An Introductory Research Experience in Mathematics for Undergraduates

Abstract

This paper offers a strategic initiative designed to boost the level of collaborative mathematical research involving undergraduate mathematics students at Butler University. It describes goals, program design, logistics, and outcomes for an 8-day intensive summer experience in which undergraduate mathematics majors engaged in original mathematical research at an introductory level.     

Successfully Mentoring Undergraduates in Research: A How To Guide for Mathematicians

Abstract

Undergraduate research occurs in a variety of mathematical fields and in diverse settings, but all mentors of undergraduates face a number of common considerations. This article is a brief guide to help faculty with various levels of previous mentoring experience lead students in research projects. In particular, we discuss the issues of picking appropriate research problems, recruiting students, setting expectations, moving research forward, and helping students to communicate their work.     

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.     

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.     

Play and Literacy: A Collaborative Action Research Project in Preschool

The article describes a collaborative action research in a preschool in Reykjavik. The participants were two preschool teachers who collaborated with researchers at the University of Iceland. The project was set up as a professional development course for the teachers. Emphasis was placed on continuity in children's education, integration of play and learning, and the connection between play and emerging literacy. Data were gathered using video recordings, photos, interviews, observations, notes from meetings, documents, and diaries. The findings indicate that participation in this action research empowered the preschool teachers and influenced their practices and ideas. They became more aware of the value of play in children's learning. They did not, however, change their former practices in which they worked on literacy during specific, well-defined periods: their beliefs and practices in this regard seemed to be constrained by traditions in which play and learning are separate entities.     

Mentoring Undergraduate Interdisciplinary Mathematics Research Students: Junior Faculty Experiences

Abstract

To be successful, junior faculty must properly manage their time in the face of expanding responsibilities. One such responsibility is supervising undergraduate research projects. Student research projects (either single or multi-student) can be undertaken as a full-time summer experience, or as a part-time academic year commitment. With many potential undergraduate research formats, and with different types of students, junior faculty may find challenges in forming their research group, establishing a structure that promotes student productivity, picking an appropriate project, or in effectively mentoring their students. This article draws from the authors’ experiences to help junior faculty navigate these complexities so that all parties reap the benefits of undergraduate research in interdisciplinary mathematical disciplines.     

Introduction to the Special Issue on Interdisciplinary Conversations (Part 2): The Impact of Interdisciplinary Conversations on Courses

Abstract

The two parts in this special issue address interdisciplinary conversations involving mathematics courses in the first 2 years of undergraduate work. The special issue was inspired by work funded by the National Science Foundation under a grant titled “SUMMIT-P.” The special issue includes papers written about projects both from SUMMIT-P and from outside of SUMMIT-P. Part II focuses on what the results of interdisciplinary collaboration look like in the classroom.     

Flattened Hierarchy Through Drama-Based Pedagogy: A Graduate Student Instructor and Two Undergraduates Partner on Classroom Research

In this paper, the authors describe their journey from a teacher-student relationship to that of research partners and co-authors, thus providing a case study situated within the literature on students as partners. The instructor's use of drama-based pedagogy organically facilitated this journey both by flattening the hierarchy between teacher and students, and by being the subject under study. As a research group, the authors designed and collaborated on a scholarship of teaching and learning (SoTL) project. They analyzed existing classroom data to study the effects of drama-based pedagogy on their classroom environment and presented findings at conferences and through publication. This collaboration between a graduate student instructor and her undergraduate learners benefited all parties from both research and professionalization perspectives, which mirrors positive outcomes in the students as partners literature. The partnership can thus serve as a model for similar partnerships with minimal institutional infrastructure. Graduate students become research mentors and gain greater access to their students' classroom experiences, while undergraduate students explore the next step of an academic career track by conducting and disseminating original research as equal partners. The authors highlight reciprocity in their collaboration and call on institutions to facilitate this kind of partnership with funding and institutional support.     

Community of Inquiry (CoI): A Framework for Social Work Distance Educators

ABSTRACT

The Community of Inquiry (CoI) framework, a research-based seminal work, provides a structure for integrating a collaborative constructivist approach in course design, implementation, and evaluation. The CoI framework suggests that by fostering three essential elements – social presence, cognitive presence, and teaching presence – a community of inquiry can be created to promote student engagement and learning. This paper will present the concepts of the CoI framework for social work educators to consider for distance education course design, implementation, and evaluation.     

