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The Emerging Scholars Program (ESP, known by other names) is a highly-structured workshop attached to academically-rigorous math courses to increase success of historically-underrepresented students. Created in the early 1970s by Dr. Philip Uri Treisman at the University of California, Berkeley, the initial focus was African-Americans in a calculus course seeking a doctoral degree in mathematics. Since then it has been used with a variety of student groups. ESP is used at colleges across the U.S.

Commissioned by the College Board's National Task Force on Minority High Achievement, this report presents a history of the Emerging Scholars Program, a proven strategy for increasing the number of underrepresented minority students who achieve at high levels in freshman calculus (and in initial freshman courses in several of the sciences, including chemistry, physics, and biology), and discusses the lessons that have been learned over the years from efforts to disseminate the Emerging Scholars Program to a number of institutions.

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The Academic Excellence Workshop demonstrates that achievement of underrepresented minority students in mathematics and subsequent persistence in SME majors may be associated less with precollege ability than with in-college academic experiences and expectations.

Over the past five years, the Mathematical Association of America, with support from the National Science Foundation, has explored the teaching of mainstream Calculus 1 at the postsecondary level, where by "mainstream" we mean those courses that can be used as part of the prerequisite stream to more advanced postsecondary mathematics. We surveyed 213 colleges and universities, 502 instructors, and more than 14,000 students to learn who takes Calculus 1 in college, why they take it, their preparation for this class, and their experience in this class. We also began to identify the characteristics of those classes that are most successful in encouraging students to continue their pursuit of mathematics. Following up on these surveys, teams of researchers visited twenty of these institutions, including community and technical colleges, liberal arts colleges, and public and private universities, to see firsthand what some of the best programs were doing. Here are some findings from this study, findings that should be of interest to those who are preparing students to succeed in college-level mathematics. A full account of the results of the study has been published in Bressoud, Mesa, and Rasmussen (2015); links to this report and research papers from the study are posted at www.maa.org/cspcc.

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In fall 2010, the Mathematical Association of America undertook the first large-scale study of postsecondary Calculus I instruction in the United States, employing multiple instruments. This report describes this study, the background of the students who take calculus and changes from the start to the end of the course in student attitudes towards mathematics and intention to continue in mathematics.

This paper describes the development of a Peer-Led Guided Inquiry (PLGI) program for teaching calculus at the University of South Florida. This approach uses the POGIL (Process Oriented Guided Inquiry Learning) teaching strategy and the small group learning model PLTL (Peer-Led Team Learning). The developed materials used a learning cycle based on three phases of inquiry: exploration of a model, concept invention, and application. Fifty minutes weekly of lecture in Engineering and Life Sciences Calculus were replaced by the PLGI curriculum, where students worked in groups with peer leaders as instructors. The main outcomes measured were pass and withdrawal rates for sections using this approach compared to historical and concurrent sections not using PLGI. Our results showed higher pass rates in Life Sciences Calculus (18% gain in comparison to historical sections and 8.2% gain in comparison to concurrent non-PLGI sections). In Engineering Calculus, we also saw higher pass rates for PLGI sections (18.2% gain in comparison to historical rates and 4.0% gain in comparison to concurrent non-PLGI sections). Withdrawal rates also declined for both Life Sciences and Engineering Calculus. Both sexes had greater pass rates and lower withdrawal rates in both types of calculus. PLGI sections showed higher pass rates for African-American students in life sciences (16.5% gain in comparison to historical sections and 8.7% gain in comparison to concurrent non-PLGI sections). The impact of PLGI for African-American students was more dramatic in Engineering Calculus (24.9% gain in comparison to historical sections and a 17.6% gain in comparison to concurrent non-PLGI sections).

