College-level 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.

A Research Introduction for Early College Students: Based on the OSU–HBCU Pilot Project

We joined an initiative to engage faculty and undergraduate students in research by scheduling regular early college-level mathematics research presentations with pre- and post-lecture exercises. While our program featured six talks that were predominantly in the mathematical biosciences, the concept of creating themed topics for presentations can be extended to other areas of mathematical research, and the length of the program can also be scaled. This article discusses three of the presentations, including QR codes to access their recordings. The purpose of this article is to present the materials of the talks from this initiative and how faculty members can use the materials for potential explorations with students. The hope is the audience may use these, as presented, for study with students, with minimal start-up investment and to use this as a model for future undergraduate research efforts.

The Application of Geogebra in Teaching Open and Inner Sets in Metric Spaces

Topology of metric spaces is a standard and important course at the college level mathematics studied at University of Mumbai. As the course is abstract, students feel it as a difficult course and hence tend to develop a fear. In this paper, we will see how to use the open-source software GeoGebra to teach the concepts of this course effectively. We will concentrate on the topics of open set and interior set. GeoGebra applets are created for various examples in different metric spaces to teach these concepts efficiently.

The meaning landscape of the concept of the total derivative in multivariable real analysis textbooks: an analysis based on a new model of meaning

AbstractIn this paper, we propose a novel conceptual framework tailored for modeling the meaning of mathematical concepts in university-level mathematics, addressing their rigorous nature and their relationships with related concepts as well as interpretations in various contexts. Within this framework, we present a model of meaning for the concepts of total differentiability and total derivative that provides a variety of possible interpretations and aspects. We then use the proposed model of meaning as a tool for analyzing three different textbooks for mathematics majors on the topic of multidimensional differentiability. Our paper is an example of a subject matter analysis of a topic in university mathematics carried out in a structured way. The model of meaning for total differentiability presented in this paper could inspire course design and analysis including the design of assignments and assessments for students. Moreover, it could serve as a valuable research tool for further analyses. For example, it could be used as a framework for analyzing courses taught or as a basis for developing a test instrument to assess students’ understanding. With our textbook analysis, we begin to examine the landscape of textbooks regarding differentiability concepts in the multidimensional case, shedding light on the diversity of meaning facets that are covered in the textbooks. These results could be useful for guiding instructors and learners in selecting and using textbooks for teaching and learning based on their respective needs.

Prevailing Themes Across Corequisite Mathematics Courses: A Systematic Review

Adopting corequisite mathematics models to accelerate students’ completion of their introductory college-level mathematics course in their first year of college is prevalent across higher education institutions. This systematic review demonstrates the known research, evidence, and diversity of implemented corequisite mathematics models for prevailing themes across peer-reviewed articles.

Capacity Building in Mathematics and Statistics Learning Support in Norway and the Czech Republic (MSLS Net)

This report describes the final meeting of the project "Capacity Building in Mathematics and Statistics Learning Support in Norway and the Czech Republic (MSLS Net)" held at the Tomas Bata University in Zlín, Czech Republic (June 12-14, 2023). Provision of mathematics and statistics learning support (MSLS) is developing rapidly in many parts of the world and activity in Norway and the Czech Republic has been accelerated significantly through this EEA Grants funded project. Representatives of each of the five partner institutions worked on creating a summary of good practices in tutor training, designing learning resources, and in delivering, monitoring and evaluation of mathematics and statistics support. Provision varied considerably across the institutions and the centres represented demonstrated diverse and innovative ways in which mathematics support is evolving. Outputs from the project include a Handbook on good practice and a booklet concerned with mathematics support centre tutor training, including pedagogic training and learning resources for the development of the tutors as described below. Finally, consideration turned to the value of establishing a professional network to continue this important work. The report will be relevant to other international groups interested in working in university level mathematics and statistics support.

