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This article describes the outcomes of a faculty partnership between a math professor and a composition professor to improve the final paper in a research-focused senior capstone math course. Much attention has been paid in recent years to the importance of undergraduate research experiences and how to best create and support such endeavors. However, little space has been dedicated to helping math faculty design and scaffold writing assignments to support their students' development as scholars. We describe how our partnership took place, the changes we made to existing assignments and the creation of new ones, and an assessment of our efforts completed by an interdisciplinary group of faculty and students, which showed marked improvement in the areas of information literacy, critical thinking, and quality of writing. [ABSTRACT FROM AUTHOR]

This paper describes the implementation of a STEM scholarship program which utilized a holistic approach to providing a multi-dimensional student support system. The program has been successful in encouraging and supporting women in Applied Mathematics and Computer Science by offering a diverse suite of extracurricular opportunities, actively engaging them in organized events, research projects, and participation in STEM communities, and helping them achieve higher GPAs and shorter times to graduation. The supported women also benefitted from close mentoring relationships with the faculty mentors. The program emphasized the development of empowering settings for women's engagement and achievement, which act to sustain and expand interest in mathematics and computing, and thereby help them to see themselves as future professionals in the field. [ABSTRACT FROM AUTHOR]

This paper is written to provide ideas and guide faculty who want to design a mathematical modeling course for undergraduate mathematics majors and minors. We discuss course goals, assignments, and projects that can be used to help students gain experience relevant for careers and mathematical modeling opportunities. The authors designed this course to build students' mathematical thought processes and toolbox, ability to analyze and evaluate mathematical models, mathematical modeling skills, and teamwork skills. The course described is intended as an upper division undergraduate course with a prerequisite of differential equations. [ABSTRACT FROM AUTHOR]

Little is known about whether manipulatives can support children's inferences of the mathematical structure of word problems. The objective was to test the effects of using manipulatives during problem solving on students' understanding of the additive relationships in word problems. Third and fifth graders (N = 45) solved one-step addition and subtraction word problems that described either a mathematical action or relation. Children in each grade were randomly assigned to either a manipulatives or a paper-and-pencil condition. Problem structure understanding was assessed by the degree to which students' strategies and verbal justifications reflected the quantitative relationships described in the problem text. Performance of the fifth graders was not impacted by the use of manipulatives, but in the third grade, strategy performance with manipulatives was superior to performance without manipulatives on Relation problems. The degree to which the third graders' justifications were aligned with corresponding problem structure was positively impacted by manipulatives regardless of problem type. [ABSTRACT FROM AUTHOR]

Numerous studies affirm the importance of students' attitudes for mathematical education. This study uses mathematical autobiographical essays to examine the mathematical experiences and attitudes of undergraduate students enrolled in mathematics classes at a Midwestern University in the United States. The essays of 41 students (20 men, 21 women) out of 170 enrolled in College Algebra, Precalculus, and Calculus were analyzed using the categories of (1) confidence in mathematics ability, (2) value of mathematics, and (3) liking of mathematics. This paper provides context and theoretical depth to student reports of their attitudes in these categories. Statements at the intersections of both confidence and liking, and value and liking provide additional insights. First, students who perceive mathematics as valuable are more likely to like it. Second, the vast majority of students talk about confidence and liking together, and with a positive correlation. Further, these students tend to talk about liking or not liking mathematics because of their perceived ability in mathematics. Our study suggests the importance of proactive teaching strategies to improve students' perceptions of the value, liking of, and their confidence in, mathematics, and also suggests self-efficacy as a potential theoretical basis for this work. [ABSTRACT FROM AUTHOR]

In this paper, we assess the pedagogical approaches we employ in our US-based undergraduate mathematics courses during the COVID-19 pandemic. Our goal is to share anecdotal evidence on the use of math journals, oral exams, and learning portfolios in the synchronous online mathematics classroom. We reflect on our experience using artifacts of student materials, feedback, and dialogues. [ABSTRACT FROM AUTHOR]

