First-year Mathematics Courses Research Articles

Examining the reciprocal influence between undergraduate students’ self-regulation and approaches to learning

ABSTRACT This study explores the relationship between approaches to learning and self-regulation of learning. Approaches to learning characterise students’ intentions and strategies regarding learning and studying, divided into deep and surface approaches together with organised studying. Self-regulation of learning is a process of monitoring and directing one’s affect and behaviour in learning. It is known that self-regulation correlates with approaches to learning, but the direction of influence has not been demonstrated empirically. Measurements were taken in a first-year mathematics course on 103 Finnish undergraduates. Cross-lagged panel analysis was used to study the direction of time-lagged influence. The results revealed that significant influence existed from self-regulation to deep approach and organised studying, and from lack of regulation and external regulation to surface approach. Based on the results, we conclude that it is important for researchers and practitioners to take self-regulation into consideration when measuring approaches to learning or designing interventions.

Cultural Transitions in Mathematical Discourse: Unveiling Mathematical Writing Hurdles during the Rite of Passage

This qualitative case study delves into the intricate landscape of mathematical writing challenges faced by first-year university students undergoing the critical transition from school-level to university-level mathematical discourse. Conducted at a prominent South African university, the research, employing a purposive sampling technique, engaged thirty first-year mathematics students. Guided by the community of practice theory by Lave and Wenger, alongside van Gennep’s rite of passage analytical lens, the study sought answers to the question: What are the mathematical writing challenges encountered by first-year university students during their rite of passage period? Thematic analysis, informed by Adu's (2019) coding framework, was utilized to systematically examine common themes and patterns within the qualitative data. The findings illuminated key hurdles during this transitional phase, prominently including the inconsistency in working with mathematical notations, erroneous use of universal and existential quantifiers, and a notable confusion between the acts of illustrating and proving in mathematical contexts. In response to these challenges, the study advocates for the explicit incorporation of mathematical writing instruction to scaffold students during this rite of passage. Furthermore, it recommends a shift in the emphasis of first-year mathematics courses—suggesting a redirection from a content-centric approach to one that prioritizes the cultivation of students' new identities. This entails focused attention on teaching the customs, traditions, and adept ways of constructing and articulating mathematical proofs in the university context. The implications of this study extend beyond the immediate challenges identified, offering actionable recommendations to enhance the pedagogical strategies employed in the crucial transition period for first-year mathematics students.

Impact of the Pandemic on the University of Oklahoma’s STEM Mathematics Pathway

Using an organizational development framework, we consider different aspects related to first-year mathematics courses leading to STEM fields. We use the Weisbord six-box model to describe how the pre-pandemic structures and mechanisms helped our instructors weather COVID-19 and how changes were implemented to cope with the challenges faced. Certain practices adopted at the height of the pandemic are still in place, while others are not. We share this information as well as some of the innovations that were used to build relationships and provide informal rewards, two key aspects that are often overlooked. We also share some of the documented trends, continued challenges, and lessons learned.

How Chinese Undergraduate Students’ Perceptions of Assessment for Learning Influence Their Responsibility for First-Year Mathematics Courses

Assessment for learning (AFL) has been associated with curriculum and teaching reform for the past three decades. However, studies on undergraduate students’ perceptions of their mathematics teachers’ AFL practices are still very limited in the Chinese higher education context. This quantitative study investigated three independent variables—teacher formal feedback and support, interactive dialog and peer collaboration, and learning-oriented assessment—that influence undergraduate students’ ability to take responsibility for their learning through the mediation of the factor of active engagement with subject matter in first-year mathematics courses. One hundred and sixty-eight students from a Chinese “double-first-class” university were recruited to provide valid questionnaire data using the convenience sampling method. Partial least-squares structural equation modeling (PLS-SEM) was used to analyze the data. The results showed that interactive dialog and peer collaboration, as well as learning-oriented assessment, have a direct effect on students’ active engagement with the subject matter and an indirect effect on undergraduate students taking responsibility for their learning in first-year mathematics courses. In addition, learning-oriented assessment was the biggest factor influencing undergraduate students’ ability to take responsibility for their learning in first-year mathematics courses. This study contributes by developing a conceptual model and providing new insights into Chinese higher education sectors on factors that can improve undergraduate students’ ability to take responsibility for their learning.

