequence Reforms Zachry Rutschow asserted that students often have to take too many developmental courses for too long, which creates too many opportunities for students to drop out before completion. Instead, she continued, boot camps and other non-course-based options (e.g., summer bridge programs) could be useful to build students’ skills through brief, intensive instruction offered outside of the traditional 9 For more information about the Tennessee SAILS program, see https://www.tn.gov/thec/bureaus/academic-affairs-and-student-success/academic-programs/sails.html and Chapter 3 of this proceedings. 10 For more information about the California Early Assessment Program, see https://www.cde.ca.gov/ci/gs/hs/eapindex.asp. 11 See Chapter 3 of this proceedings to learn more about a case study on the successful use of multiple measures assessments in California. 12 Center for the Analysis of Postsecondary Readiness Institutional Survey (2016), for more information on this survey, see Zachry Rutschow and Mayer, 2018. 9

PREPUBLICATION COPY: UNCORRECTED PROOFS semester sequence, with the goal of placing students directly into a college-level mathematics course upon completion. Boot camps and non-course-based options are primarily targeted toward students who have already been evaluated as needing developmental education. These reforms are being fully implemented in Colorado, Connecticut, Kentucky, Mississippi, and Texas, though many individual institutions in other states are also offering similar alternatives for students. Zachry Rutschow shared the results of a 2012 RCT study of summer bridge programs in eight Texas community colleges, which indicated positive short-term effects on students’ enrollment in and completion of college-level courses but fewer positive effects on long-term success throughout college. Additionally, she noted that a 2010 QE study of a 5-week summer bridge program at a 4-year institution suggested more promising long-term positive effects on students’ graduation rates. The compression of developmental course material into shorter time periods (e.g., offering two developmental education courses to be completed in one semester, instead of two) is another type of structure and sequence reform highlighted by Zachry Rutschow. She noted that the target student group for this reform varies, but that 51 percent of public 2-year institutions were offering this option as of 2016 (e.g., Community College of Denver FastStart Program 13), and three states embedded this option as part of their policies and practices for community colleges. Descriptive studies demonstrated that compressed courses lead to an increase in successful completion of developmental education courses, and a QE study on the Community College of Denver’s program demonstrated an increase in the likelihood of students completing a college-level mathematics course within 3 years as compared to their peers, who were not placed in compressed courses. The co-requisite model, Zachry Rutschow explained, is another innovative approach to reforming course structure. In this case, students are placed directly into college-level courses that are paired with support(s) (e.g., tutoring, combining a developmental course with a college-level course, and/or stretching one course over two semesters to allow students to complete the course at a slower pace). Although this reform was originally targeted to students with mathematics skills just below the respective placement test cutoff score, it is expanding to include students at all levels of developmental mathematics, Zachry Rutschow explained. This increasingly popular reform is either mandated or recommended for 2-year institutions in at least 15 states. An RCT study at the City University of New York (CUNY) indicated higher pass rates in college-level mathematics courses and higher rates of accumulation of college credits as a result of students’ enrollment in the co-requisite model. Zachry Rutschow asserted that the co- requisite model seems to be the most encouraging reform of course structure and sequence undertaken to move students more quickly and successfully through developmental coursework and college-level coursework (see Chapter 4 for a deeper look into the at the co-requisite model). Instruction and Content Reforms Zachry Rutschow commented that mathematics course content is often misaligned with students’ college and career goals, and traditional modes of instruction in mathematics have not led to conceptual understanding for students. A broad reform to address this problem, she explained, has been the use of high-quality instructional practices that are intended to build all students’ conceptual knowledge through active learning, contextualized problem solving, and student-led solution methods. This approach, she continued, is recommended by a number of national mathematics and higher education organizations, owing in part to promising research results. For example, a descriptive study demonstrated that students were more likely to earn higher scores in mathematics and to describe the instruction as “useful” when faculty employed contextualized instructional models, which focus on deep conceptual learning that is contextualized within real-life situations and afford better understanding of how mathematics can be 13 For more information about the Community College of Denver’s FastStart program, see https://files.eric.ed.gov/fulltext/ED521421.pdf. 10

