Undergraduate Mathematics Students Research Articles

When perceived similarity overrides demographic similarity: examining influences on STEM students’ developmental mentor networks

BackgroundWhile dyadic faculty–mentored relationship research currently saturates the mentoring literature, recent developments suggest the need for a broader consideration of a student's mentor network. Research taking a network approach may provide deeper insights into the formation and benefits of mentorship for undergraduate students in science, technology, engineering, and mathematics (STEM) disciplines. Utilizing Developmental Mentor Network Theory and ego-centric social network analysis, this pre-registered study evaluates how the characteristics of mentees and mentors relate to both the content of support and structure of mentor networks in a large sample of White and Hispanic/Latino(a) STEM undergraduates across 12 universities.ResultsResults were nuanced but showed that perceived psychological similarity with their mentor(s) predicted both dyadic and network average levels of mentor support (i.e., psychosocial, career, role modeling) and relational satisfaction. Furthermore, results point to homophily and engagement in undergraduate research effects on mentor network structures.ConclusionsThese findings highlight the importance of using a network approach to deepen our understanding of the factors (e.g., psychological similarity) that may influence the formation and maintenance of robust and diverse supportive mentoring networks.

Academic Self-Concept Development for STEM College Students: An Analysis on Gender Difference

Using a nation-wide college student dataset, this study examines the gender disparities in academic self-concept for undergraduate students in Science, Technology, Engineering, and Mathematics (STEM) majors and investigates college experiences affecting academic self-concept in this population. Findings of the current study suggest that overall college satisfaction is the strongest positive predictor of academic self-concept for college students in STEM majors and that institutions and their members should strive to facilitate satisfactory and educationally meaningful college experiences for these students at the macro level. Also, faculty members and administrators in STEM majors should be aware of the importance of positive faculty support on students’ academic self-concept development and should continue trying to create an environment where students can experience more frequent and positive encounters with their faculty members. Lastly, our findings show that the effects of some college experiences on academic self-concept development for STEM students vary by student gender. The findings underscore the significance of the nature or type of college experiences and the corresponding gender inequity and suggest that STEM majors need to facilitate departmental environments where both male and female students can equivalently benefit from their college experiences not only for their academic development but also for other desired college outcomes.

A Validation Study Of The Saudi Version Of The Mathematics Confidence Scale Among General Education Students

The purpose of this study was to validate the Saudi version of the Mathematics Confidence Scale among undergraduate students. To achieve this, a sample of 1324 undergraduate students from various schools across Saudi Arabia was selected. The participants' demographics, including gender, grade, and type of school, were considered in order to ensure a representative sample. The participants were given the Mathematics Confidence Scale questionnaire, which consisted of 30 statements related to their confidence in mathematical abilities. Each statement was rated on a Likert scale ranging from 1 (strongly disagree) to 5 (strongly agree). The Likert scale was chosen to measure participants' responses because it allows for a more nuanced understanding of their levels of confidence in mathematics. The results indicated That the Saudi Version of the Mathematics Confidence Scale is reliable and valid. This suggests that the scale can be used effectively to assess the confidence levels of undergraduate students in mathematics in Saudi Arabia. Further research should be conducted to investigate the psychometric properties of the Saudi Version of the Mathematics Confidence Scale using IRT models. IRT models can provide more in-depth analysis of item response patterns and help identify specific areas where students may be lacking confidence in mathematics. They can also help determine whether certain items on the scale are functioning as intended and provide insights for improving the scale's overall validity and reliability

Pre-service Mathematics Teachers and Undergraduate Mathematics Students' Metaphorical Perceptions of the Concept of Mathematics