Transforming mathematical identity: changes in one international student’s positioning during first-year mathematics tutorials

In many countries, international students form a distinct cohort in first-year mathematics courses. For these students, the transition to university mathematics may demand significant adaptation. A research-based understanding of their experiences would enable host universities to provide effective support as they transition from school mathematics in their home countries to a foreign university context. In this study we analyse four episodes in which an international student from China interacted with the tutor during collaborative first-year tutorials at a New Zealand university. The first two episodes occurred near the start of the semester, and the others towards the end. The analysis reveals changes in the student’s positioning of herself over successive episodes as she embraced local classroom norms. We propose that her positioning shift facilitated a process through which the tutor was able to support her mathematics learning more effectively.

Predicting Student Success in Co-remediated General Education Mathematics Courses at a Large Urban Public University

Placement and support of students in first-year mathematics courses at institutions of higher education has long been a consequential issue. In a bid to address it, many systems and institutions of higher learning have elected to implement a co-remediation framework in place of pre-remediation, due in large part to the prohibitive cost of the latter, both in terms of financial resource, as well as student academic progress. Accompanying this evolution has been the expansion of the introductory mathematics curriculum beyond algebra to include statistics and quantitative reasoning. The present study discusses three distinct introductory mathematics courses at a large urban public M.S. granting institution in the U.S., with the goal of identifying the characteristics that correlate with success in each. Conditional probability and non-completion rate analyses were implemented to compare student performance in each course. Predictive models were then trained and validated, building insight concerning the differential relationships of demographic and academic covariates with course completion.

An effective method of assessment for first-year mathematics in an Australian university

ABSTRACT A carefully constructed method of assessment using short, formative, invigilated in-tutorial quizzes is investigated to see how successful this method is compared to previous assessment tasks. We look at whether student engagement increased, given that students who enter university often face issues with the transition from school, and engagement is a factor affecting their success. First-year mathematics courses see a wide variety of students from various mathematical backgrounds who may not know or have little experience with, how to approach their tertiary study. This paper presents a way of using assessment to engage and motivate students who are studying first-year mathematics at university. Assessment is an essential feature of student learning and it is important to use it effectively to benefit the education and learning practices of students. Our study focuses on a particular method of assessment which we found to be successful. We will introduce this method and analyse its effectiveness using both quantitative and qualitative data obtained from a cohort of students enrolled in a large first-year mathematics unit in an Australian university. Furthermore, we give the academic a list of guidelines should they wish to adapt this assessment into their own teaching practices.

An analysis of the relationship between high-school pre-calculus and university calculus grades

First-year mathematics instructors at universities across North America and the globe have been noticing a decline in the mathematics skills and preparation of their incoming students, who have been failing out of first-year mathematics courses at alarming rates. Though some universities have implemented placement or diagnostic tests to measure students’ preparedness, many still use high school grades as the only indicator of readiness for university mathematics. However, researchers have questioned how effective these high school grades are at predicting success in university mathematics classes due to factors such as mis-aligned teaching methods, curriculum, and grade inflation. This study analyzes the relationship between grade 12 Pre-Calculus grades and first year university Calculus grades at a large Canadian university over the period from 2001–2015 in an attempt to quantify previous research in a large-scale, longitudinal manner. Results show that there is a significant disconnect between these grades, that the disconnect has been growing over time, and that it is is quite significant for students who are not performing well at the Calculus level. Recommendations moving forward include the implementation of placement examination in a wide-scale manner, and increased communication and collaboration between K-12 and university mathematics educators and administrators.

Reforming the Teaching and Learning of Foundational Mathematics Courses: An Investigation into the Status Quo of Teaching, Feedback Delivery, and Assessment in a First-Year Calculus Course

Several universities are witnessing an increase in students’ enrolment in mathematics-intensive programmes over the last decades. This increase has come with the price of high failure rates in foundational mathematics courses, which poses challenges to mathematics teaching and learning in higher education. It is therefore inevitable, for some universities, to transform the teaching and learning of mathematics to more student-centred approaches that engage the students mathematically and enhance their success rates. We approach this transformative effort by investigating students’ perception of teaching, feedback, and assessment as a first step in reforming the teaching of a first-year mathematics course at a Norwegian university. The results of both quantitative and qualitative analyses of the data generated using a questionnaire from 107 (80 men) engineering students show that the status quo of teachings offers little support for learning. The teaching is dominated by teacher-led instruction, note-taking, and large pieces of proof which make learning difficult for students during class activities. The results also show that the current structure of the course offers limited formative feedback to students and that the assessment tasks require restructuring to capture students’ time and effort. We discuss the implications of these findings and make some recommendations for improvement.