The goal of this chapter is to describe what it might mean for college level mathematics teaching to be culturally responsive and illustrate how culturally responsive collegiate mathematics teaching and learning can look. Our focus is on effective college mathematics instruction for non-mathematics majors in service courses like calculus and liberal arts mathematics. Culturally responsive courses in the mathematics major are possible, but require a more extensive discussion about the specific nature and purpose of the mathematics major within a department before change is possible. After providing some background, we offer common views of college mathematics teaching in the overlapping contexts of academic, workforce, and social justice concerns. Secondly, we give several short examples from the perspective of college professors about the nature of their instructional practices, including cultural responsiveness. Thirdly, we address the nature of culture and the repertoires college students and instructors build – of ways of seeing, communicating about, and engaging with these concerns. Fourthly, we provide two detailed examples of culturally responsive teaching and curricula in courses that currently exist along with some of the successes documented in these courses. We close with suggestions for how to improve the educational environment for students and instructors through the tenets of culturally responsive pedagogy. Throughout, we connect our observations with existing critical educational theories. That is, we employ common academic mathematics cultural practices: we start with some background information and several motivating examples, give some definitions (after already having used key terms in context), provide two extended examples, making connections along the way, and conclude with a summary of what we think these all show.

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This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate this blended instruction as a local representative of the US calculus reform movements that helped foster it. These reform movements tended to emphasize problem-solving as well as multiple mathematical registers and quantitative modelling. Our statistical analysis reveals the influence of the blended traditional/reform calculus instruction on students' ability to solve calculus-related, non-routine problems through repeated measures over the semester. The calculus instruction in this study significantly improved students' performance on non-routine problems, though performance improved more regarding strategies and accuracy than it did for drawing conclusions and providing justifications. We identified problem-solving behaviours that characterized top performance or attrition in the course. Top-performing students displayed greater algebraic proficiency, calculus skills, and more general heuristics than their peers, but overused algebraic techniques even when they proved cumbersome or inappropriate. Students who subsequently withdrew from calculus often lacked algebraic fluency and understanding of the graphical register. The majority of participants, when given a choice, relied upon less sophisticated trial-and-error approaches in the numerical register and rarely used the graphical register, contrary to the goals of US calculus reform. We provide explanations for these patterns in students' problem-solving performance in view of both their preparation for university calculus and the courses' assessment structure, which preferentially rewarded algebraic reasoning. While instruction improved students' problem-solving performance, we observe that current instruction requires ongoing refinement to help students develop multi-register fluency and the ability to model quantitatively, as is called for in current US standards for mathematical instruction.

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In this paper, we provide a report of preliminary findings of the Morgan State University (MSU) Student Engagement in Mathematics through an Institutional Network for Active Learning (SEMINAL) project and its focus on culturally responsive teaching (CRT) as an active learning framework for pre-calculus instruction. The paper concludes with a summary of wins and challenges faced by MSU's Mathematics Department. Lessons learned by MSU SEMINAL will help inform other departments on implementing CRT in a pre-calculus course.

This study suggests a lack of mathematical confidence, rather than a lack of mathematically ability, may be responsible for the high departure rate of women. While it would be ideal to increase interest and participation of women in STEM at all stages of their careers, our findings indicate that if women persisted in STEM at the same rate as men starting in Calculus I, the number of women entering the STEM workforce would increase by 75%.

This dissertation focused on inequity in calculus instruction through a two-part study that built on the findings from an earlier exploratory study. The exploratory study, conducted in the same department, revealed connections between personal theories of mathematics intelligence that doctoral student instructors (DSIs) held for themselves and those that they held for their students. The first component of the dissertation project was a design intervention study that examined a practice-based approach to preparing DSIs to give students equitable feedback, a core instructional practice, in their postsecondary calculus instruction. The second component was a comparative investigation of teacher/student interactions across identity difference in postsecondary calculus instruction. Four of the instructors from the intervention study were observed and interviewed throughout their first semester of teaching to examine their interactions with their undergraduate students across identity difference. The three articles in this dissertation focus on the findings from this second study. The findings suggested that the DSIs, who were members of overrepresented groups (i.e., majoritized students identifying as men and Asian or White), held some common understandings about what in meant to do mathematics well, which they used as lenses for gauging their own and others’ potential to successfully navigate mathematics as a discipline. Moreover, evidence from this study indicated that when the DSIs viewed students through these lenses that they noticed different characteristics for minoritized and majoritized students, even when they exhibited similar behaviors. These impressions formed the DSIs’ opinions about the potential of their students, which systematically disadvantaged women, especially those identifying as Latina and Black. Finally, the findings suggested that the DSIs acted on their ideas about intelligence through their teaching practices, creating differentiated access to learning opportunities and marginalizing minoritized students. The resulting inequitable approaches to instructional practices may reduce domain identification and motivation, create lower expectations, and depress performance for minoritized students in mathematics classrooms as explored in the pre-calculus case presented in the third article. These findings support the need for the design of equitable approaches to mathematics instructional practices and the explicit preparation of postsecondary instructors to engage in them.

