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PREPUBLICATION COPY: UNCORRECTED PROOFS 1 Introduction 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, at the National Academy of Sciences building in Washington, DC. This 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. GOALS OF THE WORKSHOP 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 communityâs progress in this domain, as guided by the questions in the planning committeeâs Statement of Task (see Box 1-1). Participants (i.e., workshop planning committee members, presenters, and attendees) 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 servedâ(1) those who even with access to reforms do not succeed and (2) 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. 1

PREPUBLICATION COPY: UNCORRECTED PROOFS BOX 1-1 Statement of Task A planning committee will plan a 2-day open workshop that will explore the effectiveness of postsecondary developmental (remedial) mathematics courses, with particular attention to the students who are unsuccessful in these courses. The workshop will explore the challenges these students face, promising approaches, and areas where additional research is needed. The workshop will focus on the following questions: 1. Which students are well-served by the current offerings in developmental mathematics? How do we define âwell- servedâ and what are indicators of student success in developmental mathematics? How do we define which students are included here? 2. What is the size of the total population that is not well-served? Are there subgroups within this group and how do needs or challenges vary across them? How do Adult Basic Education students fit in? 3. What is known about why some students are not well-served? What do we need to know in order to serve them better? 4. Are there examples of successful approaches? What are the components of these programs (considering interventions both within and outside of the classroom)? What is needed in order to implement the more successful approaches? 5. What are the potential challenges and what strategies can be used to address them? What are the next steps? 6. What are the gaps in the research base and what are the key directions for research, both short and long-term? After the workshop, a Proceedings of a Workshop of the presentations and discussions at the workshop will be prepared by a designated rapporteur in accordance with institutional guidelines. ORGANIZATION OF THIS PROCEEDINGS This workshop was organized by an independent planning committee in accordance with the procedures of the National Academies. The planning committeeâs role was limited to setting the agenda and convening the workshop. (See Appendix A for the workshop agenda, Appendix B for biographical information for the planning committee members and workshop presenters, and Appendix C for the full list of in-person workshop participants). This proceedings summarizes the discussions that occurred throughout the workshop and highlights key points raised during the presentations, moderated panel discussions, and small group discussions among the workshop participants. This chapter outlines the scope of the workshop, including the goals, guiding questions, and an opening discussion on the importance of mathematics education. Chapter 2 presents the current landscape of developmental mathematics education, with attention to reform efforts and equity concerns. Chapter 3 describes student demographics and course-taking experiences in developmental mathematics, with specific data and commentary on what works for whom across four diverse state contexts. Chapter 4 discusses promising models for change in developmental mathematics education, with consideration for the context of broader transformations in undergraduate education. Chapter 5 presents strategies to build capacity for continuous educational improvement. Chapter 6 highlights participantsâ ideas for next steps and a vision for the future of developmental mathematics education. 1 1 Videos of presentations and additional materials prepared or compiled for this workshop can be found at http://sites.nationalacademies.org/DBASSE/BOSE/Developmental_Math/index.htm. 2

PREPUBLICATION COPY: UNCORRECTED PROOFS In accordance with the policies of the National Academies, this proceedings was prepared by the workshop rapporteurs as a factual summary of what occurred at the workshop. The workshop did not attempt to establish any conclusions or recommendations about needs and future directions, focusing instead on issues identified by the workshop presenters and participants. Statements, recommendations, and opinions expressed are those of individual presenters and participants, do not represent the views of all workshop participants or the planning committee, and are not necessarily endorsed or verified by the National Academies. They should not be construed as reflecting any group consensus. WELCOMING REMARKS Howard Gobstein, workshop planning committee chair and executive vice president of research, innovation, and science, technology, engineering, and mathematics (STEM) policy at the Association of Public & Land-grant Universities, described developmental mathematics education as âone of the most pressing education issuesâ of this era and emphasized that mathematics continues