Building Capacity for Undergraduate Research in Mathematics: A Case Study at Georgia College

The Georgia College mathematics department has reimagined its major requirements to integrate meaningful undergraduate research experiences. We have developed and implemented a multi-year action plan to transform our major. In this article we discuss how the department has developed and implemented a year-long research experience as a capstone requirement. We address how we gained faculty and student buy-in, built a curriculum to support the experience, and developed assessment and evaluation tools. We conclude with a discussion of challenges and next steps in the program.     

Smooth Transition for Advancement to Graduate Education (STAGE) for Underrepresented Groups in the Mathematical Sciences Pilot Project: Broadening Participation through Mentoring

The Smooth Transition for Advancement to Graduate Education (STAGE) project was a three-year pilot project designed to mentor undergraduate students primarily from under-represented groups in the mathematical sciences. The STAGE pilot project focused on mentoring students as they transitioned from undergraduate education to either graduate school or a career in the STEM workforce. We discuss the various mentoring structures, the STAGE pilot utilized, and how those structures affected programmatic outcomes. In addition, we discuss challenges we faced in mentoring undergraduates and special considerations we made when mentoring students from under-represented groups.     

数学教育跨学科卓越奖（IEME奖）：表彰和促进数学教育跨学科“合作”“领导力”及“影响力”

介绍了美国德克萨斯农工大学数学教育跨学科卓越奖的建立背景、缘由和重大意义.有别于数学教育界和数学界的其它奖项,该奖项强调了认识和重视数学教育的跨学科性和跨学科协作的重要性;并将其作为促进数学教育(作为一个跨学科领域)发展的机制.此外,也提供有关此奖项的申报资料及以往得奖者的表彰介绍,以突显该奖项的宗旨.     

Citing as a sourcing practice: students’ citing self-selected online sources in their essays (Las citas como práctica del uso de las fuentes: las citas de fuentes en línea seleccionados por los estudiantes en sus trabajos)

ABSTRACT

This study examined upper secondary school students’ citations of self-selected online sources in their essays. Students (n = 140) conducted online inquiry about either effects of social media on people’s quality of life (SM) or allowance of genetic manipulation of organisms (GMO). Students, working either individually or in pairs, explored online sources with the help of a graphic organizer, after which they composed their essays. To capture the quality of citations identified in the essays, they were evaluated in terms of accuracy and richness of source features. Further, regression analysis was used to examine the effect of topic, grade level and work mode on the number and quality of citations. Results showed that students seldom cited sources in their essays, and when they did, citations were mostly accurate but less often rich in source features. When writing about SM, students most frequently cited media sources, while sources with ideological, political or religious motives were frequently cited in GMO essays. Students’ grades and work modes predicted the number of citations and number of accurate citations.     

The W(h)ine Club: women finding joy in academic work

The W(h)ine Club is a multidisciplinary women's research team which has been working together for the past 10 years. The idea for this Viewpoint piece grew as we participated in a Women in Research programme. The aim of the programme was to improve academic publications among women. A group of us in the programme found ourselves repeatedly referring to a time when we had worked together in a research project and the absolute joy we had experienced working together. We decided to write this reflection as the story of the W(h)ine Club, a space in which we complained, drank lots of wine, laughed and researched. All at the same time! What we realised was that women academics working together was a wonderful way to do research. Sharing our joys and sadness was often the glue that kept the team together and we learnt about research without realising it. In this Viewpoint we show that learning to research can be fun and that the bonds built in this process are powerful and validating.     

A roadmap for forming successful interdisciplinary education research collaborations: a reflective approach

Current literature about interdisciplinary education research is focused on three points: conceptual definitions of interdisciplinarity, the need for interdisciplinary research to tackle the advent of problem-based research and the positive curriculum outcomes to be gained from interdisciplinary research. While this research is important, it does not always include an account of the often complex and politicised interactions that might affect the outcomes of interdisciplinary research groups. This paper provides one possible ‘roadmap’ for successful interdisciplinary collaboration. It is based on a reflective case study of the authors’ own formation of an interdisciplinary research group and the practical resolutions to both the theoretical and the practical issues involved in achieving interdisciplinarity in education research.     

