Developmental Mathematics Research Articles

STEM Enrollment Decision Trees as Graduation Predictors for Community College Students Enrolled in Remedial Mathematics

Objective/Research Question: Community college graduation rates are typically quite low, and developmental mathematics enrollment and coursetaking patterns may constrain academic outcomes. To identify ways in which community college graduation rates may be improved, decision trees were utilized to examine the STEM coursetaking patterns of N = 5,065 students who matriculated in remedial mathematics. Methods: The research design was guided by Tinto’s academic and social integration framework, which provided an analytical lens for identifying how decision trees facilitate academic decision making when academic and social integration is limited. Decision trees identified course sequence rules to predict graduation, which can be used to formulate course pathways for community college advisors and their students. Results: Nine rules from the decision tree were identified, which could be used to advise community college students in coursetaking that aligns with career aspirations. The most important variable predicting graduation was completing College-Level Mathematics, which included Algebra II, Statistics, Precalculus, and survey mathematics courses. General education sciences courses such as Astronomy, Geology, Environmental Science, and Marine Biology were the most important science courses predicting graduation. Conclusions/Contributions: Results suggest the importance of College-Level Mathematics in providing the skills necessary for students to be successful in subsequent STEM coursework and persist to graduation. Designating specific academic pathways may improve social and academic integration and graduation rates, providing continuity as students work with different advisors to choose majors and plan course sequences. Transparent, accessible enrollment planning fosters programmatic consistency and student agency in selecting coursework that will maximize their success.

Success in Asynchronous Courses Through Increasing Student’s Social Presence

Online education has fundamentally altered the educational landscape, enhancing accessibility and flexibility for learners. However, a notable limitation of asynchronous learning modalities is the diminished interpersonal engagement inherent in traditional face-to-face pedagogical contexts. This empirical inquiry investigates the impact of deliberately integrating highly interactive instructional activities within online asynchronous developmental mathematics courses. Three principal thematic categories emerged through the iterative design process of these activities. Each category is delineated and exemplified, followed by exploring course policies conducive to student achievement in interactive learning contexts. Following a grounded theory approach, this study scrutinizes course outcomes alongside student and instructor evaluations at the semester’s end. Findings suggest incorporating social interactive activities yields positive effects on course outcomes.

The Role of Multiple Measures in Community College Developmental Mathematics

Objective: Developmental education provides postsecondary students requisite skills to take credit-bearing coursework. Yet, racial disparities exist in which students are most likely to be placed into developmental education. The present study investigates how multiple measures of students’ mathematics background ameliorate racial disparities in developmental math outcomes among U.S. community college students. Methods: The High School Longitudinal Study of 2009 was used to identify sample participants ( n = 3,650) who attended a 2-year postsecondary institution (community college) within 3 years of high school graduation. A series of logistic regression models were employed with developmental math outcomes as dependent variables predicted by multiple measures of student’s math background and demographic covariates. Results: Compared to White students, Black and Hispanic students had poorer developmental math outcomes; however, inclusion of multiple measures of high school math experiences reduced racial disparities. Multiple measures significantly reduced developmental math enrollment by 13% for Black students and 15% for Hispanic students, improved developmental math passing rates for Black students by 25% and Hispanic students by 25%, and improved passing rates for the first college-credit bearing math course for Hispanic students by 73%. Conclusion: The present study highlights how multiple measures of students’ math background might be an important lever for more racially-equitable placement processes. For Black and Hispanic students, the most influential high school measures were high school math GPA, highest high school math course, and math motivation. More work is needed to fine-tune how multiple measures can be used to increase access and equitable outcomes for students.

The Digital Shift: Is the Trend of Transferring Developmental Mathematics Coursework to Computerized Adaptive Learning Environment Effective?

The Digital Shift: Is the Trend of Transferring Developmental Mathematics Coursework to Computerized Adaptive Learning Environment Effective?