Undergraduate and Instructor Perspectives on Learning in First-Year Mathematics Courses in the United States: A Case Study in Calculus

This paper reports on post-secondary student and instructor perceptions of teaching practices they see as supporting student success in calculus. The study used a mixed-methods design, combining survey, classroom observation, and interviews. Analysis identified two central clusters of survey response, each aligned with one of two well-specified aspects of self-regulation: coping intention or learning intention. In the coping intention factor, students sought supports to reduce uncertainty, such as having precise instructions and predictable question types on tests. Interview analysis offered insight into ways of coping in situations that students experienced as high-stakes—where the goal of self-regulation was to survive. The learning intention factor included student reports on knowledge of the prerequisite mathematics for the course and assertions that they had responsibility for their learning (rather than assigning it to the instructor). Interviews shed light on how students managed responsibility and motivation in the context of being challenged in mathematics learning. Implications for future research and for instruction attend to the complex dynamics of cognition, affect, motivation, and regulation in the teaching and learning of calculus.

Personalised Emails in First-Year Mathematics: Exploring a Scalable Strategy for Improving Student Experiences and Outcomes

Widening participation initiatives in higher education have grown overall student numbers while also increasing the diversity of student cohorts. Consequently, enhancing student experiences and outcomes has become increasingly challenging. This study implemented personalised emails in two first-year mathematics courses as a scalable strategy for supporting students with diverse needs. Impact on student experience and outcomes was assessed through surveying and statistical comparisons to previous cohorts. It was found that students perceived the personalised emails favourably and believed the intervention would contribute to them achieving better grades. This translated to a statistically significant improvement in both student experience and academic performance in one of the courses. The results imply that personalised emails are well-suited to courses taken in students’ first semesters of university study, aiding those transitioning to the higher education environment by fostering feelings of belonging, supporting effective engagement, and easing navigation of university systems and processes.

The Impact of a Mathematics Bridging Intervention on the Inclusivity of a University Economics Programme

The inclusivity of all students in the University Economics programme is in danger due to a high failure rate in the first-year mathematics course. This study investigates whether participation in a bridging course, and what aspects of it, can contribute to equal opportunities and increased inclusivity in the Mathematics for Economists course, and henceforth reduce the failure rate. It adds to the meager European literature on remedial course effectiveness. Through the use of ordinary least square regression analyses, a significant positive effect of participation in the bridging course was found for the student group as a whole. Furthermore, the results indicated that participation was particularly valuable for the least mathematically prepared students.

Basic mental models of integrals: theoretical conception, development of a test instrument, and first results

A basic mental model (BMM—in German ‘Grundvorstellung’) of a mathematical concept is a content-related interpretation that gives meaning to this concept. This paper defines normative and individual BMMs and concretizes them using the integral as an example. Four BMMs are developed about the concept of definite integral, sometimes used in specific teaching approaches: the BMMs of area, reconstruction, average, and accumulation. Based on theoretical work, in this paper we ask how these BMMs could be identified empirically. A test instrument was developed, piloted, validated and applied with 428 students in first-year mathematics courses. The test results show that the four normative BMMs of the integral can be detected and separated empirically. Moreover, the results allow a comparison of the existing individual BMMs and the requested normative BMMs. Consequences for future developments are discussed.

Assessing and Modeling Student Academic Practices and Performance in First-Year Mathematics Courses in Higher Education

Objectives: This research brief explores literature addressing developmental education to identify successful interventions in first-year math courses in higher education. Our goal is to describe the relationship between students’ academic practices and their final course grade in their first-year math courses.
 Method: Data on 3,249 students have been gathered and analyzed using descriptive statistics and predicative analytics. We describe the Math program, which includes a supplemental support component, and the environment under which it was created. We then examine the behavior between students’ participation in supplemental support and their academic performance.
 Results: We used classification and regression tree algorithms to obtain a model that gave us data-driven guidelines to aid with future student interventions and success in their first-year math courses.
 Conclusions: Students’ fulfillment of the supplemental support requirements by specified deadlines is a key predictor of students’ midterm and final course grades. 
 Implications for Theory and/or Practice: This work provides a roadmap for student interventions and increasing student success with first-year mathematics courses.
 Keywords: First-year mathematics courses, supplemental support, higher education