Increasing success rates in calculus is of critical importance for improving the pipeline to careers in STEM. The Arlington Undergraduate Research-based Achievement in STEM (AURAS) project,
partially funded by the National Science Foundation, implemented the Arlington-Emerging Scholars Program (A-ESP) to address these pipeline issues. The A-ESP intervention involves engineering, mathematics, chemistry, and physics intended majors in an intensive supplemental workshop setting in which students encounter calculus tasks at a deeper more conceptual level. We compare the mathematical experiences of A-ESP students versus non-A-ESP students in the same lecture (n=93) in the context of their performance on departmental exams. In general, A-ESP students outperform non-A-ESP students on departmental exams, but in an effort to further improve curriculum, items in which A-ESP students drastically outperformed their counterparts or vice versa were back-mapped to the homework, labs, and A-ESP tasks. Findings suggest that on items where A-ESP students outperformed the non-A-ESP students the tasks students worked in the A-ESP problem sets tended to be more conceptual or abstract. However, on the items where non-A-ESP students outperformed the A-ESP students, the A-ESP tasks tended to resemble ordinary homework tasks. Thus, on typical primarily procedurally based calculus exams, the conceptual and abstract tasks appear to be boosting student performance and ultimately helping them successfully complete the course. The implications of this work will be discussed as well as ways to follow up on the findings.

This review considers research related to mathematics education and cooperative learning, and it discusses how teachers might assist students in cooperative groups to provide equitable opportunities to learn. In this context, equity is defined as the fair distribution of opportunities to learn, and the argument is that identity-related processes are just as central to mathematical development as content learning. The link is thus considered between classroom social ecologies, the interactions and positional identities that these social ecologies make available, and student learning. The article closes by considering unresolved questions in the field and proposing directions for future research.

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Through a multi-year, national calculus study, researchers have recently identified seven characteristics of successful college calculus programs. We identified these seven characteristics by visiting five doctoral-granting mathematics departments with successful calculus programs and uncovering the common traits among them. These seven traits common among the collection of five universities were: robust GTA teaching preparation, coordination of courses, support of active learning, comprehensive placement strategies, collection and attention to local data, abundant student supports, and rigorous content. Further analysis and reflection on the previously gathered data indicates that the earlier study actually identified characteristics of calculus programs that successfully serve a majority white or Asian and male population. In this article, I argue that attention to an eighth characteristic comprised of diversity, equity and inclusion practices along with the other seven can enable a department to create a truly successful calculus program by understanding and attending to the unique needs of historically marginalized populations.

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Our large, mixed-methods study examines cognitive and affective outcomes of inquiry-based learning (IBL) in a variety of undergraduate mathematics courses at four universities. Student outcomes are measured by pre/post-survey items, self-reported gains and historical transcript data. Students in IBL courses report higher cognitive and affective gains than do non-IBL students. IBL students also report increase in motivation and interest, whereas non-IBL students’ motivation drops after mathematics courses. The historical transcript data also shows IBL students’ higher interest compared to their non-IBL peers. These benefits of IBL instruction are especially important for women and low achieving students, who are often under-served by the traditional college mathematics courses. Our findings suggest that IBL instructional methods support positive learning outcomes in various groups of students, including those under-served and under-supported by the traditional college mathematics courses.