to be a barrier to degree completion for many students, particularly for students of color. Barriers to learning mathematics, he continued, can severely limit opportunities for hundreds of thousands of students, as success in mathematics relates to postsecondary enrollment, career advancement, financial stability and upward mobility, quality of life, and societal contributions. Gobstein explained that recent research on and reforms to developmental mathematics education, as well as the engagement of dedicated faculty, policy makers, and administrators, has increased the number of students able to succeed in their first credit-bearing mathematics course. However, despite this progress, he continued, a significant portion of students are still not succeeding in mathematics. Gobstein asserted that the system is failing these students, and âthe problem is magnified as many of these students are becoming the majority population in the United States as their demographics shift.â This issue, then, is also âabout the equitable future of our country . . . [and] understanding mathematics is foundational to helping to address this.â The mathematics education community, he continued, is faced with a substantial challenge; but with a better understanding of how to best serve students via the promising reforms under way, it is possible to eliminate existing barriers and reach the remaining cohorts of students. In addition to the goals of the workshop already discussed above, Gobstein raised more specific guiding questions to be considered over the course of the two-day workshop: â¢ What do we know about present student success? What works well, where, and for whom? â¢ For whom does it not work? What do we know about the students who are not currently well served, and where are they? â¢ What do we need to do to significantly broaden student success? What more do we need to know both to advance progress and to keep track of our improvements? â¢ What is involved to move the field from individual programmatic attempts to systemic changes at scale and to make this normative to the system (i.e., how to eliminate the mathematics barrier for students and make âno barrierâ the new normal)? He reiterated that it is important to the mathematics education community, and to the nation as a whole, to eliminate the mathematics barrier that often constrains the education and career decisions of hundreds of thousands, perhaps millions, of students each year. Gobstein concluded his remarks by saying that this workshop is an opportunity to convey to many stakeholders, and to the nation more broadly, the important next steps in this field. THE VALUE OF MATHEMATICS EDUCATION AND THE NEED FOR REFORM Linda Braddy, former deputy executive director of the Mathematical Association of America (MAA) and current vice president for academic affairs at Tarrant County College (a community college 3

PREPUBLICATION COPY: UNCORRECTED PROOFS in Texas), moderated the workshopâs opening panel discussion. Joined by two mathematics professors, she invited conversation on the importance of mathematics education, the role that mathematics plays in the student experience, and the need for developmental mathematics reforms to increase success for all students. During her tenure at MAA, Braddy co-wrote A Common Vision for Undergraduate Mathematical Sciences Programs in 2025 2 and the MAA Instructional Practices Guide, 3 two national documents reflecting efforts by the mathematics societies, in particular, to create vehicles for assessing where consensus exists around teaching and learning mathematics. Trained as a pure mathematician, panelist Mark Green is professor emeritus of mathematics at the University of California, Los Angeles (UCLA). Owing to his experience leading the National Science Foundation (NSF)-sponsored Institute for Pure and Applied Mathematics that fosters interactions in mathematics and other disciplines, his expertise lies in the intellectual footprint of mathematics, broadly speaking. He is also the incoming chair of the Board on Mathematical Sciences and Analytics at the National Academies. With 41 years of teaching experience, panelist Paula Wilhite was a charter faculty member and is now division chair of mathematics, physics, and engineering at Northeast Texas Community College, an institution that serves a significant percentage of Hispanic students. 4 She also serves as the chair of the Developmental Mathematics Committee of the American Mathematical Association of Two-Year Colleges (AMATYC), a committee made up of nearly 400 members. Reflecting on current perceptions of mathematics education, Braddy, Green, and Wilhite agreed that traditional approaches to developmental mathematics education (i.e., algebra-calculus pathway), in particular, have proven to be ineffective for an increasing number of students (see Chen, 2016). Additionally, Braddy shared what she referred to as a âstriking statisticâ: only 10-15 percent of jobs require the intense use of college algebra or Algebra 2 from high school. Struck by how low that percentage was, she asserted that more innovative mathematics pathways that provide alternatives to the algebra pathway are needed to reach the masses of students who need strong mathematics competencies and analytical skills in preparation