Post Developmental Mathematics: Experiences in College Algebra for STEM Students

Post Developmental Mathematics: Experiences in College Algebra for STEM Students

THE SYSTEM OF CORRECTIVE AND DEVELOPMENTAL EDUCATION OF MATHEMATICS FOR PRIMARY SCHOOL STUDENTS WITH INTELLECTUAL DEVELOPMENT DISABILITIES

The article discloses the problem of corrective and developmental mathematics education for primary school students with impaired intellectual development. It has been established that in the psychological and pedagogical literature there are quite a lot of studies devoted to the problem of failure of elementary school students. It was revealed that inclusive remedial and developmental education classes are one of the effective forms of differentiated education, which allows students with intellectual disabilities to learn the main school curriculum and creates favorable opportunities for their development. The current state of mathematics teaching methods in inclusive classes of remedial and developmental education is analyzed. It has been proven that special educational conditions must be created to learn mathematics. The methodical recommendations for conducting lessons and studying individual sections and topics are analyzed, the peculiarities of using methods and techniques are indicated. It was established that most of the recommendations are aimed only at children with mentalretardation, which are not always effective for all students in remedial and developmental classes.A system of corrective and developmental work in mathematics with students of elementary school of corrective and developmental education has been developed, which takes into account the state of knowledge, peculiarities of learning the material by students and strengthens the corrective and developmental potential of mathematics, which includes: changing the structure of the content of educational material (the presence of preparatory stages aimed at forming prerequisites for the successful learning of mathematics; a change in the sequence of learning due to the joint and simultaneous study of family sections and topics, as well as reciprocal actions); methods of consolidation of didactic units, presentation of information in a visual form, methods of comparison, generalization, induction, analogies; authorʼs complexes of corrective and developmental exercises on mathematical material, which allow solving educational, developmental and corrective tasks, which allows to increase the quality of knowledge and contributes to the improvement of studentsʼ cognitive activity. General recommendations for teaching mathematics in inclusive remedial and developmental classes for students with intellectual disabilities have been formulated. We see prospects for further research in the disclosure of teachersʼ readiness for activities aimed at primary school studentsʼ mastery of educational material in mathematics in inclusive classes of remedial and developmental education.
 Keywords: inclusive classes; remedial and developmental education; mathematics; elementary school students; academic failure; cognitive processes; mental activity; intellectual development disorders.

Latino Men’s Sense of Belonging Experiences in a Community College Developmental Mathematics Classroom

Using a phenomenological approach, we examined the sense of belonging for first-generation Latino men enrolled in a developmental mathematics course at a Hispanic-Serving Institution. The focus was on faculty-student interactions that fostered a sense of belonging. Data were collected through individual, semistructured interviews. Participants revealed specific instructor practices and qualities that created a sense of belonging. The results inform faculty on experiences that create a sense of belonging within a mathematics classroom.

Integrating learning support: the relationship between first-year seminar enrollment and student success in developmental mathematics

ABSTRACT Nearly half of all students in the United States are placed into at least one developmental course in college. Many of these students fail to complete developmental course sequences and persist to degree completion. First-Year Seminars are one of several high-impact practices associated with increased persistence, retention, and graduation rates of college students. Inverse probability of treatment weighting (IPTW) was used to explore the effect of concurrent first-year seminar enrolment on the academic achievement of students placed into developmental mathematics. Study results indicated that students who self-selected into a first-year seminar were more likely to earn a passing grade in their developmental mathematics course and have higher overall GPA. These results may inform strategies for integrating learning support with instruction for academically underprepared college students.

Illustrating Productive and Unproductive Cognitive Interactions in an Online Intermediate Algebra Course

Universities have drawn on an assortment of strategies to address the learning challenges and high attrition rates of developmental mathematics students. One of those strategies has been utilizing computer adaptive instruction (CAI) mathematics software. Reports about the efficacy of CAI vary from glowing to unfavorable. This article presents an instrumental case study, meaning that the purpose is to examine and describe a single case in depth to explain observed phenomena and illustrate a theory [Baxter and Jack 2008. Qualitative case study methodology: Study design and Implementation for novice researchers. The Qualitative Report. 14(4): 544–559]. The phenomena described in this article is productive and unproductive student interactions with a CAI environment. The vignettes in this article illustrate how students, even the same student, can have both productive and unproductive interactions with a CAI system. The vignettes are followed by recommendations for curriculum, instruction, assessment, and further research. Although these recommendations are gathered from observations of student interactions with CAI software in an asynchronous online Intermediate Algebra course, the observations have implications for different modes of instruction (e.g., synchronous online, flipped, hybrid, or face-to-face) that utilize online homework systems.