Abstract: This study aims to compare the metaphors developed by the students of the Pre-service Mathematics Teachers (PMT) and the students of the Undergraduate Mathematics (UM) regarding the concept of mathematics and to determine how the metaphors are distributed as to the variables level of class and the department. For this purpose, hermeneutic phenomenology was used as a type of phenomenology design- one of the qualitative research methods. This study was conducted during the 2021/22 academic year with a total of 57 UM students studying at the Faculty of Arts and Sciences of a public university in the Southeastern Anatolia Region, and a total of 68 PMT students studying at the Faculty of Education at the same university. Data was collected through an interview form and analysed with content analysis. It was concluded that many metaphors are necessary in order to explain the concept of mathematics in a holistic way and that the respondents considered mathematics with its positive and negative aspects, as well as embracing it in daily life. It was also observed that the respondents’ perceptions of mathematics differ depending on the level of class and the department. For example, while the PMT students approached mathematics with a more concrete viewpoint, the UM students adopted an abstract mind-set. The reason for this result is believed to be related to the fact that the curricula applied for the PMT students contains less abstract expressions and theoretical lessons than that of the UM students, and also makes students active, offers a constructivist learning environment, and aims to train mathematics teachers rather than training them to become mathematicians. 
 Keywords: Metaphor, mathematics education, phenomenology, pre-service mathematics teachers, undergraduate mathematics

Students’ mathematical thinking of the tree concept: an integration of APOS with Tall’s three worlds of mathematics

ABSTRACT In this study, we investigate students’ mathematical thinking of the tree concept, a fundamental concept in graph theory, using a combination of the APOS theory and Tall’s three worlds of mathematics. The qualitative research describes here is a phenomenological study drawing on task-based interviews with 18 undergraduate mathematics students. The findings indicate that students preferred to think in the embodied world when solving tasks related to the tree concept. This type of thinking, despite its great value, should not prevent students from thinking in the symbolic and formal worlds. Furthermore, the findings indicate that almost half of the participants had difficulties with the acyclicity and connectivity concepts, which are necessary prior knowledge to help students develop Process and Object for the tree concept. The results also suggest that more opportunities could be provided for students to engage with tasks that related to Process and Object in the three mathematics worlds.

Comprehensive Exploration of the Archimedean Property: Insights and Proofs for Undergraduate Mathematics Students

Comprehensive Exploration of the Archimedean Property: Insights and Proofs for Undergraduate Mathematics Students

Exploring Undergraduate Students’ Psychological Stress in the Mathematics Classroom with Fitness Trackers

ABSTRACT Math anxiety and academic distress, two interrelated forms of psychological stress, are pervasive problems for undergraduate mathematics students. Most of the research in this area has taken a broad view of the impact this stress has on students’ learning across an entire course or, more broadly, the entire curriculum for their degree. To complement this existing body of research, this paper serves a dual purpose: First, to provide insight into undergraduate students’ day-to-day classroom stress, and secondly, to explore fitness trackers as a tool for in situ detection of student anxiety or stress in the classroom. To accomplish the first objective, we conduct a phenomenographic analysis to explore the variation in 29 students’ reported experiences of psychological stress within a session on roots of polynomial functions. We identified 7 categories of description. For the second objective, we recorded the students’ heart rate during the same lesson. We clustered students heart rate variability plots according to our categories of description and employed a logistic regression model to estimate the probability that a student will report experiencing psychological stress given their heart rate variability. Our results show that fitness trackers can produce measures that serve as a predictor of self-reported emotional change.

THE EFFECTS OF USING FLIPPED CLOUD LEARNING WITH ADVANCING MATHEMATICAL THINKING APPROACHES ON UNDERGRADUATE STUDENTS’ MATHEMATICAL CRITICAL THINKING