Sustainability of the 4.0 Revolution in University-Level Mathematics Classrooms: Disruptions, Adaptability

Sustainability of the 4.0 Revolution in University-Level Mathematics Classrooms: Disruptions, Adaptability

Changing Mathematical Paradigms at the University Level: Feedback from a Flipped Classroom at a Peruvian University

The university-level mathematics teaching adopted by many professors is still a traditional classroom, and many students’ perception of mathematics is that it is a complicated subject. The operationality of the flipped classroom proposal implemented at a university has a potential that can be used to change the perception that university students and teachers have towards the mathematics course, as well as to change the methodology of many teachers on how they teach their courses in the classroom. This research is the result of the implementation of the flipped classroom methodology in the basic mathematics course that is part of the professional careers of the engineering faculty of a Peruvian university. The aim of this study was to analyze the impact of applying the flipped classroom on academic results and attitudes towards mathematics, with an experimental group of 227 students and a control group of 215 students. The academic results were measured at each of the stages indicated in the course syllabus, T1, partial exam, T2 and final exam; attitudes towards mathematics were also assessed at cognitive, procedural and affective levels at the end of the university semester. The Kolmogorov-Smirnov normality test was applied and yielded a value of p = 0.00, indicating that the grades obtained by the students did not follow a normal distribution. With the data obtained, the Mann-Whitney U test was performed, obtaining a p = 0.00 value (α = 0,052 tails). p < α makes us conclude that there are statistically significant differences between the scores of the experimental group compared to the control group. The results show a significant improvement in the academic performance and positive attitudes of students who took the course using the flipped classroom compared to those who did not use this methodology.

Demographic Factors Affecting the Job Satisfaction of Mathematics Teachers: A Case Study of Kathmandu Municipality

Job satisfaction is a crucial factor for professionals. Job satisfaction among teachers reflects their high levels of professional motivation. This study investigated the effect of demographic factors on job satisfaction among secondary mathematics teachers in the Kathmandu Municipality. In quantitative research, a cross-sectional survey research design was used in this study. The data was collected through a validated structural questionnaire, which consisted of ten items on job satisfaction and eight demographic variables. The structural questionnaire was administered to a sample of 136 mathematics teachers over the course of one month (17 August–16 September). Data were entered in SPSS Version 26, and frequency, percentage, and multiple linear regression were used in the analysis of the data. The results of this study revealed that there is no statistically significant effect of demographic variables on the job satisfaction of mathematics teachers. Based on the findings of this study, I contend that demographic variables have no effect on job satisfaction among mathematics teachers. The study's limitations include the fact that demographic variables (gender, age, school type, school area, teaching experiences, educational level, and job position) explained only 6% of the variation in job satisfaction. Future research should be done on a larger scale to increase the number of demographic variables and sample sizes in other parts of Nepal and by other subjects' teachers. Similar studies could be done with basic-level and university-level mathematics teachers in Nepal.

Sticking together in a world full of sharks: pre-service teachers’ perspectives of mathematics content courses

Secondary mathematics pre-service teachers (PSTs) are required to take university-level mathematics content courses to develop their mathematical content knowledge. Although PSTs’ experiences as students play a major role in the types of teachers they become, there is limited research investigating the experiences of PSTs engaging in these courses. Thus, our study used a series of semi-structured interviews to provide first-hand accounts of PSTs’ experiences. Findings suggest that PSTs experienced a range of challenges, including difficulties connecting with and understanding course content, and being ignored and dismissed by mathematics instructors. To cope with these challenges, PSTs became reflective practitioners and considered how their experiences in these courses applied to their learning as future teachers. PSTs also developed a community with each other that grew out of needing support with mathematical content, but evolved into collegial friendships. While PSTs were able to find positive features within negative experiences, this study highlights the need to understand PSTs’ experiences in these courses so that effective improvements can be made.