We report on our work to build an applied theory for intercultural competence development for mathematics teaching and learning in secondary and tertiary settings. We use research in social anthropology and communications to investigate the nature of intercultural competence development for mathematics instruction among in-service secondary mathematics teachers and college faculty participating in a university-based mathematics teacher professional development program. We present results from quantitative and qualitative inquiry into the intercultural orientations of individuals and some groups (teachers, teacher-leaders, university faculty and graduate students) and offer details on the development of case stories for use in the professional development of mathematics university teacher educators, in-service teacher leaders, and secondary school teachers.

While traditional methods of teaching and learning Calculus have served some students well for many decades, national curriculum guides and problematic student outcomes highlight multiple changing realities and foster a greater awareness that ask the mathematics community to interrogate these traditional approaches. In response, the mathematics faculty at Centre College and Southwestern University (both small liberal arts colleges located in the southern United States) engaged in a thoughtful, collaborative re-envisioning project focused on evolving the entire calculus sequence to better meet the needs of the modern student. We decided to incorporate more modeling and realistic applications that utilize large data sets, include “new” ideas in each course for students who have studied calculus in high school, incrementally increase the challenge from one course to the next, and explicitly encourage persistence through the calculus sequence and beyond. In this paper, we discuss the development of this re-envisioned modern calculus sequence as an example of a successful curricular reform project, to include: (a)designing the courses with an eye toward inclusion and reducing barriers, (b) developing the courses independent of current textbooks, (c) making the hard decisions about what content stays, what content evolves, what content is added, and what content is let go, and (d) suggesting how to implement this process at other institutions.

Mathematics is not a race-neutral subject. Access and opportunity in mathematics for students of color in the United States continue to be limited. While a great deal of attention has been given to increasing the number of underrepresented minority students in the mathematics pipeline, there is little consideration of who they are as learners or the context in which their mathematics learning takes place. We argue that culturally relevant instruction coupled with teaching for social justice can motivate marginalized students to learn mathematics. Throughout this conceptual article, we (a) explore the theoretical frameworks underlying culturally relevant pedagogy (CRP) and social justice pedagogy (SJP), (b) present illustrative cases of mathematics teaching that reveal the possibilities and challenges associated with these pedagogical approaches, and (c) offer to the field of teacher education recommendations related to the successful use of CRP and SJP within today's classrooms.

Introductory mathematics courses, including precalculus and calculus, largely influence Black and Latin* students’ persistence and sense of belonging in STEM. However, prior research on instruction in these courses for advancing more equitable outcomes is limited. This paper presents findings from a study of 18 Black and Latina/o students’ perceptions of introductory mathematics instruction as a racialized and gendered experience at a large, public, and historically white research university. Sociological perspectives of logics and mechanisms of inequality guided an analysis of Black and Latina/o students’ group interview responses on how instruction perpetuates racial and gendered oppression. Two logics were identified: (i) Instructors hold more mathematical authority than students in classrooms; and (ii) Calculus coursework is used to weed out students ‘not cut out’ for STEM. These logics, coupled with the influence of broader sociohistorical forces (e.g., cultural scripts of behavior, stereotypes), gave rise to mechanisms of inequality through seemingly neutral instructional practices that reinforce racial-gendered distribution of classroom participation and STEM persistence. Our findings inform implications for STEM higher education researchers and mathematics faculty to foster socially affirming STEM instruction, especially in introductory courses.

Undergraduate mathematics education can be experienced in discouraging and marginalizing ways among Black students, Latin* students, and white women. Precalculus and calculus courses, in particular, operate as gatekeepers that contribute to racialized and gendered attrition in persistence with mathematics coursework and pursuits in STEM (science, technology, engineering, and mathematics). However, student perceptions of instruction in these introductory mathematics courses have yet to be systematically examined as a contributor to such attrition. This paper presents findings from a study of 20 historically marginalized students’ perceptions of precalculus and calculus instruction to document features that they found discouraging and marginalizing. Our analysis revealed how students across different race-gender identities reported stereotyping as well as issues of representation in introductory mathematics classrooms and STEM fields as shaping their perceptions of instruction. These perceptions pointed to the operation of three racialized and gendered mechanisms in instruction: (i) creating differential opportunities for participation and support, (ii) limiting support from same-race, same-gender peers to manage negativity in instruction, and (iii) activating exclusionary ideas about who belongs in STEM fields. We draw on our findings to raise implications for research and practice in undergraduate mathematics education.