The flipped learning approach of instruction sees classroom lectures moved outside of classrooms through devices and technology. Homework is moved inside classrooms as learning activities. Due to the COVID-19 outbreak, cloud-based education platforms - the organization of the educational environment in the cloud as a tool to enable teaching and learning - have been widely deployed to support online instruction. In this study, flipped cloud learning, incorporating approach of advancing mathematical thinking, were conducted in Mathematical Analysis course to study students’ mathematical critical thinking. A quantitative method, using a pre-test-post-test design, was employed with a group of 56 undergraduate mathematics students. The research instrument was a mathematical critical thinking ability test. The quantitative data were analyzed using the descriptive analysis, n-gain and t-test. The findings revealed that students had statistically significant mathematical critical thinking of higher than 60% of the full score at the .05 level. There was an increase in students’ mathematical critical thinking abilities with a mean n-gain of .64, which was moderate. The findings also show that the students’ mathematical critical thinking was significantly enhanced by this approach at .05 level. Thus, it could be summarized that integrating strategy for advancing mathematical thinking into flipped cloud learning positively affected students’ mathematical critical thinking. The results also suggest that this reformed learning approach might be usefully employed as an instruction model in the new normal context.

Education

The Education section in this issue presents two contributions. In `"Nesterov's Method for Convex Optimization," Noel J. Walkington proposes a teaching guide for a first course in optimization of this well-known algorithm for computing the minimum of a convex function. This algorithm, first proposed in 1983 by Yuri Nesterov, though well recognized in computational optimization in the presence of large data as a more efficient tool than the steepest descent method, is still absent in most modern textbooks on optimization. The author of the present article develops an elementary analysis of Nesterov's first order algorithm that parallels that of steepest descent but with an additional requirement proposed by Nesterov. Two cases are discussed. The first concerns an unconstrained minimization problem, while the second includes closed convex constraints represented using infinite penalization of the cost. More generally, the cost function becomes the sum of a smooth convex function and a lower semicontinuous convex function. Several student-level exercises are included in this paper. Results are nicely illustrated by an example of a signal recovery problem and a discussion of the Uzawa algorithm for optimization problems with constraints defined by inequalities involving convex functions. The second paper, "A Comprehensive Proof of Bertrand's Theorem," is presented by Patrick De Leenheer, John Musgrove, and Tyler Schimleck. It concerns the behavior of the solutions of the classical two-body problem and states that, among all possible gravitational laws, there are only two exhibiting the property that all bounded orbits are closed: Newtonian gravitation and Hookean gravitation. Historically, even if Newton was aware that there are to specific gravitational laws having the above property, it was only two centuries later, in 1873, that Bertrand realized that these are the only ones. Bertrand's theorem, due to its important consequences, has been integrated into the undergraduate curriculum in theoretical mechanics, but its proof, accessible to undergraduate mathematics or physics students, seems to be absent from modern textbooks. Although Bertrand's original paper did not contain a precise proof, V. Arnold proposed a sketch of it based on six subproblems. Among other contributions, this article provides a complete proof of the sixth subproblem under a specific assumption imposed on the magnitude of the force in the motion model. Under this assumption, a complete proof of Bertrand's theorem is then given, incorporating also earlier contributions by other authors. Still, comprehensive does not mean simple here, and this paper may be used to conceive several research projects for advanced-level undergraduate students in mathematics or physics.

Research on the Reasons for Incomplete Learning of Mathematics Textbooks by Undergraduate Mathematics Students

Recently, the China government has increasingly attached importance to the development of basic science. As the reserve talents to promote the development of mathematics, undergraduates majoring in mathematics have received the attention of researchers for their mathematics learning. However, in practice, their learning of mathematics textbooks is not comprehensive. Through interviews, coding methods, and quantitative analysis methods, the main reasons are investigated and analyzed in this paper. The conclusions are as follows: (1) The content of the textbook and the exercises at the end of the lessons are too difficult and beyond students' ability. (2) Teachers have lazy behaviors and ask too little of their students. (3) Students themselves are lazy and take exams very seriously, lacking motivation and initiative to learn. To change this situation, the mathematics textbook can be improved to explain profound theories in simple language. Teachers can also tighten the requirements for their students. In addition, mathematics majors should also improve their requirements for themselves, overcome inertia, and reasonable scheduling, and pay more attention to the use and study of mathematics textbooks.

