First-year Mathematics Research Articles

Computational Thinking Readiness Level of First-Year Students of Mathematics Education

The main objective of this study was to measure the level of computational thinking readiness in prospective first-year mathematics education students. In addition, this study also aims to identify factors that influence their level of readiness towards computational thinking. This research is qualitative and descriptive in nature. This study describes first-year mathematics education students' mathematical computational thinking ability based on the theory of mathematical computational thinking. This study was conducted on first-year mathematics education students in the academic year 2023/2024. There were 16 first-year mathematics education students, all of whom were taken as samples in this study, to obtain more in-depth information about the computational thinking ability of first-year mathematics education students for further research development. The instruments used to collect data on first-year mathematics education students' mathematical computational thinking ability are (1) a mathematical computational thinking ability test and (2) an interview. The data obtained were calculated using statistical tests, and the results will be explained in depth. The mean score of the first-year mathematics education student's computational thinking ability test was 59.68, indicating that students generally have a fairly good level of computational thinking ability.

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.

An Improved Unbounded-DP Algorithm for the Unbounded Knapsack Problem with Bounded Coefficients

Benchmark instances for the unbounded knapsack problem are typically generated according to specific criteria within a given constant range R, and these instances can be referred to as the unbounded knapsack problem with bounded coefficients (UKPB). In order to increase the difficulty of solving these instances, the knapsack capacity C is usually set to a very large value. While current efficient algorithms primarily center on the Fast Fourier Transform (FFT) and (min,+)-convolution method, there is a simpler method worth considering. In this paper, based on the basic Unbounded-DP algorithm, we utilize a recent branch and bound (B&B) result and basic theory of linear Diophantine equation, and propose an improved Unbounded-DP algorithm with time complexity of O(R4) and space complexity of O(R3). Additionally, the algorithm can also solve the All-capacities unbounded knapsack problem within the complexity O(R4+C). In particular, the proof techniques required by the algorithm are primarily covered in the first-year mathematics curriculum, which is convenient for subsequent researchers to grasp.

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.

Ensuring Validity and Reliability in Algebra Midterm Assessment: A Comprehensive Approach to Test Development and Analysis

First-year mathematics education students often face challenges with College and Advanced Algebra assessments. This study aimed to develop and validate a 100-item multiple-choice midterm test for College and Advanced Algebra, ensuring the test's validity and reliability. The test was designed following a structured process that included creating a Table of Specifications (TOS) based on the approved syllabus. To ensure content accuracy and relevance, the test was reviewed by three subject matter experts and evaluated for clarity by 15 students. Pilot testing was conducted with 82 fourth-year Bachelor of Secondary Education Mathematics (BSEd Mathematics) students. The pilot test results underwent detailed item analysis, focusing on metrics such as the difficulty index, discrimination index, and overall reliability using the Kuder-Richardson Formula 20 (KR-20). Of the 100 items, 22 were retained, 48 were revised, and 30 were discarded. The test achieved a reliability coefficient of 0.876, indicating strong internal consistency. The findings suggest that the validated test questionnaire is a dependable tool for accurately assessing students’ knowledge in College and Advanced Algebra, providing valuable feedback for educators and students.

Emergency Remote Teaching in Higher Education Institutes: A Taxonomy of Challenges Faced by First-Year Mathematics Students in the Pacific Region

Emergency Remote Teaching in Higher Education Institutes: A Taxonomy of Challenges Faced by First-Year Mathematics Students in the Pacific Region

First-year university students’ understanding of function concepts encountered in Grade 12 Mathematics: a case study

This article focuses on first-year university students’ understanding of concepts related to third-degree polynomial and trigonometric functions that they encountered during their study of Grade 12 mathematics. In this study three online questions from two firstyear mathematics quizzes at the University of KwaZulu-Natal were analysed. The first question focused on the characteristics of a polynomial function, while the second and third questions focused on the characteristics of trigonometric functions. The characteristics included calculus-related concepts, for example, intervals of increase or decrease, concavity and local extrema. It was found that about a fifth of the participants (n = 557), science students who studied the core mathematics module Introduction to Calculus, had difficulties in answering those calculus-related questions compared to determining the general non-calculus characteristics, for example, the range and domain. The study also found that about a quarter of the participants lacked relational understanding with regard to calculus-related concepts. This study recommends that lecturers need to spend more time on calculus-related concepts of a function that focus on relational understanding.

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.

Mathematics Online Baseline Assessment: Senior Phase First-year Student Teachers’ Views

Problem-solving and enquiry-based learning are integral in the Mathematics and Science curriculum in South Africa through online-based assessment. Online assessment has rapidly gained recognition because of technology. In this paper, the authors explored the views of online baseline assessment among Senior Phase First-year Mathematics Student Teachers. The researchers adopted a qualitative research method. Data was collected from the participants using an online Google form developed into a questionnaire. The participants in this study were first-year students enrolled for the Bachelor of Education in Mathematics at a university in a rural province of South Africa. The first-year student teachers were exposed to the senior phase baseline assessments through the licensed online Computer Aided Mathematics Instruction (CAMI) tool. One hundred and sixteen (116) senior-phase student teachers completed the online questionnaire. This study used convenience sampling since it was the most appropriate method to conveniently invite the participant. The findings revealed that first-year student teachers were enthusiastic and motivated to write the baseline assessment on computers for the first time. The result also showed that several first-year student teachers experienced difficulties solving mathematics problems using computers. This study recommends more intensive research on student teachers' views on online assessment regarding gender and time.