for careers that do not necessarily require a STEM degree. Green pointed out that although UCLA has a general quantitative requirement for all students, a growing number of majors specifically require mathematics and/or statistics credits. For example, life sciences requires calculus and statistics; physical sciences, engineering, and climate sciences require mathematics; psychology, sociology, political science, public affairs, international development studies, global studies, and communication require statistics; and cognitive science, neuroscience, psychobiology, economics, business economics, and the science-focused anthropology track all require both mathematics and statistics credits. Furthermore, he continued, as workforce needs evolve alongside the emergence of new disciplines, the mathematical skill sets that students need will continue to change. He added that the stakes are high for students and their future opportunities will be limited if they do not know mathematics. Braddy explained that the principle behind multiple mathematics pathways, a common developmental mathematics reform approach, is that students would be more prepared for future opportunities by taking the specific types of mathematics tailored to their respective careers. She endorsed the notion of evolving multiple mathematics pathways beyond the current algebra/calculus, statistics, or quantitative reasoning pathways to appreciate different focuses of the mathematics, such as for nursing and the health sciences where communicating effectively with mathematical language is an important skill set. Wilhite shared that Northeast Texas Community College has implemented multiple mathematics pathways for students as a way to provide the variety of mathematics that is needed to fulfill the 2 For more information about A Common Vision for Undergraduate Mathematical Sciences Programs in 2025, see https://www.maa.org/sites/default/files/pdf/CommonVisionFinal.pdf. 3 For more information about the MAA Instructional Practices Guide, see https://www.maa.org/sites/default/files/InstructPracGuide_web.pdf. 4 For more information about enrollment at Northeast Texas Community College by race/ethnicity, see https://datausa.io/profile/university/northeast-texas-community-college#enrollment. 4

PREPUBLICATION COPY: UNCORRECTED PROOFS requirements of each major. Each mathematics pathway âopens up the world to a different set of students,â Green shared. Students with strong inductive reasoning skills might be attracted to statistics courses; students with strong critical thinking skills and a curiosity for real-world problems might take an interest in mathematical modeling; and students drawn to programming would benefit from courses that stress algorithmic thinking. He referenced the National Research Councilâs report The Mathematical Sciences in 2025 (National Research Council, 2013), noting that how well a student learns mathematical concepts is also directly influenced by how interested he/she is in those concepts and how they relate to who the student hopes to become in the future. Without access to the appropriate postsecondary-level mathematics pathways and related skill sets, students could be limited in terms of their career options and opportunities for upward mobility, Green reiterated. Wilhite emphasized that implementation of mathematics reforms, such as multiple mathematics pathways, is not without its challenges and criticisms. Many ânaysayers,â she explained, believe that multiple mathematics pathways limit studentsâ opportunities for advanced courses or careers in STEM and that they do not offer the same level of rigor as college algebra. However, she stressed that forcing all first-year students to take college algebra is what truly limits studentsâ opportunities for the future. Braddy added that data can be used to demonstrate to the ânaysayersâ that reforms help students by eliminating barriers that affect career goals and potential for upward mobility. In preparing to implement mathematics education reforms, Wilhite shared that institutional leaders should consider how to do the following: evaluate studentsâ progress, understand what it means to succeed in each type of mathematics, support students who change majors, and adapt faculty training and staffing levels. She highlighted several staffing challenges related to the implementation of the co- requisite reform model, in particular, but underscored that ânone of these challenges are insurmountable.â The co-requisite model is a shift from the longer developmental mathematics sequence; 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). Wilhite explained that this often presents a scheduling challenge, in that the model tends to prompt particularly large enrollments in the fall semester and smaller enrollments in the spring semester. Institutions, she continued, could provide balance by addressing English co-requisites in the fall and mathematics in the spring as one approach to overcoming staffing issues. Another challenge for staffing noted by Wilhite relates to the expertise and qualifications of mathematics instructors. Given the nature of the nationâs data-driven economy, Wilhite wholeheartedly supports including statistical analysis in mathematics curricula; however, she expressed concern about