治学琐谈（上）

进行史学研究必须以历史唯物主义理论的指南：掌握考证的必要研究手段;恰当处理微观研究与宏观研究的关系;认真做好史料卡片;充分认识史学领域知识更新的特点。     

The Impact of Research on Policy: A Case of Qualifications Reform

The relationship between research and policymaking has been discussed repeatedly. However, the debate tends to be in general, abstract terms or from a macroeconomic perspective with any examples described in a fairly cursory way. Despite the inherent complexity of the research-policy interface, analyses tend to homogenise ‘research’ and ‘policy’ as coherent entities with discussions often focusing on products (research and policies) rather than on the relationships between producers (researchers and policymakers). Here, we take one piece of research on qualifications that has influenced policy rhetoric over the last 5 years. We trace the career of the research from its production in the late 1990s in order to understand the conditions of its dormancy, re-emergence and use over the ensuing years. The paper serves to document the case, which is important in its own right, but also proposes a typology of ways in which research gets adopted and adapted into policy.     

大数据时代网络教育学习成绩预测的研究与实现--以本科公共课程统考英语为例

合适的数据分析技术能使我们借助网络学历教育学生在学习和管理系统中产生的数据和信息,发现相关规律,进而为网络学历教育教学和管理流程的优化提供有益的决策依据。本文采用数据挖掘中数据分类C5.0决策树方法,通过分析网络学历教育本科学生英语学习及相关信息,实现了对其英语统考成绩的预测。在分析英语统考前景预测的目标特性后,在SPSS的Clementine 12.0数据挖掘环境中,历经数据提取、数据预处理、决策树构建和决策树优化等步骤,本研究构建了网络教育本科英语统考成绩的预测模型,并提出了模型实现方法;同时对模型相关属性的重要性进行了分析,提出了提高网络教育本科学生英语学习水平和统考通过率的相应策略。     

The Language in Chinese Mathematical Texts Before AD 1300: A Case for Logical Abstraction

While there seems to be a general consensus that literacy should include the ability to deal with basic reading, writing, and arithmetic, a view is growing that literacy is in fact more than equipping learners with sets of essential skills (Wells, 1981; Schoenfeld, 1985; Bereiter & Scardamalia, 1987; Cumming, 1990; Wells & Chang-Wells, 1992). Olson (1994) reviews in his book The World on Paper a large number of studies in the field of psychology, sociology, history, and linguistics and concludes that modern literacy in the West is characterized by a new way of looking at written texts and the representation the texts project. In the contemporary East, while many countries including China are striving for economic development and modernization, the question of why science and modernity did not first develop in some oriental cultures such as China, which used to be the most advanced, remains interesting but unanswered. In the light of Olson's discussion regarding literacy and Western modernity, this paper adopts a cognitive-linguistic perspective and examines the social conditions in which ancient Chinese mathematics struggled to develop. Examples and experiences in ancient Chinese mathematical texts are presented to reveal the close relationship between modernity, literacy, and written language. In response to a new interest in a context-rich approach to mathematics teaching, the paper also discusses its implications for the mathematics curriculum.     

Experience,represent, apply (ERA): A heuristic for digital engagement in the early years

This paper presents an heuristic that underpinned the development of a range of early years applications (apps) as part of the Early Learning Science, Technology, Engineering and Mathematics (STEM) Australia (ELSA) project (2016–19). The heuristic was developed to address a range of challenges that accompany the use of digital technologies in the year before formal schooling. These include the role of digital technologies in play-based learning environments, screen time and the importance of agency when young children are using digital technologies. In an increasingly digital world, the issue of screen time looms large as a particularly contested aspect of technology use by young children. The ELSA project responded to this challenge by developing a pedagogical framework that embedded digital technologies into context-rich, play-based STEM learning. The Experience, Represent, Apply (ERA) heuristic discussed in this paper is a component of the project's overall pedagogical framework and provides early years educators with the opportunity, and the know-how, to integrate digital technologies into STEM activities through intentional teaching and play-based engagement. It was evident from educator feedback at the four days of workshops we delivered, and in other comments throughout the year long trial, that the educators were able to embrace the cyclic nature of the ERA heuristic and ensure that the time spent on the tablet (Represent) was connected to contextualised learning opportunities (Experience and Apply). Importantly, the tablets provided affordances for the children to utilise User Generated Content (UGC) to support active engagement when using the tablets.