Effects of Self-Explanation on the Expansion and Indulgent of Mathematics Teaching: Case of the Students of the University of Wachemo

The main goal of this study is to investigate the effects of self-explanation in improving proof comprehension in mathematics instruction: the case of Wachemo university undergraduate mathematics students of academic year 2020/2021. Moreover it is intended to find out interconnection between students achievement in mathematics and self-explanation in proof comprehension. To assess student’s self-explanation ability we applied self-explanation test and attitude test at the beginning and at the end to assess student’s character change to ward mathematics. In this study there are 48 students participated in both control and experimental groups. This study showed that the effectiveness of self-explanation in proof comprehension in mathematics courses. This also leading to recommend for curriculum developers to consider in self-explanation. One of the most strong findings of research is that conceptual indulgent is an important elements of expertise hence self-explanation is the tool to enhance students conceptual understanding, along with realistic knowledge and technical facility. The alliance of realistic knowledge, procedural expertise, and conceptual indulgent makes all three components operational in powerful ways. So that self-explanation has prominent effect in supporting students to achieve the intended objectives in proving theorems. Of these, two areas were measured quantitatively: student achievement in calculus and transformation geometry, and self-concept toward these courses. Those quantitative research findings are presented in chapter four with the details of the data collection procedures, the quantitative results, and an analysis of the outcomes.

Teaching Mammalogy in the 21st century: advances in undergraduate education

Abstract In the past 30 years, leaders in undergraduate education have called for transformations in science pedagogy to reflect the process of science as well as to develop professional skills, apply new and emerging technologies, and to provide more hands-on experience. These recommendations suggest teaching strategies that incorporate active learning methods that consistently increase learning, conceptual understanding, integration of subject knowledge with skill development, retention of undergraduate students in science, technology, engineering, and mathematics (STEM) majors, and inclusivity. To gain insight into current practices and pedagogy we surveyed members of the American Society of Mammalogists in 2021. The survey consisted of both fixed-response questions (e.g., multiple-choice or Likert-scale) and open-ended questions, each of which asked instructors about the structure and content of a Mammalogy or field Mammalogy course. In these courses, we found that lecturing was still a primary tool for presenting course content or information (x¯= 65% of the time); nonetheless, most instructors reported incorporating other teaching strategies ranging from pausing lectures for students to ask questions to incorporating active learning methods, such as debates or case studies. Most instructors reported incorporating skill development and inclusive teaching practices, and 64% reported that they perceived a need to change or update their Mammalogy courses or their teaching approaches. Overall, our results indicate that Mammalogy instructors have a strong interest in training students to share their appreciation for mammals and are generally engaged in efforts to increase the effectiveness of their teaching through the incorporation of more student-centered approaches to teaching and learning.

Pythagorean Triples, Complex Numbers, Abelian Groups and Prime Numbers

Pythagorean triples can be represented by points of the unit circle with rational coordinates. These points form an abelian group, and we describe its structure. This structural description yields an enumeration of the normalized Pythagorean triples with a given hypotenuse. It also gives rise to an effective method for producing all such triples, and this effective method seems to be new. This paper is intended for the general mathematical audience, including undergraduate mathematics students. Therefore it contains background material, explanations, examples and drawings; and the proofs are complete.