Critical Conscience for Construction of Knowledge in Mathematics Education

The process of constructing knowledge in mathematics education is critical in developing it as a discipline with an impact on the field of teaching, learning, and assessment based on theory and practice. How do mathematics educators perceive the processes of knowledge construction in mathematics education? It may have an implication in the methods of teaching, learning, and researching to enrich this discipline. In this context, the purpose of this study was to explore the Nepali mathematics educators’ perspectives on critical conscience for the construction of knowledge in mathematics education. The research participants were five university-level mathematics educators who participated in in-depth interviews on critical conscience in mathematics education. The qualitative thematic analysis of the interview data unveiled four major thematic groups in terms of four idiographic passes– culture, communication, collaboration, and context (4Cs); discourse, dedication, deliberation, and development (4Ds); equity, engagement, elaboration, and extension (4Es); and formation, fusion, frame of reference, and faculty of cognition (4Fs). The thematic interpretations of critical conscience may portray the paradigmatic assumptions of ontological, epistemological, and axiological primacy of mathematics education from the participants’ views. Policy and pedagogical implications of the themes have been discussed.

A neural network solves, explains, and generates university math problems by program synthesis and few-shot learning at human level

We demonstrate that a neural network pretrained on text and fine-tuned on code solves mathematics course problems, explains solutions, and generates questions at a human level. We automatically synthesize programs using few-shot learning and OpenAI's Codex transformer and execute them to solve course problems at 81% automatic accuracy. We curate a dataset of questions from Massachusetts Institute of Technology (MIT)'s largest mathematics courses (Single Variable and Multivariable Calculus, Differential Equations, Introduction to Probability and Statistics, Linear Algebra, and Mathematics for Computer Science) and Columbia University's Computational Linear Algebra. We solve questions from a MATH dataset (on Prealgebra, Algebra, Counting and Probability, Intermediate Algebra, Number Theory, and Precalculus), the latest benchmark of advanced mathematics problems designed to assess mathematical reasoning. We randomly sample questions and generate solutions with multiple modalities, including numbers, equations, and plots. The latest GPT-3 language model pretrained on text automatically solves only 18.8% of these university questions using zero-shot learning and 30.8% using few-shot learning and the most recent chain of thought prompting. In contrast, program synthesis with few-shot learning using Codex fine-tuned on code generates programs that automatically solve 81% of these questions. Our approach improves the previous state-of-the-art automatic solution accuracy on the benchmark topics from 8.8 to 81.1%. We perform a survey to evaluate the quality and difficulty of generated questions. This work automatically solves university-level mathematics course questions at a human level and explains and generates university-level mathematics course questions at scale, a milestone for higher education.

The three worlds and two sides of mathematics and a visual construction for a continuous nowhere differentiable function

A rigorous and axiomatic-deductive approach is emphasized in teaching mathematics at university-level. Therefore, the secondary-tertiary transition includes a major change in mathematical thinking. One viewpoint to examine such elements of mathematical thinking is David Tall’s framework of the three worlds of mathematics. Tall’s framework describes the aspects and the development of mathematical thinking from early childhood to university-level mathematics. In this theoretical article, we further elaborate Tall’s framework. First, we present a division between the subjective-social and objective sides of mathematics. Then, we combine Tall’s distinction to ours and present a framework of six dimensions of mathematics. We demonstrate this framework by discussion on the definition of continuity and by presenting a visual construction of a nowhere differentiable function and analyzing the way in which this construction is communicated visually. In this connection, we discuss the importance to distinguish the subjective-social from the objective side of mathematics. We argue that the framework presented in this paper can be useful in developing mathematics teaching at all levels and can be applied in educational research to analyze mathematical communication in authentic situations.