With constantly changing political landscapes affecting the ability of college students with minoritized identities of sexuality and/or gender (MIoSG; Vaccaro et al., 2015) to thrive on campus, higher educators need to understand student reported stressors to design more inclusive learning environments. Building from minority stress theory and using data from a grounded theory study with 56 collegiate STEM students with MIoSG, this paper documents stressors that students reported as contributing to diminished wellbeing. We used constant comparative grounded theory analysis to identify stressors shared by all participants, which included lack of belonging and invisibility in competitive STEM cultures as well as exclusionary interactions with STEM peers. Recommendations include the design and delivery of holistic education and support services on campus. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In the fall of 2009 and in the spring of 2012, supported by the National Institute of General Medical Sciences (NIGMS) in the National Institutes of Health (NIH), we designed a course "Phylogenetic Analysis and Molecular Evolution" (PAME), the first cross-listed course across three different colleges (College of Arts and Sciences, College of Engineering, and College of Agriculture). This course was the first at the author's university. The course will be made available to graduate students and advanced undergraduate students in biology and computer science, and undergraduate student in statistics and mathematics at regional universities and colleges. The graduate students will learn how to gather sequence data, use bioinformatics tools, and analyze biological data using mathematics and statistics throughout the project. In this paper, we propose an online course on PAME facilitated with the statistical software RStudio on Amazon Web Service (AWS). [ABSTRACT FROM AUTHOR]

Math Girls $ \mathbb {R} $ R ock! is a year-long, two-tiered mathematics mentoring program that prepares female undergraduate mentors to facilitate high school girls' engagement in challenging mathematics concepts through a dynamic after-school program. In this article, we describe the distinct educational component of this program in which female faculty members mentor female undergraduate mathematics and mathematics education students in researching and developing the content to be presented at the high schools. In addition, we discuss some of the feedback collected from program participants about various aspects of this program relating to the involvement of the undergraduate students. In conclusion, we share advice for those interested in starting and running similar outreach programs. [ABSTRACT FROM AUTHOR]

Combining mathematical and physical understanding in reasoning is difficult, and a growing body of research shows that students experience problems with the combination of physics and mathematics in reasoning beyond the introductory level. We investigated students' reasoning about boundary conditions (BCs) for the diffusion equation by conducting exploratory task-based, think-aloud interviews with twelve undergraduate students majoring in physics or mathematics. We identified several difficulties students experienced while solving the interview task and categorized them using the conceptual blending framework. This framework states that in reasoning, people draw from separate input spaces, in this case the mathematics and the physics input space, to form a blended space, where they make connections between elements from these spaces. To identify difficulties, we used open coding techniques. We observed few difficulties in the physics space. In the mathematics space, we identified several difficulties that we clustered in two main groups: findings about the mathematical meaning of BCs, and findings about reasoning with functions of two variables. Lastly, we identified four ways in which blending failed. Starting from our findings, we formulate recommendations for teaching and future research. [ABSTRACT FROM AUTHOR]

We describe the design and implementation of lessons in undergraduate abstract algebra that integrate applications to teaching high school mathematics. Each lesson consists of a pre-activity, class activity, homework set, assessment questions and detailed instructor notes. The included applications intend to bridge advanced mathematics concepts to secondary school mathematics content for prospective secondary mathematics teachers, as well as provide instructors with a useful resource. Each lesson includes four guiding features: addressing meaningful content; making connections to mathematics teaching; emphasizing active learning; and providing comprehensive notes for instructors. Interviews with instructors and their students document how the instructors adapted the lessons to their classrooms and how the lessons influenced undergraduates' mathematical understanding. [ABSTRACT FROM AUTHOR]

Previous studies have suggested that problem-posing activities could be used to improve the teaching, learning, and assessment of mathematics. The purpose of this study is to explore undergraduate engineering students' problem posing in relation to the integral-area relationship. The goal is to help fill a gap in tertiary level research about students' mathematical problem posing, particularly of engineering students. The mathematical problem posing of 135 undergraduate engineering students was explored using four problem-posing tasks and semi-structured interviews. The findings indicate that many of the problems the students posed were solvable and in a pure mathematics context, while those problems students attempted to set in a real-world setting did not provide a realistic situation. In addition, students faced a number of difficulties when posing problems related to the integral-area relationship and mathematics in general, and several students had a limited understanding of the applications and uses of the integral-area relationship in the real-world. This study suggests that using problem-posing activities in teaching and assessment can help identify engineering students' mathematical understanding and misunderstanding. Furthermore, using problem-posing tasks can help developing engineering students' understanding of the applications of integral calculus. More broadly, the findings suggest that problem-posing tasks could be used more often, alongside problem-solving tasks, as part of the teaching and assessment of mathematics at the university level. [ABSTRACT FROM AUTHOR]

Setting specific, challenging goals motivates employees to exert greater effort in their jobs. However, goal-setting may have unintended consequences of also motivating unethical behavior. The present study explores these consequences in the context of other features of goal-setting in organizations, how goals are framed and rewarded, to determine the tradeoff between performance and ethical behavior. Undergraduate students were incentivized to complete math problems using different outcome frames and incentive structures and were also provided an opportunity to cheat. Findings demonstrate that when goals rewarded with piece-rate incentives are framed as a loss, performance increased, though cheating behavior increased as well. [ABSTRACT FROM AUTHOR]