Rarely Discussed and Often Ignored: Classroom Factors Affecting Black Students’ Experiences in Developmental Mathematics

We present findings from a study about obstacles that Black students who succeeded in developmental mathematics in community college reported having endured in those mathematics classrooms. To understand the types of obstacles that can arise for students in these classrooms, we analyze data using two frameworks: mathematics identity and dimensions of mathematics classrooms. Study participants faced obstacles in three categories: (a) impressions of faculty’s instructional practices for problem solving; (b) negative race-related perceptions they believed classmates had about them; and (c) perceptions about instructors’ expectations. These findings contribute to literature on Black students’ progress in mathematics by identifying obstacles experienced by students who achieve in these courses and can also inform professional development learning for mathematics faculty.

Classroom Data Visualization: Tracking Individuals During Group-Centered Instruction

Understanding students’ participation in collaborative classroom settings is important in a variety of educational contexts, with implications for teaching, research, and equity. Using data from a group-centered developmental mathematics class, this research brief illustrates novel quantitative representations of students’ group participation and their instructor’s classroom activity. Presenting an overview of classroom activities based on audio data, the diagrams show a variety of patterns, including each group’s progression through assigned tasks, some students’ exclusion from discussions of those tasks, and the teacher’s patterns of interaction with groups. The representations provide new ways that researchers might approach and present multilayered classroom data.

High school transcript placement in developmental mathematics courses: A case study at one college

Historically, college students who require remediation in mathematics have been placed into developmental mathematics courses. Accurate placement is important for student success; inaccurate placement in a low-level course could lengthen a students’ time to degree completion. Placement policies have tended to focus on a high-stakes placement test, but more holistic approaches have been recommended. This study investigated success outcomes for students placed with a holistic approach of evaluating high school transcripts. Students who were placed into one of three developmental mathematics by their high school transcript at a suburban community college in North-eastern United States were selected for this study. A non-experimental, retrospective research study was conducted. Archival data of students who took a developmental mathematics course from fall 2015 through spring 2019 and had a high school transcript on file were chosen for this study. Findings from chi-square analyses indicated that high school transcripts that consider mathematics course grades are a viable placement option for developmental math courses, particularly the two lower-levels. However, lower than desired success rates suggest that placement is only the first step to increasing student achievement. A lack of high school transcripts suggests some students would prefer to take a placement test, particularly for students in the upper-level course on a college algebra path. A challenge for community college advisors will be creating an equitable placement policy for students who do not have a recent high school transcript.

College Developmental Mathematics Students' Understanding of Fraction Operations

Students enrolled in post-secondary developmental mathematics courses hold mathematical misunderstandings that begin prior to their college careers. Specifically, these students struggle with the conceptual understanding related to fractions, ratios, and proportions. The Common Core State Standards in Mathematics outline standards for K-12 mathematics education. Standards for fractions, ratios, and proportions are found in grades 3-7. Through a research instrument, collegiate developmental mathematics students were investigated regarding their understanding of these standards. It was determined that participants showed evidence of limited knowledge of the examined areas involving fractions, ratios, and proportions. Because it seems that this lack of understanding is rooted early in their educational careers, and is continued throughout students' academic careers, it is hoped that this work can be a starting point for future work in this field that may apply to investigating ways to bridge these gaps in mathematical understanding.

A Socio-Ecological Outcome Investigation of the Student Engagement, Achievement, and Satisfaction of Latino Men in Community College Developmental Mathematics

ABSTRACT To understand how to best support Latino male community college students, we used the Socio-Ecological Outcomes (SEO) model to examine factors associated with their achievement and college satisfaction. Specifically, we leveraged data from the Community College Survey of Student Engagement (CCSSE) and situated our study in developmental mathematics, given its potentially gatekeeping effects in postsecondary education. In a subsample of Latino men in community college developmental mathematics courses (N = 1,140), we conducted two regression models with GPA and satisfaction as outcomes and various predictors from the SEO model such as background, environmental, academic, and campus factors. Results indicated that academic preparedness, being of older age, college support from friends and family, and use of academic-related resources were positive predictors for both outcomes. Sense of belonging was positively associated with college satisfaction. Conclusions and implications for how CCSSE variables can be used in conjunction with the SEO model are discussed.