PREPUBLICATION COPY: UNCORRECTED PROOFS applied in practical life. Zachry Rutschow’s review of the research revealed a recent QE study of the Integrated Basic Education and Skills Training (IBEST) program in Washington and other similar programs, which showed that both college credit and professional certificate accumulations increased for students who had received high-quality instruction; a recent RCT study of programs similar to IBEST revealed positive effects on both students’ academic outcomes and their labor market outcomes. The implementation of cohort-based design instruction (i.e., learning communities) was an early instructional reform effort that typically paired two courses (e.g., two developmental-level courses or one developmental mathematics course with a college-level course). In more intensive versions of the approach, instructors would collaborate across the two courses to ensure an overlap in content. This intervention is targeted to all students and promotes students’ social cohesion and abilities to make connections across academic disciplines. Descriptive and QE studies have shown connections between learning communities and high levels of student engagement and student persistence. Zachry Rutschow synthesized RCT results from studies at Queensborough Community College and Houston Community College, which indicated that students in learning communities succeeded in developmental mathematics courses at higher rates than their peers; however, these studies have shown moderate effects on the accumulation of mathematics and total academic credits and no positive effect on student persistence. Although learning communities were most popular in 2000, Zachry Rutschow explained that these interventions are not implemented as often as some of the others, given how challenging they are to execute successfully and given the model’s limited long-term positive effects. As a result, she continued, there has been a decrease in the number of research studies conducted on this particular intervention. Self-paced instruction is a type of reform in which course content is separated into short skill- building modules and is often paired with diagnostic assessments. Students typically work independently with an online tutorial or in a computer laboratory with a facilitator. Zachry Rutschow remarked that this reform is targeted to all students and as of 2016 was offered by 40 percent of public 2-year institutions across the United States. This reform has been mandated in Virginia and North Carolina and is now endorsed in Florida, Idaho, and West Virginia. The original intent of this model was to accelerate students’ progress through developmental mathematics, given that they only had to complete corresponding modules to strengthen specific skills and could bypass other aspects of the course. However, studies indicate that technology-based instruction can be difficult for both students and educators. Descriptive studies in North Carolina, Tennessee, and Virginia; a QE study in Tennessee; and an RCT study in Texas all showed that students actually tended to slow their pace when taking modular courses. Zachry Rutschow surmised that this reform might not be the most effective strategy to accelerate students through developmental mathematics. Owing to an increase in the number of careers that require statistical and quantitative literacy, the multiple mathematics pathways model has emerged as another type of reform in response to the traditional “algebra-for-all” approach to mathematics education, Zachry Rutschow commented. The multiple mathematics pathways approach aligns mathematics course content directly with students’ intended majors and careers (e.g., quantitative literacy for humanities majors, statistics for social and health sciences majors, and calculus for STEM majors), often integrates high-quality instruction, and accelerates students’ progress through developmental mathematics. Although this reform was originally targeted toward students with higher-level mathematics skills, it is expanding to target students placed in multiple levels of developmental mathematics. According to Zachry Rutschow, 41 percent of public 2- year institutions offer multiple mathematics pathways—Carnegie’s Statway and Quantway programs 14 and the Dana Center Mathematics Pathways (DCMP) 15 are examples of successful programs of this set of reforms, and many states (e.g., California, Indiana, Massachusetts, Michigan, and Texas) have adopted these pathways as part of their policies. Zachry Rutschow described an RCT study of multiple 14 For more information about Carnegie’s Statway and Quantway programs, see https://carnegiemathpathways.org and Chapter 4 of this proceedings. 15 For more information about the DCMP program, see https://www.utdanacenter.org/our-work/higher- education/dana-center-mathematics-pathways and Chapters 3 and 4 of this proceedings. 11