This article describes a program of demanding courses offered in an academic community to nontraditional and at-risk, first- and second-year students at a research university. The delivery of instruction uses multiple pedagogies, including collaborative learning and labs where students work together under the guidance of undergraduate assistants. A research study showed that students in the program perform better than traditional students in equivalent courses. In addition, this study provides strong evidence that when students of the program take the same subsequent classes offered to the general university population, their success rates match or exceed those of their traditional classmates.

The failure to successfully complete gateway calculus courses often prevents ethnic minority students from pursuing science and engineering majors. Research suggests that this failure to succeed is caused more by social factors than by attributes related to ability. This article presents the findings of an evaluation study done of the Wisconsin Emerging Scholars Program, a non-remedial, multicultural workshop approach to learning calculus. Through its emphasis on community and collaboration, it is more culturally relevant and designed to foster substantial participation from underrepresented ethnic minority groups. The Wisconsin Emerging Scholars Program also helps to alleviate the problems of isolation and lack of support that can occur at universities. When the program is implemented optimally, a community of confident calculus learners who outperform traditional students academically emerged.

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In 1989 members of the Department of Mathematics at the University of Illinois at Urbana-Champaign (UIUC) implemented the Merit Workshop Calculus Program. Based on Treisman-style workshop calculus, the UIUC program was intended to address the problems of low success rates of students from underrepresented populations, and of failure to retain these students in mathematics- and science-based majors. The authors conducted their investigation by examining transcript records for patterns of (a) performance in first-semester calculus; (b) performance in courses that require first-semester calculus as a prerequisite; and (c) persistence at the university, especially in majors requiring calculus. Analyses included gender and ethnicity effects. The results indicate that the Merit Workshop Calculus Program had a positive impact for both genders and for several ethnic groups (African-American, Caucasian, and Hispanic). Particularly dramatic results were noted for women and for Hispanic students. The results reported here are important because they are based on longitudinal data and distinguish differential effects for both well- and underrepresented populations.

This article reports on an innovative approach to teaching Calculus I which was initiated in a two-semester course designed for students at risk of failing Calculus I. The treatment consisted of voluntary oral assessments offered before every written examination. Analyses showed that the treatment students did significantly better than the control group on course grades as well as a common final exam that tested both concepts and procedures. Treatment students designated at-risk due to their placement scores at the outset of the course, completed Calculus I, were retained at the university, and enrolled in and passed Calculus II at dramatically higher rates than at-risk students in the control group. Subsequently, orals have been introduced in large lecture classes with promising results.

Although urban Latinas/os have participated in mathematics workshops in urban universities for over three decades as part of the Emerging Scholars Program (ESP), few studies have explored Latina/o students’ perspectives of how and why these learning environments support them in attaining mathematical success. This article presents an in-depth case study of how Vanessa, a Latina undergraduate student from an urban community, simultaneously constructed her mathematics and racial identities as she engaged in a culturally diverse, collaborative ESP Calculus I workshop situated within broader sociopolitical contexts. Vanessa’s story was selected because she offered a unique perspective of how encountering identity-affirming workshop spaces aided her in constructing a strengthened self-perception as a Latina mathematics learner. Her counter-story challenges dominant ideologies that disregard the importance of viewing Latina/o students’ mathematics participation and learning as racialized forms of experience.

In this article, the author presents a qualitative multiple case study that explored how two urban Latina/o undergraduate students' emerging mathematical and racial identity constructions influenced their participation in a culturally diverse, Emerging Scholars Program, Calculus I workshop at a predominately White urban university. Drawing on critical race theory and Latina/o critical theory, cross-case analysis illustrates that participants' emerging mathematical and racial identities--co-constructed with their other salient identities--contributed to positively shifting their participation by: (a) changing their perceptions of their and peers' mathematics abilities, (b) allowing them to challenge racialized mathematical experiences, and (c) strengthening their comfort levels in the workshop environment. The Latina/o participants' counter-stories support that the sociopolitical nature of identity development and participation in mathematical learning contexts should be embraced because it provides additional knowledge regarding how and why Latina/o students attain mathematical success.

