CRP: Collaborative Research Project (A Mathematical Research Experience for Undergraduates)

Abstract

The Collaborative Research Project (CRP)—a mathematics research experience for undergraduates—offers a large-scale collaborative experience in research for undergraduate students. CRP seeks to widen the audience of students who participate in undergraduate research in mathematics. In 2015, the inaugural CRP had 100 undergraduate participants from across the United States; they collaborated on a month-long research effort applying tropical geometry to phylogenetics. CRP is envisioned as an annual event, one that scales to accommodate large numbers of interested students. This article describes the motivation for CRP, its structure, and the results of its inaugural iteration, and closes by assessing its future.     

Teaching Spilling by Column and Context Forms

Abstract

Two groups of undergraduate students participating in a field experience as part of the undergraduate teacher preparation program were compared on the basis of the supervisory practice of the cooperating/mentor teacher. Both groups received a traditional orientation to student teaching and supervision. In addition, the experimental group had teachers that received an in-depth training in supervision using a specific framework, Praxis III/Pathwise (Educational Testing Service, 1995). Results demonstrated statistically significant differences in favor of the experimental group on 11 of the 19 variables investigated.     

The role of perceived support and local culture in undergraduate research mentoring by underrepresented minority faculty members: findings from a multi-institutional research collaboration

ABSTRACT

Undergraduate research is value-added experiential learning that cultivates creative and intentional learners in and out of the classroom. However, only recently have researchers begun investigating the mechanisms related to mentoring undergraduate researchers, with scant attention being paid to the experiences of underrepresented minority (URM) faculty members. Using unique data collected from an online survey of faculty members (overall N = 215, URM n = 25), we find departmental and institutional support to be the key factors correlated with mentoring undergraduate research students. Reported support is more influential for URM faculty than white faculty, providing evidence of the importance of institutional policy as a mechanism to facilitate URM faculty participation in the high impact practice of mentoring undergraduate researchers. The findings are discussed in the context of institutional initiatives designed to support student and faculty success in the 21st century.     

Introduction to the Special Issue on Perspectives and Experiences on Mentoring Undergraduate Students in Research: Part I

Abstract

This issue is the first of a special PRIMUS two-part issue collecting articles from experienced faculty mentors. We offer it as a valuable resource for faculty leading undergraduate research programs. It is inspired by the “Regional Faculty Workshop on REU Issues” in 2013 and the Joint Mathematics Meeting 2015 Mathematical Association of America’s “Themed Session on Perspectives and Experiences on Mentoring Undergraduate Students in Research.” This issue consists of seven papers focusing on the larger issues involved in creating, running, and sustaining an undergraduate research program in mathematics.     

Unpacking Rouché’s Theorem

Abstract

Rouché’s Theorem is a standard topic in undergraduate complex analysis. It is usually covered near the end of the course with applications relating to pure mathematics only (e.g., using it to produce an alternate proof of the Fundamental Theorem of Algebra). The winding number provides a geometric interpretation relating to the conclusion of Rouché’s Theorem, but most undergraduate texts give no geometric insights that lead to an understanding of why Rouché’s Theorem holds. In addition, most texts do not inform students that a stronger version of the theorem exists. In this paper we present a simplified proof of the stronger version, which is a suitable topic for students to pursue as a short project, and provide a geometric argument for the weaker version. Finally, as a project for advanced students, we unpack a standard application of this theorem as used in control systems: the Nyquist stability criterion.     

Empirical validation of a modern genetics progression web for college biology students

ABSTRACT

Research in learning progressions (LPs) has been essential towards building understanding of how students’ ideas change over time. There has been little work, however, into how ideas between separate but related constructs within a multi-faceted LP relate. The purpose of this paper is to elaborate on the idea of progression webs to model connections within and between related constructs simultaneously, and to explain and demonstrate the efficacy of path analysis towards validating a hypothesised progression web for understanding of modern genetics. Specifically, we evaluate strength of evidence for a progression web based upon multiple related constructs within a multi-faceted LP describing undergraduate biology students’ understanding of genetics. We then utilise the progression web to generalise theory around how undergraduate students understand relationships between related genetics concepts, and how they use simpler concepts to scaffold those which are more complex.     