PREPUBLICATION COPY: UNCORRECTED PROOFS mathematics pathways at CUNY that indicated highly promising results around the completion of college-level mathematics courses as well as the accumulation of credits. Student Support Reforms Zachary Rutschow shared that many students with developmental course needs often have limited knowledge of experiences and expectations at the postsecondary level, and described the additional supports that have been implemented to help these students navigate the system of higher education, build skills, and develop an attachment to college in general. One way, she described, is through success courses (i.e., study skills courses or student orientation courses), and according to a 2009 survey of 1,000 institutions, success courses were offered at 87 percent of 2- and 4-year institutions as either stand-alone courses or in combination with a developmental course. Success courses, she continued, are targeted toward students with multiple developmental education needs, and they have the potential to improve students’ psychosocial skills, to increase students’ familiarity with their institutions, and to improve students’ study skills. Additionally, students can often earn either developmental or college-level course credit upon completion of a success course. A number of studies suggest that success courses lead to positive short-term effects on student persistence, credit accumulation, and grade achievement; however, longer-term studies suggest that these impacts are not sustained over time, she explained. Zachry Rutschow shared that another way to increase support for developmental education students is by providing tutoring and supplemental instruction (i.e., a peer or instructor is paired with a class and facilitates a separate support section). Tutoring and supplemental instruction initiatives are targeted toward all students, and many postsecondary institutions have established tutoring centers. Additionally, Alaska, California, Colorado, Kentucky, Ohio, and West Virginia all currently encourage supplemental instruction to enhance the success of developmental education students. An RCT study showed that tutoring could achieve modest effects on credit accumulation and persistence for students when paired with other supports. Zachry Rutschow’s synthesis also highlighted descriptive studies of supplemental instruction, which indicated increased positive results for students, including higher grades and grade point averages, lower course withdrawal rates, and higher persistence rates. Intensive advising—more regular interactions with advisors through multiple modes of communication (e.g., in-person meetings, email, phone, text messaging)—is a third way for all students to be better supported and informed about important academic deadlines and milestones, Zachry Rutschow explained. To facilitate this high and frequent level of engagement with their students, advisors who participate in intensive advising programs often have reduced advising caseloads. Although intensive advising models can be difficult to scale, the use of technology to facilitate communication between students and their advisors is encouraging, according to Zachry Rutschow’s review of the literature. Intensive advising over multiple semesters has been shown in an RCT study to increase student persistence. However, she commented that, in general, when student support reform models have been implemented on their own, they have not shown as many positive effects on academic progress as other reform models or as when used in combination with other reform initiatives. Comprehensive Reforms Zachry Rutschow asserted that individual, short-term interventions show fewer positive effects on student success than more comprehensive, long-term interventions. Thus many academic institutions are taking a more holistic approach to reform that integrates a combination of the previously described strategies in the form of guided pathways or wrap-around support models. Unlike the multiple mathematics pathways programs, which focus on course content by aligning mathematics coursework with a student’s major or career interest, the guided pathways model emphasizes comprehensive student support by mapping courses for completion, providing strong advising and student supports, offering accelerated developmental courses, delivering early alerts and interventions, and striving for coherent learning outcomes. Targeted to all students, at least 250 postsecondary institutions in 10 states currently 12

PREPUBLICATION COPY: UNCORRECTED PROOFS have guided pathways programs. Zachry Rutschow’s research highlighted the findings of descriptive studies of guided pathways, which indicated that students accumulate more credits faster during their first year in college and have better completion rates in college mathematics and English than students who attended college before the implementation of guided pathways. However, these studies, she continued also specified small decreases in both student persistence rates and overall pass rates in college courses. The CUNY Accelerated Study in Associate Programs (ASAP) program16 and the CUNY Start program, 17 Zachry Rutschow explained, are examples of comprehensive reforms that provide wrap- around support. CUNY ASAP, she continued, supports full-time students with one or two developmental needs by providing intensive advising, paired courses, a study skills course, and tuition waivers, while CUNY Start focuses on providing comprehensive support to students with low skill