A Nautical Instrument Lying of the Plane in Teaching the Concepts of Chord and Arc of Circumference

Background: This work follows in the direction of research dedicated to articulating historical instruments to teach mathematics. Objectives: To analyse the use of the instrument to find the altitude of the Sun as a didactic resource for teaching and learning the concepts of chord and arc of a circle in the education of undergraduate students in mathematics. Design: The research takes place through a university extension course that uses the theoretical and methodological foundations of the teaching guidance activity. Setting and Participants: The research environment is the training of students at the State University of Ceará. The training action was attended by 12 participants. The choice criterion was that they were studying for a degree in mathematics, and the selection took place in the order of enrollment in the activity. Data collection and analysis: From the assumptions of the teaching guidance activity, data collection was carried out with the recording of videos and audio, photographic records and students’ writings, while the analysis was based on connections and interconnections on the action of the subjects, and on the conceptual nexuses. Results: The new instrument to find the altitude of the Sun has didactic potential to work with the concepts of arc and chord of circumference because, from it, these concepts are mobilised as practice, and it is possible to see how they relate. Conclusions: The new instrument to find the altitude of the Sun can be explored in the interface between history and mathematics teaching as a resource to favour teaching and learning, whether in basic education or higher education.

Undergraduate Mathematics Students’ Reported Use of Learning Resources Towards Accessing Mathematics

The topic of resources for learning mathematics commonly becomes of interest during times of disruption and rapid change in education. The considerable research on undergraduate mathematics students’ resource use largely focuses on learning resources in the form of material technologies and texts. Concerned that contemporary decisions about resourcing for learning in mathematics may take the form of simply adding material resources, we identify the need for research that is designed around a broader notion of learning resource, and which focuses on what resources students use, as well as how they use multiple resources individually and together towards accessing mathematics. Thus, in our qualitative study of undergraduate mathematics students’ resource use, we adopt a socio-cultural notion of resources as material, human, spatial, temporal and linguistic, and of resource use as transparent. We investigate six students’ resource use, reported in weekly learning logs and focus group interviews. We show that students used material technologies and texts, and human and linguistic resources in three spaces − the live lecture, informal study and tutorial − with study time available for mathematics central to their choice of resources and how they used them. How students put these multiple resources to work (or not) towards accessing mathematics involved complex, agentic, individual work. Students’ use of the lecturer’s writing on the chalkboard, talk and gestures to make lecture notes in the live lecture is an example of this. Our findings offer insights into how lecturers can select learning resources, and also support students to use these towards accessing mathematics.

Experienced provers’ uses of contexts while engaging in combinatorial proof of binomial identities

Combinatorial proofs of binomial identities involve establishing an identity by arguing that each side enumerates a certain set of outcomes. In this paper, we share results from interviews with experienced provers (mathematicians and upper-division undergraduate mathematics students) and examine one particular aspect of combinatorial proof, namely the kinds of contexts that experienced provers used to establish combinatorial proofs of binomial identities. Our findings show that overall, our participants used a variety of contexts in their work; we also demonstrate ways in which previous experiences influenced the contexts they chose, and we offer some instances in which features of a context supported their combinatorial proof production. We offer some theoretical implications of our work, and we conclude with a discussion of limitations and avenues for future work.

Lived Experiences of Former STEM Undergraduate Mentors of an Afterschool Mentoring Program: An Interpretative Phenomenological Analysis

Studies have identified gaps in the development of undergraduate students in science, technology, engineering, and mathematics (STEM). Students lack communication and problem-solving, impeding employment opportunities post-graduation. It is essential to prepare students for employment in STEM fields, as these fields remain in high demand and offer competitive wages for economic stability. Research has revealed that students gain critical thinking and problem-solving skills through students mentoring experiences. Evidence surrounding the inclusion of active learning strategies for in-classroom pedagogy has expanded in recent years, but the support mechanisms beyond the classroom remain unclear. Herein, we followed students for a decade after participation in our mentoring pre-professional training program, Nebraska STEM for You (NE STEM 4U). This phenomenological study utilized interviewing techniques and descriptive statistics to demonstrate how a midsized, metropolitan university STEM mentoring program supported the development of NE STEM 4U participants. We found that engagement in an after-school mentoring program provided participants with a model of mentorship. Participants also developed transferable professional and personal skill sets, including communication, perspectives, conflict resolution, and professional development.