how to staff these courses, since many instructors are not adequately prepared to teach statistical analysis. The American Mathematical Society and the MAA released a statement in 2014 that begins to address this gap: it recommends that instructors should have extensive experience with statistical analysis and a minimum of two courses on their transcripts that prepare them to teach statistical methods in an introductory statistics course. Green described a similar concern about recruiting qualified faculty to teach new courses in big data, which are emerging as part of undergraduate curricula across the United States (e.g., the University of California, Berkeleyâs Data8, an exploratory course in big data). Experts in big data tend to avoid teaching careers, given the more attractive opportunities that exist in industry. However, joint appointments, in which experts would spend half of their time teaching and half of their time working in industry, could address this potential faculty shortage, Green explained. Braddy agreed that institutional leaders should anticipate and consider how to address the challenges that will arise from scaling mathematics pathways programs, which requires the addition of more courses and more qualified instructors. She added that although relying on adjunct faculty is not the optimal solution for staffing problems for a variety of reasonsâthey often receive low pay and have poor working conditionsâ adjunct faculty are often mathematics practitioners who have unique expertise that is incredibly beneficial for students. Furthermore, she continued, mathematics departments could also draw on resources and 5

PREPUBLICATION COPY: UNCORRECTED PROOFS training from the NSF-supported MAA initiative StatPrep, 5 which has created hubs in and around urban community colleges to help mathematics faculty become more proficient in teaching modern statistics. Panelists invited audience members to share their questions and observations about the importance of mathematics education and mathematics education reform. Vilma Mesa, associate professor of education and mathematics at the University of Michigan, observed the limited number of changes that have occurred in mathematics education during the past 50 years. She emphasized that problems within the field of mathematics education are very difficult to solve. Green echoed Mesaâs concerns and noted that the pace of change in higher education is âglacial,â at best, referencing the 15 years that it took from the awareness of the need for a course in big data at UCLA in 2004 to finally receiving approval to implement a data theory track in 2019. In order to better understand how to revise mathematics curricula, more conversations are needed about the institutional constraints that determine which students take which courses, Mesa asserted. Philip Uri Treisman, founder and executive director of the Charles A. Dana Center at The University of Texas at Austin, 6 emphasized the need to monitor the growing need for quantitative competency through the mathematical sciences in undergraduate and graduate education, and Green proposed that the mathematics community should conduct decadal studies to better document the educational implications of mathematics, including specific uses of mathematics in other fields. Before the panel concluded its discussion, Wilhite introduced the topic of academic rigor in mathematics courses, endorsing The University of Texas at Austin Charles A. Dana Centerâs statement that ârigor in mathematics is a set of skills that centers on the communication and the use of mathematical languageâ (Charles A. Dana Center, 2019). Green championed this definition of rigor and pointed out that each type of mathematics has a standard of what it means to understand concepts and perform tasks well. Supporting Wilhiteâs earlier declaration that pathways actually expand choices for students, Treisman wondered if evidence from studentsâ transcripts exists to identify the career options available to students who have completed college algebra, which would support the notion that college algebra actually keeps studentsâ options open to be engineers or mathematicians. Treisman noted that his own research shows almost no students graduating with a degree in engineering or mathematics who took college algebra or pre-calculus as a college student; significantly more students take calculus in high school and are therefore entering college with richer mathematics backgrounds than was the case 10 or 15 years ago. Wilhite agreed that students who complete college algebra rarely move on to take another college-level mathematics course such as calculus. In fact, college algebra is considered a terminal course, with very few exceptions, she continued. Braddy reiterated that because many students are not served well by the current approach to mathematics education (i.e., the college algebra pathway) which can impact career decisions, the need for reform becomes even more important. 5 For more information about StatPrep, see http://statprep.org. 6 The mission of the Dana Center is to âsupport seamless transitions for all studentsâ by âcreating pathways for successâ and providing âsupport at every level.â See https://www.utdanacenter.org/who-we-are/our-mission for more information. 6