levels and three developmental needs. Additionally, Zachry Rutschow shared that students can enroll in the CUNY Start program full or part time, at a negligible cost, and they receive instruction in reading, writing, and mathematics via a cohort model prior to matriculation in college. Zachry Rutschow noted that these two programs are just beginning to scale and thus are not yet as widespread as guided pathways programs. Nevertheless, preliminary findings from an RCT study of the CUNY Start program suggest that CUNY Start students are both progressing through developmental courses and enrolling at higher rates after completing the program. Studies of CUNY ASAP have revealed impressive positive results, she explained, with improved student outcomes, increased credit accumulation, and a near-doubling of the rate of students graduating with an associate’s degree within 3 years. DISCUSSION In response to a question from Julie Phelps, professor of mathematics at Valencia College, about research on individual reforms, Zachry Rutschow suggested that intensive (i.e., reforms that change instruction or the sequencing of courses) and comprehensive reforms seem to hold the most potential for improving students’ overall academic success. Reflecting back on the data presented by Zachry Rutschow which showed that low-income students and students from underrepresented groups are overrepresented in developmental mathematics, Aditya Adiredja, assistant professor of mathematics at the University of Arizona, wondered what the data would show if one controlled for race and socioeconomic background in experiments that measure the effectiveness of reforms? Would the recommendations about the most promising approaches remain the same? Zachry Rutschow replied that some of the studies do include subgroup analyses and most disaggregate to evaluate the effects of reforms on closing the achievement gap, and the results have been encouraging. Rebecca Fitch, former project manager for the Civil Rights Data Collection at the U.S. Department of Education, asked if there are any efforts under way to make schools and communities that feed into local 2-year institutions more aware of what students need to do and know to be prepared for college-level mathematics. Zachry Rutschow noted that some states have attempted alignment across K–12 and postsecondary institutions, especially through early assessment programs. EDUCATIONAL EQUITY AND DEVELOPMENTAL MATHEMATICS REFORM While the most common reforms in developmental education—assessment and placement, structure and sequence, instruction and content, student support, and comprehensive reforms that embrace 16 For more information about CUNY ASAP, see http://www1.cuny.edu/sites/asap and Chapter 5 of this proceedings. 17 For more information about the CUNY Start program, see http://www1.cuny.edu/sites/cunystart and the latter part of Chapter 4 of this proceedings. 13

PREPUBLICATION COPY: UNCORRECTED PROOFS one or more of these strategies—have proven successful in some instances, Zachry Rutschow revealed that these reforms are not reaching all students, and even in cases in which the data suggest that the reform approach is successful, some students are still not well served (Zachry Rutschow, 2019). The workshop’s panel on educational equity and mathematics reform brought together both educators and leaders from national education initiatives to discuss current inequities in the developmental mathematics landscape as well as strategies to better serve students from underrepresented populations in this era of reform. Before sharing their perspectives on student equity issues in developmental mathematics education, panelists provided brief overviews of their professional experiences and research interests. Panel moderator James Dorsey, a self-professed “child who could not do math,” is the president and chief executive officer of the College Success Foundation, 18 a national education reform program that helps students enroll in and complete college. Previously, Dorsey was an executive director and president of Mathematics, Engineering, Science Achievement (MESA) 19—an almost 50-year-old program started in California that builds pathways to degrees and careers in science, technology, engineering, and mathematics (STEM) for students from backgrounds that are historically underrepresented in mathematics-based fields. This program specifically supports students through success courses, intensive advising, supplemental instruction, and leadership preparation. This successful program has been replicated in several other states, including Florida, Georgia, New York, Texas, and Washington. Panelist Aditya Adiredja, an assistant professor of mathematics at the University of Arizona, focuses his research specifically on equity issues in undergraduate mathematics education. As an alumnus of the Professional Development Program at the University of California, Berkeley, he has a particular interest in “how reform efforts serve black and brown students” and how deficit narratives negatively impact classroom interactions—for instance, faculty might treat students in developmental mathematics as though they cannot do mathematics compared to students in calculus, thereby negatively influencing how the mathematical work of students in developmental mathematics is perceived and creating different opportunities for different groups of students. As the senior project director of the Opportunity Institute,20 panelist Pamela Burdman reconceptualizes the role of mathematics in education equity with the purpose of informing policy through a project called Just Equations. 