Undergraduate time-use: a comparison of US,Chinese, and Russian students at highly selective universities

ABSTRACT

Patterns of students’ time-use can provide important insights into student learning and development in higher education. Previous empirical studies conducted in developed countries do not allow us to generalize findings on time-use patterns for students from countries with different national systems. This paper aims to identify national differences in undergraduate patterns of time-use and their links with the individual characteristics of students. The sample (N?=?166,919) was derived from highly selective universities from three countries: the USA, China, and Russia. Significant differences in undergraduate time-use patterns in three countries were observed. In addition, significant interaction effects between national variables and individual characteristics were found. The results allow us to conclude that there are national differences in the power and direction of links between time-use patterns and individual characteristics.     

Yes we can: towards assurance of learning by scholarly academics through a praxeology of the scholarship of teaching

ABSTRACT

This article explores how Revan’s praxeology and learning formula act as the foundation for the authors’ enactment of the scholarship of their teaching practice. Linking to accreditation requirement of assurance of learning the authors describe two undergraduate courses that they teach and reflect on how Revan’s praxeology of systems alpha, beta and gamma and his learning formula, L?=?P?+?Q provide a framework for understanding and enacting their scholarship of teaching. They offer their experience and reflection for other academics to engage with the scholarship of their respective practice.     

Using Graph Talks to Engage Undergraduates in Conversations Around Social Justice

Abstract

We present a mathematical activity called graph talks as a new pedagogical routine to intertwine social justice issues and mathematics. Adapted from number talks, graph talks involve students analyzing, interpreting, and discussing real-life data represented in graphs. Graphs may be strategically selected to both highlight a relevant social justice issue while also reinforcing the mathematics content of the course. We report on experiences using graph talks in undergraduate mathematics content courses for future teachers in the USA, and provide examples of the undergraduates doing mathematics while analyzing the social justice context of the graphs.     

Undergraduate research as a student engagement springboard: Exploring the longer-term reported benefits of participation in a research conference

ABSTRACT

Background: Undergraduate research is evident in many forms across higher education: in journals, at conferences and on research placements. It is widely reported that undergraduate research can encourage the development of discipline-specific and transferable communication skills and, in some cases, a more complex development of higher-order critical appraisal. Recent studies of extracurricular undergraduate research conferences have also found that participants report a development of self-authorship and an appreciation of the conference as liminal and transformative space. With many published studies measuring immediate feedback surrounding conference events, there is also a need to explore participants’ reflections over a longer term period of time.

Purpose: This small-scale project investigated participants’ self-report of whether and in what ways participation in a non-assessed, extracurricular undergraduate research conference had impacted their academic and professional practices, one year after their involvement in the conference.

Method: The qualitative study took place over two academic years with participants from an undergraduate conference which was held annually. The investigation adopted an action research methodology and completed two cycles of research. Data were collected firstly through an online survey with open questions, yielding feedback from 44 respondents. Focus groups were then conducted with nine of these students to explore this data further. A thematic approach was used to analyse the data.

Findings: The two cycles of data collection and analyses resulted in the identification of four central themes: (1) general positive impact on studies or career; (2) the development of presentation skills and personal confidence; (3) the development of research skills and perspectives; (4) an increased engagement with extracurricular opportunities.

Conclusions: Overall, our analysis identified that participants reported a development in communication skills and an enhanced relationship with the concept of ‘research’ and self-authorship. Students’ report that participation directly led to increased engagement with additional extracurricular activities is particularly noteworthy, as it contributes something new to the growing body of literature surrounding undergraduate research. More widely, the study suggests the potential for undergraduate conferences to act as springboards for increased extracurricular engagement.     