Calculus I at post-secondary institutions has historically been perceived as a "filter" that blocks access to professional careers in STEM fields. This perception is further validated when the failure rate in the course is high and experiences are often negative. Failure in Calculus I is commonly identified in the literature as a grade of D or F or a withdrawal from the course. Here, Pilgrim and Gehrtz discuss improving success rates in Calculus I for Physical Scientists I courses offered at the Colorado State University and strategies for instruction in a Calculus I classroom.

This article reports findings from a research and professional development project at two high schools located in low-income, urban communities of color. The project collaborates with teachers on improving their instructional practices, using a framework of culturally relevant mathematics pedagogy, which is described in detail here. We present results from a qualitative and quantitative analysis of mathematics instruction in 68 classroom observations of seven teachers. In particular, we use culturally relevant mathematics pedagogy as a lens through which to analyze instruction and the associated opportunities to learn mathematics provided to students.

Workgroup is an optional pass/fail supplemental course to Calculus that emphasizes collaborative work in a small group setting. We conduct a mixed-methods study to evaluate the effectiveness of Calculus 1 Workgroup on student performance in Calculus 1 for Engineers. We analyze a dataset that contains 733 observations and 35 predictor variables. We use AnswerTree software by SPSS to create decision trees to assess the biggest predicting factors for Calculus 1 course-grades. We then compare Workgroup students and non-Workgroup students based on factors resulting from AnswerTree, including predicted grade point average (PGPA), to evaluate the effectiveness of Workgroup on student performance. We find that in the academic year of 2013 -2014, Workgroup did not significantly improve performance in Calculus. We also analyze a survey taken by Workgroup students to have a better understanding of student attitudes toward Calculus, Workgroup, and Oral ssessments, a large component of Workgroup. Within the subgroup of Workgroup students, we compare students who are required to enroll in Workgroup to those who choose to enroll. We show that students who enroll in Workgroup have a higher PGPA on average than those who do not enroll. Further, we show that students who are required to take Workgroup (by scholarship) have a significantly higher PGPA than students who choose to enroll in Workgroup. Yet, we find no significant difference in course grade between required Workgroup students, non-required Workgroup students, and non-Workgroup students. Lastly, we note a correlation between
the requirement to take Workgroup and attitude toward Workgroup.

This article uses Culturally Relevant Pedagogy (CRP) and Culturally Responsive
Teaching (CRT) as the theoretical frameworks and qualitative metasynthesis as the methodological framework to synthesize qualitative research published between 1994 and February of 2016. Initial
searches produced 1,224 articles, but through a process of appraisals, 12 articles were synthesized to understand how researchers interpret mathematics teaching practices that support CRP and CRT in pre-kindergarten through 12th grade. There were five findings focused on teacher practices, classroom interactions, and student experiences with CRP and CRT within mathematics education, including: caring, context, cultural competency, high expectations, and mathematics instruction.

The article focuses on the application of National Center for Academic Transformation (NCAT) mathematics course redesign programs or emporium model to solve the learning problems of higher education in U.S. It defines course redesign as the process of rethinking whole courses to attain better learning results at a lower cost by taking advantage of information technology. It highlights the four phases of innovation involved in the iterative process of course redesign namely experimentation, modification, replication, and expansion from 2006-2010.

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Strong prerequisite skills are essential to student success in the calculus sequence; however, many students arrive in Calculus I with weaknesses that are difficult for them to overcome. In this paper, we describe an approach to early incentivized remediation of prerequisite material in a Calculus I course. We present data that supports the idea that a lack of prerequisite knowledge is a significant hurdle for students, but also that participation in the remediation program is correlated with student success. In addition, the program allows for the very early identification of students at high risk of failing. The program is easy to implement, and it would be adaptable to a variety of other courses for which prerequisite knowledge is essential for success including science courses, engineering courses and other mathematics courses.