21 Similar to Adiredja, Burdman studies the narratives that are told and the assumptions that are made about education that undermine equity and justice. She endorsed the definition of mathematics equity as “the inability to predict mathematics achievement and participation based solely on student characteristics such as race, class, ethnicity, sex, beliefs, and proficiency in the dominant language” (Gutierrez, 2007) and noted that the education system in the United States is far from achieving equity (Burdman, 2018). The architecture of mathematics is built on misconceptions about mathematics learning—in other words, who can and cannot learn mathematics and the notion that mathematics is about speed and right or wrong answers. This architecture is also framed by existing educational inequities—mathematics as a gatekeeper, differential access to high quality curriculum and instruction, and teacher biases—which result in negative psychological effects on students, she explained. As a result, women, low-income students, adult learners, and students of color, in particular, are having negative experiences in mathematics. Burdman declared that “this is not fair to students...but it is also really not fair to math,” which as a discipline suffers without the inclusion of these groups of students. “It is not the purpose of math to make students’ lives difficult, to make them anxious, or to hate math,” she asserted. Instead of serving as a means to categorize or discourage students, mathematics could “expand professional opportunities, [be used to] understand and critique the world, and [elicit] wonder, joy, and beauty” (National Council of Teachers of Mathematics, 2019). She emphasized that redesigning the 18 For more information about the College Success Foundation, see https://www.collegesuccessfoundation.org/. 19 For more information about the MESA program, see https://mesausa.org. 20 For more information about the Opportunity Institute, see https://theopportunityinstitute.org. 21 For more information about the Just Equations project, see justequations.org. 14

PREPUBLICATION COPY: UNCORRECTED PROOFS architecture of mathematics to create equitable opportunities requires working across multiple dimensions: content, instruction, assessment, and readiness policies and practices. Panelist Maxine Roberts is the assistant director of knowledge management for Strong Start to Finish, 22 an initiative of the Education Commission of the States. Strong Start to Finish focuses on developmental education reform with the goals of (1) increasing the number and proportion of students who are placed into and complete gateway mathematics and English within their first year of college and (2) aligning this with a program of study. Strong Start to Finish is also interested in supporting students of color, low-income students, and adult learners. This is achieved in three ways: (1) engaging with systems that are scaling developmental education reforms, (2) supporting a network of institutions that are advancing developmental education in key areas, and (3) deepening knowledge about how reforms are enacted. Roberts is particularly interested in unpacking the reforms to determine whether there are missing elements that, when added, could substantially improve the student experience. Specifically, in her work, she considers the classroom experiences that African American and Latino students have in developmental education and how this relates to their academic progress. Additionally, she considers how faculty and peer engagement influence the development of students’ mathematics identities (i.e., How do they view themselves as mathematics learners and doers?). Roberts explained that “so many times, it is easy to say, well, gosh, these students are not ready, and that is the deficit perspective.” Panelist Joanna Sánchez is a program manager at Excelencia in Education,23 a nonprofit organization in Washington, DC, whose mission is to accelerate Latino student success in higher education through data, practice, and leadership. Excelencia in Education highlights programs across the United States that have successfully supported Latino students in higher education through its annual “Examples of Excelencia” 24 awards and provides an evidence base of best practices for mathematics education in its “Growing What Works” database. 