Modelling water systems in an introductory undergraduate course: Students’ use and evaluation of data-driven,computer-based models

ABSTRACT

Introductory undergraduate courses present an opportunity to use disciplinary concepts in solving authentic problems. Making complex natural systems accessible to students through computer-based models allows them to practice making evidence-based predictions and communicate understanding. Despite the importance of modelling tools in formal classrooms, gaps exist in our understanding of how post-secondary students engage in computer-based modelling. Introductory courses, particularly in the hydrosciences, typically do not use these tools. This mixed methods study examines students’ model-based reasoning about a water-related issue over two years in response to a flipped course model. Students in an introductory water course learned basic hydrologic content and used a computer-based water model to complete a project. Data came from a pre-/post-course assessment, student assignments, and student interviews. Results of quantitative and qualitative data analyses show that students in the revised version of the course (Year 2, n?=?53) increased their understanding of core hydrology concepts and performed better on their evaluation of a computer-based water model, than students in the initial course (Year 1, n?=?38). We tentatively attribute these observed changes to increased active learning opportunities surrounding computer-based modelling of water systems. Findings contribute to science literacy development, undergraduate science learning environment design, and undergraduate scientific modelling.     

Critical qualitative research as a means to advocate for Latinas in STEM

Abstract

The current administration of the United States has brought to the forefront the hostile sociopolitical climate found within this diverse country as Americans continue to grapple with the intentional, residual effects of the systemic maintenance of oppression. The purpose of this study is to understand the perceptions of climate in the persistence of Latinas pursuing an undergraduate engineering degree. More specifically, this empirical study utilized critical consciousness to frame the counternarratives of how 11 Latinas experience their double bind status in engineering. The subsequent three themes emerged from data analysis: (1) desiring to relate to minoritized populations/women; (2) experiencing sexism on a pervasive level; and (3) discrediting their engineering competency. The authors then offer policy recommendations based on the findings.     

Cultivating a Culture of Undergraduate Research at a Public Comprehensive University

Abstract

Winthrop University is a public comprehensive university of about 6000 students, 5000 of whom are undergraduates. The Department of Mathematics offers a baccalaureate degree in mathematics, but has no graduate degree programs. As late as 2009, there was essentially no undergraduate research in the department. At this time, faculty made efforts to cultivate a research program that would motivate faculty to pursue more scholarly opportunities and include undergraduates in their scholarship. These efforts began with in-house-sponsored summer programs that lasted a few weeks and grew over the subsequent 5 year period to several externally funded undergraduate research programs, including a National Science Foundation-sponsored Research Experience for Undergraduates program. In this paper, we discuss some lessons we learned in developing a culture of undergraduate research. We focus on the advantages and challenges of undergraduate research at primarily undergraduate universities, offer advice for starting or growing a research program, and provide resources for funding undergraduate research.     

Interpersonal process recall: a novel approach to illuminating students’ software development processes

Background and Context: Encouraging undergraduate programming students to think more about their software development processes is challenging. Most programming courses focus on coding skill development and mastering programming language features; subsequently software development processes (e.g. planning, code commenting, and error debugging) are undervalued. Moreover, many of these processes involve tacit thinking that is often seemingly invisible, meaning it can be difficult for teachers to identify and address shortcomings in student processes.

Objective: In this paper, we employ a novel approach called Interpersonal Process Recall (IPR) to encourage students to think more about their software development processes.

Method: We conducted IPR sessions with five undergraduate programming students—we screen captured them working on programming assignments, and then used the screen captures to stimulate reflection. IPR is hallmarked by several key features, namely its developmental (rather than evaluative) focus, and the use of a facilitator to guide reflection in a structured way.

Findings: We found IPR was useful for both the teaching staff and the students, revealing incongruence between the value students placed on certain development processes and what they actually do in practice.

Implications: IPR is a novel approach for shining a light on student software development processes. We hope this paper encourages other practitioners to consider adding IPR to their toolbox of approaches for encouraging students to reflect on their software development processes.     

Teachers and students’ perception of competence-based education in the agricultural higher education system (Case of a student cooperative in Iran)

Purpose: This quantitative study sought to investigate the perceptions of teachers and students regarding competency-based education (CBE) principles at the College of Agriculture at Razi University.