Students’ Experiences of Tippy Tube Video-assisted Learning during the COVID-19 Lockdown in an Open and Distance Learning Environment

The University of South Africa (Unisa) College of Education (CEDU) set up Tippy Tube as an online educational video channel to engage lecturers around the country. The outbreak of the novel coronavirus (COVID-19), which was declared a global pandemic on 11 March 2020, imposed a lockdown period from February to August 2021. This article reports on a study that explored how the use of Tippy Tube optimised support to first-year mathematics education students at Unisa during the lockdown. Moore’s Transactional Distance Theory (TDT) underpinned the study. The study used a qualitative research design to explore students’ views on whether the Tippy Tube tool had optimised student support in the mathematics education module during the lockdown. The module has five units and five Tippy Tube videos were developed for each unit. Open-ended questionnaires were administered to 100 purposively sampled first-year mathematics education students. Only 21 respondents completed the questionnaires. Thematic analysis was then used to analyse the data from the open-ended questionnaire responses. The findings of the study revealed that Tippy Tube video-assisted learning had benefitted the students in mathematics education. Further, the study findings suggested that lecturers can consider using the Tippy Tube tool to teach students mathematics and other disciplines as they are able to replay the videos for the purpose of clarity if they did not understand the videos during live presentations.

Learning first-year mathematics fully online: Were students prepared, how did they respond?

This paper reports on empirical results from a study that investigated first-year mathematics students’ preparedness for, and response to, online learning. With the appearance of COVID-19 in 2020, lecturers were forced to make sudden changes to the established face-to-face learning environments, and students were expected to adapt to these changes. The idea of a blended learning environment is not new, and students globally have demanded flexibility in mathematics learning environments for some time. However, the idea of a sudden change in environments, particularly to fully online, was new to most lecturers and students. Key aspects in an online environment are students’ ability to self-regulate their learning, and the availability and accessibility of technological resources. Quantitative data from the self-developed questionnaire were collected early in 2021, at a public university in South Africa, from a large sample over several modules. Results indicate students are partially prepared for learning fully online, with significant effect on performance.

Online learning and peer support: Exploring the use of WhatsApp in first-year mathematics

Online learning and peer support: Exploring the use of WhatsApp in first-year mathematics

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 empirical study of mathematical creativity and students’ opinions on multiple solution tasks

Creativity and problem solving are considered to be twenty-first-century competencies, therefore promoting mathematical creativity should be an important part of school mathematics. The study presented in this paper is inspired by the notion of mathematical creativity and the utilization of multiple solution tasks (MSTs) to investigate students’ creativity. Multiple solution tasks are mathematical tasks with an explicit requirement to be solved with different methods. For the purpose of the study, we used a textbook question which allows multiple solution pathways as our research instrument. This MST was administered to first-year mathematics students (18–20 years) along with additional questions related to their experience in school mathematics. The results of the study showed that students had difficulties complying with the demands of the task, but generally have a positive disposition toward MSTs. Moreover, the results underline the necessity of incorporating MSTs in mathematics classroom teaching to create a more coherent corpus of mathematical knowledge. The study also provides an example of how a regular textbook task can be used as an MST.

The transition from school to university mathematics in different contexts: affective and sociocultural issues in students’ crisis

Understanding the secondary–tertiary transition is not only an educational matter, but also an inclusion and equality matter as mathematics qualifications lead to better employment and better earning for students. Research on what causes the crisis associated to this transition has so far focused on the impact of cognitive and epistemological changes in university mathematics. Recently, attention has been given to sociocultural and affective issues, which indicate the impact of diverse contexts on such event in the students’ life. Here we present a study investigating the experiences of first-year mathematics students in three European countries. The study adopted the framework of transition as a rite of passage and to detect the changes in attitudes towards the mathematics which originated the crisis, the three-dimensional model for attitude towards mathematics (TMA) was used. Data consist in one questionnaire translated into three languages and administered to students in the first year of study. Most of the questions were open-ended, and the data were analysed first qualitatively and then quantitised. Results show that while the transition experiences of the students may seem on the surface uniform, some significant differences emerge for motivation to join mathematics degrees, motives for changes in perceived competence, and impact of university mathematics formalism. We hypothesise a link between these changes and the differences in educational environments in the three countries. We conclude with highlighting the need for more research of this kind to understand the secondary–tertiary transition in the educational context in which it happens.

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.

Mathematical Knowledge for Teaching in Further Education and Training Phase: Evidence from Entry Level Student Teachers’ Baseline Assessments

This paper investigates entry-level student teachers' mathematical knowledge for teaching in the Further Education and Training phase (FET) through Baseline Assessment. The study employed a quantitative research technique. The data collection instrument was a mathematics subject knowledge test (Baseline Assessment) for FET phase student teachers. Purposive and convenient sampling methods were employed in the study. The study enlisted the participation of 222 first-year mathematics education student teachers from a rural Higher Education Institution (HEI) specialising in FET phase mathematics teaching. One hundred and seventy-five (175) student teachers completed the Baseline Assessment for all grades in this study (10, 11, and 12). The Baseline Assessment findings were examined using descriptive statistics. The results revealed that student teachers have a moderate knowledge of mathematics topics in the FET phase at the entry-level. In addition, an adequate level of understanding for teaching Grades 10 and 12 Patterns, Functions, Algebra, Space and Shape (Geometry), and Functional Relationships. While the elementary level of understanding for teaching grade 10 Measurement, Grade 11 Patterns, Functions, Algebra, and Trigonometry and Grade 12 Space and Shape (Geometry). There is no level of understanding for teaching FET phase Data and Statistics and Probability. The paper suggests that student teachers must develop a comprehensive understanding of the mathematics curriculum with the assistance of teacher educators in HEIs.