25 Drawing on her personal experience as a student from the Texas border, she observed that students who are successful in mathematics tend to have access to opportunities that others may not have, which reinforces the need for reforms that eliminate inequitable trajectories for students. Moving into the moderated question-and-answer portion of the panel, Dorsey asked the panelists to discuss the dominant narrative of success in developmental mathematics reform—which is centered on achievement gap, quantitative data, and race/ethnicity—and to consider how this dominant narrative affects student outcomes. Burdman claimed that the student experience is missing from the dominant narrative. Although quantitative data help to gauge progress, they do not necessarily indicate why and for whom a program is successful. Adiredja suggested taking a few steps back and first evaluating the dominant methods that are used to investigate this issue. He made a distinction between controlling for race and disaggregating data by race in the research, the latter of which he says leads to the idea of closing the achievement gap. Such discussions, he continued, can then lead to implicit deficit positioning of non-white students to “catch up” to the dominant students (i.e., white and Asian students and certain East Asian students, in particular). Adiredja explained that controlling for race instead would allow the focus to shift, prompting the study of particular groups of students on their own and a better understanding of the kinds of reforms that could help these specific students succeed. Although successful mathematics course completion and subsequent degree completion are important desired outcomes of reform efforts, Dorsey asked panelists to share other ideal reform outcomes that would be relevant to the development of students’ identities and career pathways. Roberts hoped that reform efforts could prompt more developmental mathematics students to enroll in STEM- related courses for the sake of general learning (as opposed to only for career preparation), while 22 For more information about Strong Start to Finish, see https://strongstart.org. 23 For more information about Excelencia in Education, see https://www.edexcelencia.org. 24 For more information about the Examples of Excelencia awards, see https://www.edexcelencia.org/programs-initiatives/examples-excelencia. 25 For more information on the Growing What Works database, see https://www.edexcelencia.org/programs-initiatives/growing-what-works-database. 15

PREPUBLICATION COPY: UNCORRECTED PROOFS Burdman said it would be ideal for students to develop quantitative literacy in ways that are meaningful for their respective careers and their lives. Sanchez and Adiredja both expressed hope that students would see themselves reflected more often in a diverse professoriate as a result of reform. Adiredja added that although the dominant narrative about the importance of enrolling in STEM courses is informed by aspirations for economic stability, career mobility, and global competitiveness, he simply wished for students to experience the joy of learning mathematics. He stressed that for “the folks who went through the system and succeeded, some carrying the title of ‘the first,’ we often do not talk about the personal costs it takes to get there…oftentimes that journey to get there is not the most joyful.” Thus, Adiredja feels that one of the goals of his work is actually to foster joyful mathematics and STEM learning experiences for students. Acknowledging the disproportionate representation of certain populations in STEM fields and the specific groups of students who have struggled to succeed in mathematics, Dorsey asked the panelists how mathematics reform could be used as a lever to enhance equity, particularly in STEM fields. Sanchez emphasized that successful programs exist, such as the Emerging Scholars Program, that focus specifically on Latino students’ success through postsecondary studies and into the professoriate using a cohort-based model. One program that began in 2005 in the Department of Mathematics at The University of Texas at Austin and incorporated the Emerging Scholars Program is still thriving today and is expanding across the University of Texas system. Taking a different approach to Dorsey’s question, Adiredja described the “status that is conferred to people who know mathematics” and championed the value of helping students to develop the “mathematical efficiency” to be able to participate rather than be shut out of conversations among people with mathematical understanding. Referencing a conversation that took place among the panelists prior to the panel discussion, Adiredja noted that Dorsey himself benefitted from a self-paced mathematics course, even though it was not a “recommended” approach based on the research shared by Zachry Rutschow, which indicated that this approach tended to slow student progress. Adiredja described Dorsey’s experience as one that could be inaccurately interpreted as “statistical noise” in student data. When looking at student data as a whole instead of thinking about students’ individual experiences, he continued, opportunities to serve students, especially those in underrepresented populations, are missed. To enhance equity, Roberts suggested that the mathematics education community should first consider the dominant perspective of “success” and whether students are excluded if they do not fit precisely in that definition. She referred to a conversation she had with several African American students who defined success not as the receipt of a passing grade but rather as the ability to explain mathematical concepts to people in an understandable way. Roberts underscored the need to look closely at the groups of students that comprise developmental education and “tap into the knowledge” that they have; redefining “success” will broaden the pool of