Impact of first-year mathematics study groups on the retention and graduation of engineering students

ABSTRACTMany interventions have been proposed to improve the retention and graduation rates of engineering students. One such intervention is to use study groups for first-year college students; such groups provide a structured environment in which the students can learn course material from each other outside of class and can provide the students with a sense of community. In this paper, we report on the impacts fostered by study groups in first-year mathematics courses on the odds of retaining and graduating engineering students. Students who participated in the study groups are compared to students of similar academic preparation who did not participate in such groups. It is found that student participation in study groups is significantly associated with the higher odds of being retained in engineering studies through the first 3 years of college. The results reported here are not as certain for the effect of study group participation on 5-year graduation odds for engineering students and some possible reasons for this are discussed.

Factors Affecting the International Students Success in a First-Year Mathematics Courses at ZUST

Factors Affecting the International Students Success in a First-Year Mathematics Courses at ZUST

Rethinking course structure: increased participation and persistence in introductory post-secondary mathematics courses

High failure and withdrawal rates in introductory post-secondary mathematics courses are a problem locally, nationally, and internationally. This leads to first-year mathematics courses creating a closed door, or a barrier, to further study of mathematics, of STEM disciplines, and in University as a whole. In this article, the authors describe the implementation of a modified course structure in a first-year undergraduate mathematics course. The new structure makes use of a combination of mastery learning strategies together with the beneficial effects of small class sizes to address the issues of historically high failure and withdrawal rates and low grade-point averages. Results show that careful planning of the structure of a course can have a positive effect on student success, and thus on attitude towards mathematics.

Factors affecting student success in a first-year mathematics course: a South African experience

In spite of sustained efforts tertiary institutions implement to try and improve student academic performance, the number of students succeeding in first-year mathematics courses remains disturbingly low. For most students, the gap between their mathematical capability and the competencies they are expected and need to develop to function effectively in these courses persists even after course instruction. In this study, an instrument for identifying and examining factors affecting student performance and success in a first-year Mathematics university course was developed and administered to 86 students. The overall Cronbach's Alpha coefficient for the questionnaire was found to be 0.916. Having identified variables from prior research known to affect student performance, factor analysis was used to identify variables exhibiting the greatest impact on student performance. The variables included prior academic knowledge, workload, student approaches to learning, assessment, student support teaching quality, methods and resources. From the analysis, students' perceptions of their workload emerged as the factor having the greatest impact on student's performance, followed by the matriculation examination score. The findings are discussed and strategies that can be used to improve teaching and contribute to student success in a first-year mathematics course in a South African context are presented.

A Holistic Approach to Promote Student Engagement and Learning in a First-year Mathematics Course

Agricultural mathematics was first introduced in 2008 to address the deficiencies in mathematics education of incoming agricultural students at the University of Queensland—Gatton Campus, Australia. The course is offered to first-year Bachelor of Applied Science students enrolled in a number of agricultural disciplines, and is compulsory for all those students who have not already passed senior mathematics in high school. A number of successful teaching and learning strategies were incorporated into the presentation of this course to address, not only the social isolation common to the experience of many first-year students, but also the difficulties posed by the inadequate mathematical backgrounds and, consequently, mathematical phobias many students bring to their agricultural studies. Strategies included interactive lectures using tablet personal computers, student response systems to promote student-lecturer interactions in the classroom, group work/cooperative learning to promote student-student interaction, challenging learning activities to engage students in problem solving related to agricultural disciplines, and provision of recorded interactive lectures for flexible learning. The impact of this holistic approach to student engagement and learning was assessed by the standard Teaching and Course Evaluation surveys, along with questionnaires specifically developed for this course. Feedback from students was very positive, as evidenced by high teaching and course evaluation scores during the last five years.

Student Success in First-Year University Physics and Mathematics Courses: Does the high-school attended make a difference?

This paper considers school factors that contribute to a successful transition from high school to first-year university Physics courses at the University of British Columbia by employing a two-level hierarchical model. It is assumed that there is a relationship between student performance and the high school they graduated from. It is shown that school location and type affect student performance: students from public schools in the Metro Vancouver area perform better in first year compared to students from independent schools and schools in distant communities. The study also considers rankings of schools based on student performance in first-year university Physics and Calculus courses. These university-based rankings differ significantly (essentially in reverse order) from the well-known Fraser Institute rankings based on measures internal to high schools.