Benny, Barbara, and the Ethics of EdTech

Erlwanger (1973) shook the mathematics education world when he introduced Benny, a student who successfully worked through a behavioristic curriculum. Erlwanger showed how far removed Benny’s understanding of mathematics was from expectations. Erlwanger’s legacy is the basis for this comparative case study which explores students’ actions in the modern, in-class computer-centered emporium classroom. Many striking similarities are found between Pearson’s MyMathLabs (MML) and Benny’s Individually Prescribed Instruction curriculum. In this case study we meet Barbara, a student who succeeds in MML but shows little understanding of mathematical concepts and demonstrates that the legacy of Benny is his continued appearance in our current students. However, what differentiates Benny and Barbara is more than time; it’s the inequities resulting from imposing a pedagogy with well-known problematic characteristics to developmental mathematics students. Most of these developmental students are members of marginalized communities. As such, the social justice and ethical implications of using such a course structure are explored.

A Self-Regulated Learning and Formative Assessment Program to Improve Student Achievement in Developmental Mathematics: Shifting from Paper and Pencil to Computerization

A Self-Regulated Learning and Formative Assessment Program to Improve Student Achievement in Developmental Mathematics: Shifting from Paper and Pencil to Computerization

A Numerical Indicator of Student Cognitive Engagement and Mathematical Growth

We discuss and examine a numerical indicator—the individual gain—of students’ engagement and mathematical growth in relation to an instructor’s course aims and goals. The individual gain statistic assesses the fractional amount an individual student improves initial-test to final-test. We argue that an initial-test score and a final-test score, if the two tests are related to each other and to a course focus, can provide a numerical indication of a student’s engagement with the goals and aims of the course and the extent to which a student was prepared to work toward those goals. Results on the distribution of individual gain for students in two-year college developmental mathematics courses and in sections of a course for pre-service elementary teachers are discussed. We detail and discuss advantages of the full distribution of individual gain, particularly for allowing statistical inference for differences, compared with Richard Hake’s use of mean gain of reform classes in undergraduate physics. Other instructional benefits of using the gain statistic to examine distribution of individual student gains include: a pre-test formative assessment at beginning of instruction, providing an instructor with data for specific, targeted remediation; and planning information that informs an instructor for the effectiveness of instruction for students in that cohort.

A Comparative Study of Developmental Mathematics Pass Rates for Two Student Groups: Emporium Classes and Traditional Lecture-based Classes

Since the turn of the 21st century, the emporium model has become a popular choice for colleges and universities to reform developmental mathematics. The purpose of this study is to determine overall how successful Northeast Metro College (NMC)’s emporium developmental mathematics program is as compared to its traditional lecture-based program by comparing these two programs’ student pass rates in developmental courses. This research is a non-experimental, secondary data quantitative analysis study with nonrandom convenience samples. The findings indicate that generally emporium classes prepare students for passing developmental mathematics more successfully than traditional lecture-based classes do.

Agreement between Students’ and Their Instructors’ Perceived Use of Good Practices in Undergraduate Education: Self-Reflections in Developmental Mathematics Classrooms

Best practices in undergraduate classrooms have been identified. However research on the congruence between practices of faculty members and their students is lacking. In this study, confidence intervals were used as a mechanism to compare responses of three developmental mathematics instructors and their students on a subset of items from the Seven Principles Faculty and Student Inventories. Patterns observed in the confidence intervals indicated that, among the items studied, (a) there were consistent behaviors among students across classes and (b) students’ and instructors’ perceptions were not in agreement on several items. Future studies could compare all items or conduct observations to measure congruency.

An Investigation of Differences in Student Success and Persistence Rates by Course Modality

Emporium courses have been offered as an option to reduce the amount of time students spend in developmental mathematics courses. This study investigated differences in achievement and persistence in mathematics by course modality for students enrolled in developmental mathematics at a suburban community college in the Northeast United States from fall 2015 through spring 2019. Statistically significant differences existed in final exam score and course grades by course level. For the upper two developmental mathematics courses, achievement measures in emporium courses were comparable to face-to-face courses. Thus, an emporium model that is designed to provide a semi-structured schedule, prompt feedback, and frequent interactions with tutors and faculty is a viable option for middle- and upper-level courses. The emporium modality did not appear to benefit students placed into the lowest level course (i.e., pre-algebra) as grades and persistence rates were lower compared to face-to-face courses. Online course modality was not the best option across all course levels. The results of this study may have implications for post-secondary institutions that want to begin offering developmental mathematics courses in multiple modalities.