Tales of research initiatives on university-level mathematics and primary historical sources

Tales of research initiatives on university-level mathematics and primary historical sources

Evaluating the use of e-assessment in a first-year pure mathematics module

Abstract This article presents the findings of a case study that introduced online quizzes as a form of assessment in pure mathematics. Rather than being designed as an assessment of learning, these quizzes were designed to be an assessment for learning; they aimed to academically support students in their transition from A-Level mathematics to university-level pure mathematics by providing an extrinsic motivation to engage them with their learning material early on and to emphasize the small details within proofs, such as defining notation, which are not necessarily emphasized by written homework assignments. The results obtained during the 2-year study using online quizzes show e-assessment to be a powerful complementary tool to traditional written homework assignments.

Co-requisite Remediation: An Access Ramp for College Completion

ABSTRACT Higher education’s interest in remedial college coursework and its bumpy impact on student success drove this collaboration between the mathematics department and institutional research at a small, private 4-year university. For first-time freshmen needing math remediation, national research shows that these students struggle with earning required college math credits compared with non-remedial students. A major roadblock for them is that they often do not earn credit towards their degree for remedial courses, further challenging progression through their major. This research describes the impact of one institution’s curricular innovation to prepare students more quickly for college-level math and have some of that credit count toward graduation, thus meeting the institution’s Liberal Arts Core requirement. The researchers examine a combined cohort of first-year students to determine if there is a relationship between this co-requisite math course and higher retention and graduation rates compared to other traditional types of mathematics remediation. Students taking the co-requisite remedial class retained and graduated at higher rates and were also more successful in subsequent college-level mathematics classes.

Baseball as a Quantitative Reasoning Course

This paper describes a course designed to introduce students to mathematical thinking and a variety of lower level mathematics topics using baseball while satisfying the goals of quantitative reasoning. We give suggestions for sources, topics, techniques, and examples so any mathematics teacher can design such a course to fit their needs. The course assumes no previous college level mathematics and includes statistics, linear functions, modeling, and simulation.

University-level Mathematics Pre-enrollment Education Combining Individual and Group Works in a Perfectly Distributed Asynchronous Environment

University-level Mathematics Pre-enrollment Education Combining Individual and Group Works in a Perfectly Distributed Asynchronous Environment

ALGEBRA DERSİ AKADEMİK BAŞARISI İLE PSİKOSOSYAL DEĞİŞKENLER ARASINDAKİ YORDAMSAL İLİŞKİLERİN İNCELENMESİ

The aim of this study is to examine the procedural relationship between the psychosocial factors of mathematics learning such as attitudes, motivation and satisfaction and academic achievement in redesigned college-level algebra course sections. Evaluation reports on the redesigned courses show that they have achieved a level of academic achievement equivalent to and / or better than traditionally taught courses, including university-level mathematics introductory courses. However, the reasons for equal or higher academic achievement are not fully documented in the literature. In this context, the academic success of the university-level algebra course designed using the Emporium model was chosen as the focus of this research study. In this manuscript, in addition to the psychosocial factors of mathematics learning, mathematics achievement in the context of university algebra was also examined. The data related to the psychosocial variables were obtained from a likert scale developed by the researcher, and academic achievement data from the final exam grades of the algebra course. Hierarchical multiple regression analysis was used to analyze the collected data. The results of the study indicaed that satisfaction from mathematics teaching was the only significant predictor of mathematics achievement in college-level algebra; learner motivation and satisfaction were determined as important predictors of attitude towards mathematics, and attitude towards mathematics played the role of mediating variable in the relationship between student satisfaction and motivation in introductory level redesigned university algebra courses.

Comparing Placement Policies at a Four-Year Institution

Placement policies are intended to match students with appropriate courses in order to improve student success, but how do you evaluate these policies? In this article, we evaluate four placement policies at Towson University by considering three categories of outcomes: long-term outcomes such as graduation and retention rates, short-term or discipline-specific outcomes including pass rates in one's first mathematics course, and access-related outcomes including the proportion of students enrolling in college-level mathematics courses. We illustrate why these outcomes are not informative for evaluating placement policies and discuss the need for a new measure to evaluate placement policies.