students who view themselves as successful and are recognized as successful. Dorsey shared a personal experience from 1984 when he approached the Mathematics Department at Chico State University about adding a supplemental instruction component to pre-calculus and algebra courses to better support students’ goals of attaining degrees in engineering. The chair of the department initially resisted the idea because “he had only seen one African-American [student] pass a calculus course in 8 years.” However, after a class of six students of color passed the pre-calculus course, as well as the calculus course that followed, the department chair reversed his decision and approved the development of a cohort for students of color. Today, Dorsey announced, there are 34 cohorts of these students of color who earned degrees in mathematics, physics, and chemistry. This experience illustrates the importance of developing relationships across academic departments—in this case, between the Mathematics Department, which usually acts as a gatekeeper, and the College of Engineering—to align mathematics experiences with career pathways and to provide underrepresented populations with the tools to succeed in STEM. Building on Zachry Rutschow’s presentation about reforms in developmental mathematics education, Dorsey asked panelists if the ideal outcomes that they outlined are in fact attainable by way of the current assessment, placement, and instructional reforms. Roberts pointed out that reforming structure is only part of the way to achieve student success. Students’ experiences have to be changed too, she 16

PREPUBLICATION COPY: UNCORRECTED PROOFS continued, and a focus has to be placed on enhancing students’ identities as mathematics learners and doers (see Aguirre, Mayfield-Ingram, and Martin, 2013). These more positive experiences and practices can carry forward in students who choose to become mathematics instructors in the future. Burdman accentuated the need for institutions to provide more support to students to enable them to develop agency to make authentic choices about which mathematics pathways they follow. This will help to keep the implementation of reforms aligned with the intention of the reforms, she continued, which is to promote student success in STEM rather than divert students away from STEM based on deficit assumptions of their ability. In line with this, Adiredja noted that in addition to implementing assessment, placement, and instructional reforms, it is essential for faculty to develop growth mindsets of ability. These mindsets should not be “filtered through the lens of race” (i.e., affording more growth mindset to certain students compared to others) so as to avoid negatively impacting specific groups of students. He also expressed the urgent need for reform efforts to extend further to engage with racism, sexism, and ableism dimensions. Panelists invited members of the audience to share their questions and observations about equity issues in developmental mathematics education. Citing Adiredja’s desire for students to find the joy in mathematics, online participant Sandra Byrd, who teaches at a tribal college, pointed out that “mathematics is excruciatingly painful” for some students. “Getting the students to find joy and success in math is a hard journey,” she continued. “Some of the teachers in the past have made math painful for these students, and it makes the students reluctant to approach math, to ask for help and to receive help when it is offered, and to persevere.” Roberts agreed with Byrd’s reflections and emphasized that faculty perceptions of their students have strong impacts on whether students view themselves with the potential to be successful. When “students of color, low-income students, and adult learners enter a math classroom, it is not just about learning content; it is about learning how to navigate environments that can be treacherous…and [psychologically] violent,” Roberts asserted. She described conversations with successful students who “cried as they talked about their math experiences and the struggles they had.” Thus, a balance between structural reform and the reform of relational practices is crucial, she proclaimed. Adiredja agreed that “math is [psychologically] violent” for students, but also cautioned against the tendency to respond from a deficit framework, emphasizing that lowering expectations is not the solution to address students’ mathematics trauma. Struck by Adiredja’s earlier comment about one person’s noise being another person’s signal, Mark Green declared that it is time to look at students individually, both in terms of their backgrounds and their unique learning styles. He asked panelists about the potential role of cultural competence training for developmental mathematics faculty. Although developing true cultural competence is difficult, Adiredja steered participants to resources from the K–12 domain on developing culturally inclusive pedagogy. He encouraged faculty to consider “how they view their students [and whether they are] mindful of their own sort of racial and gender biases in interpreting students’ work.” To illuminate this suggestion, Adiredja described watching a video of his own teaching, in which he saw himself “walking into a group of students [one