Improving Mathematical Problem-Solving Abilities by Virtual 5E Instructional Organization

The purpose of this action research was to improve mathematical problem-solving abilities using the virtual 5E instructional organization for undergraduate math students who required to pass the criteria of 70% of the full score. This study involved thirty undergraduate math students from one university who were enrolled in mathematical problem-solving courses for mathematics teachers during the first semester of academic year 2021. They were randomly chosen using cluster random sampling. There are three types of tools utilized in this research: 1) a plan for mathematical problem-solving abilities, 2) an assessment of problem-solving abilities in mathematics, and 3) a student behavior observation form. The statistics used in the data analysis are descriptive for calculating mean, standard deviation, and percentage. The finding showed that mathematical problem-solving abilities had been achieved. Undergraduate students in mathematics had average scores of 35.00, 46.07, and 50.19 after completing learning activities in the first, second, and third cycle, indicating 58.33%, 76.78%, and 83.65%, respectively. In the second and third cycle, all students achieved 70% of the entire score. The findings shows that experienced undergraduate students can solve mathematical problems as a proportion of the overall score when using the virtual 5E instructional organization.

Enhancing Undergraduate Mathematics Students’ Conceptual Knowledge of the Confidence Interval for the Population Mean

This study illustrates the teaching strategies that undergraduate mathematics lecturers might employ to improve their students' conceptual knowledge of the confidence interval for the population mean. The study employed an action research method. It allowed the researcher to deepen his knowledge of the subject matter by planning, acting, evaluating, refining, and learning from this experience (Koshy, 2010). The participants consisted of sixty (60) level 200 mathematics students, who were randomly selected from a cohort of mathematics students from a mid-sized university in Ghana. The students completed the tasks assigned to them in their various groups by working collaboratively together, with their lecturer helping the process. They determined the particular theorem to apply in any given situation and applied the confidence interval formula to calculate the confidence intervals. The results indicated that collaborative learning, combined with effective instructional methods, improves students' conceptual knowledge of the confidence interval. An implication of this study is that students’ prior experiences act as a catalyst to enhance their conceptual knowledge. Thus, students who have a conceptual grasp of sampling techniques can conceptualise confidence intervals with ease. The study concludes that students should thoroughly understand the definitions and theorems relating to a statistical concept before they examine concrete examples relating to confidence intervals.

Relationship between Motivation and Academic Performance in Peruvian Undergraduate Students in the Subject Mathematics

Existing literature has paid little attention to the role that motivational variables have on the academic performance of mathematics students in Peru. The objective of the study was to determine the relationship between motivation and its dimensions and academic performance in this subject. A cross-sectional and correlational study was carried out in a sample of 251 first-cycle Peruvian undergraduate mathematics students using an electronic questionnaire. The students’ academic performance was measured by their records of the Mathematics course. The motivation was assessed using a self-report instrument designed to assess students’ intrinsic motivation, extrinsic motivation, and demotivation through 28 items. For statistical processing, Spearman’s Rho coefficient and a linear regression analysis were taken into account. It was concluded that there is a weak correlation between academic performance and motivation (r = 0.222, p = 0.001 ), in the same way as intrinsic motivation (r = 0.242, p = 0.001 ) and extrinsic (r = 0.117, p = 0.003 ) and a weak correlation with the demotivation dimension (r = 0.142, p = 0.024 ). With regard to linear regression, all dimensions of motivation were predictive of academic performance; intrinsic motivation explains a 27.2% of academic performance (β = 0.732; p = 0.011 ); extrinsic motivation explains a 16.8% of academic performance (β = 0.556; p = 0.001 ), and demotivation a 12.4% (β = 0.427; p = 0.008 ). This research provides a clear contribution with results on the association between motivation and academic performance in mathematics. This study suggests that universities, teachers, and students’ families take the necessary measures and provide stimulation to increase their motivation. In the same way, it is suggested that the university, in general, implements strategies to involve the student so that the student is always clear about the reason why they are at university and finish the degree they have started.