Design: This research is a comparative analysis of two groups. The first group consists of undergraduate and graduate students majoring in agriculture who are members and non-members of student cooperatives (n?=?256). The second group consists of agricultural faculty members (n?=?59).

Findings: The results of this study show that students and teachers have different views with regard to the extent to which CBE principles are practiced in the College of Agriculture. Moreover, students with different learning patterns had different perceptions regarding the extent to which CBE is practiced, whereas teachers with different teaching patterns had the same perception of the application of CBE principles in the College of Agriculture.

Practical implications: This study has practical implications for agricultural higher education in general and colleges of agriculture in particular. Colleges of agriculture across Iran could encourage their students to establish and engage in student cooperatives so that the ‘what’ and ‘how’ aspects of CBE are put into practice.

Theoretical implications: This study has theoretical implications for CBE principles. For example, student cooperatives can be utilized by faculty members as one of the main strategies for developing CBE in agricultural colleges.

Originality/value: This study is original in that it moves from theory to practice when considering CBE.     

Introduction to the Special Issue on Perspectivesand Experiences on Mentoring Undergraduate Students in Research: Part II

Abstract

This issue is the second of a special PRIMUS two-part issue collecting articles on undergraduate research from experienced faculty mentors. We offer it as a valuable resource for faculty leading undergraduate research programs. This issue presents a collection of papers offering advice on a variety of specific topics important for leaders of undergraduate research programs. Issues of finding and designing appropriate and accessible research projects, assessing undergraduate research, and publicizing it in the media are addressed.     

The role of academic developers in embedding high-impact undergraduate research and inquiry in mainstream higher education: twenty years’ reflection

Abstract

The focus of this article is on the role of academic developers in supporting and influencing undergraduate research and inquiry, a high-impact activity. We examine the levels at which academic developers can influence undergraduate research and inquiry practices by distinguishing between staff and student practices; disciplinary and departmental practices and policies; institutional practices and policies; and national and international practices and policies. Drawing on our experiences over the last 20 years, we discuss the widening of academic development practice and consider who are the academic developers when it comes to embedding undergraduate research and inquiry in mainstream higher education.     

Mathematics in Physics Education: Scanning Historical Evolution of the Differential to Find a More Appropriate Model for Teaching Differential Calculus in Physics

Despite its frequent use, there is little understanding of the concept of differential among upper high school and undergraduate students of physics. As a first step to identify the origin of this situation and to revert it, we have done a historic and epistemological study aimed at clarifying the role and the meaning of the differential in physics and at improving curricular and teaching models in the sense of Gilbert et al. (Gilbert J.K., Boulter C., & Rutherford, M.: 1998a, International Journal of Science Education 20(1), 83–97, Gilbert J.K., Boulter C., & Rutherford, M.: 1998b, International Journal of Science Education 20(2), 187–203). We describe the contributions of Leibniz and Cauchy and stress their shortcomings, which are overcome by the alternative definition proposed by the French mathematician Fréchet, dating from early 20th century. As a result of this study, we answer to some fundamental questions related to a proper understanding of the differential in physics education (for 17–19 years old students).     

Integrating actual time usage into the assessment of examination time extensions provided to disabled college engineering students

Abstract

In this study, we suggest combining the monitoring of actual examination time used with grades in order to assess examination time extensions in terms of access provision and expected outcome. Using naturally-occurring data collected from a large sample (N?=?2315) of undergraduate engineering students, we argue that extended examination time may be regarded as providing equal access when a disabled student actually utilizes more examination time than a normally achieving student, regardless of the grade obtained. We further argue that extended examination time may be regarded as resulting in the expected outcome when a disabled student either (a) utilizes less or equal examination time and achieve grades that are lower than a normally achieving student, or (b) utilizes more examination time and achieve grades that are equal to a normally achieving student. In our data, equal access was provided in all courses (i.e. disabled students utilized more time than normal achievers), but the expected outcome (i.e. equal grades) was not observed in software and English examinations. The results of this study emphasize the importance of monitoring actual time usage in addition to performance measures when assessing examination time extensions.