Latino student, one Latina student, and one white female student]…and talking to the two women, but [his] back the whole time was against the one Latino male student…[about whom] the department [has] an established narrative…because he is taking more time, he has not graduated in 5 years, and he is struggling in the program.” Adiredja emphasized that his action was subconscious; despite his extensive research in deficit narratives, he did not realize that “at that moment…[he had] shut down that opportunity” for a student who was also dealing with mental health issues. The best way for faculty to counteract these narratives, and the resulting negative impacts on students, is to create an open dialogue with individual students to understand their needs and their experiences, Adiredja advocated. Vilma Mesa observed that this conversation on equity should include an understanding of not only what works for whom but also under what conditions. She revealed that the mathematics education community is not “counting” certain groups of students—for example, students with disabilities, first- generation college students, Native American students, Middle Eastern students, and Pacific Islander students. “By not counting these groups, we are rendering our ideology about who counts” in the education system, she asserted. Mesa explained that strategies are needed to understand how to attribute 17

PREPUBLICATION COPY: UNCORRECTED PROOFS the loss of these underrepresented students from mathematics programs, and asked panelists to share examples of promising models for change that could mitigate these losses. In response, Sanchez described an intensive 1-week success course 26 that Latino students at Cañada College take three times per year to become more successful in mathematics, as well as in a number of other disciplines. Dorsey reiterated the value of the MESA program, particularly at El Camino College in California, in supporting underrepresented students, including first-generation students, Native Americans, and Pacific Islanders, to be successful in mathematics. Echoing a previous suggestion from Adiredja, Burdman said that postsecondary educators could learn how to better support populations of students who are not being well served by studying the abundant research on reforms in K–12 mathematics education. In closing this discussion, Treisman revisited the reforms of the 1970s and 1980s, which were implemented in response to previous reforms focused on student deficits. These new reforms were organized around student assets and focused on producing professionals instead of merely eliminating the achievement gap and helping students to avoid failure. Concentrating research on understanding whether reforms are organized around student deficits or student assets could help to explain differential outcomes of programs that may appear structurally similar, he suggested. Alluding to Zachry Rutschow’s observation that new normative structures are being implemented throughout higher education, Treisman pointed out that because it is impossible to retrofit equity to systems that were not designed for it, the hope for equity lies in the space created by these new approaches to “[design] with care about who the beneficiaries are likely to be.” 26 For more information about this program, see https://canadacollege.edu/jam/mathjam.php. 18

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Increasing Student Success in Developmental Mathematics: Proceedings of a Workshop Get This Book
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The Board on Science Education and the Board on Mathematical Sciences and Analytics of the National Academies of Sciences, Engineering, and Medicine convened the Workshop on Increasing Student Success in Developmental Mathematics on March 18-19, 2019. The Workshop explored how to best support all students in postsecondary mathematics, with particular attention to students who are unsuccessful in developmental mathematics and with an eye toward issues of access to promising reforms and equitable learning environments.

The two-day workshop was designed to bring together a variety of stakeholders, including experts who have developed and/or implemented new initiatives to improve the mathematics education experience for students. The overarching goal of the workshop was to take stock of the mathematics education community's progress in this domain. Participants examined the data on students who are well-served by new reform structures in developmental mathematics and discussed various cohorts of students who are not currently well served - those who even with access to reforms do not succeed and those who do not have access to a reform due to differential access constraints. Throughout the workshop, participants also explored promising approaches to bolstering student outcomes in mathematics, focusing especially on research and data that demonstrate the success of these approaches; deliberated and discussed barriers and opportunities for effectively serving all students; and outlined some key directions of inquiry intended to address the prevailing research and data needs in the field. This publication summarizes the presentations and discussion of the workshop.

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