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1.
Benjamin Hutz 《PRIMUS》2017,27(4-5):494-507
Abstract

This article examines the use of the computer algebra system SAGE for undergraduate student research projects. After reading this article, the reader should understand the benefits of using SAGE as a source of research projects and how to commence working with SAGE. The author proposes a tiered working group model to allow maximum benefit to the students with a reasonable time requirement from the supervising faculty. Once a faculty member is familiar with the current state of SAGE functionality, it is possible to institute a long-term development plan that spans multiple years and students greatly reducing the “setup” time for new students. This model also allows the faculty member to work with a broad range of students as they can support each other. To illustrate this model, outcomes from several years of student research projects are discussed as well as the setup requirements and the process of using SAGE for research. The author worked with five different students over the course of 3 years. This resulted in two refereed undergraduate publications and 41 new additions to the SAGE code base. Of these five students, three entered graduate school, two in mathematics and one in computer science.  相似文献   

2.
ABSTRACT

Community colleges are often boxed into university models despite the unique nature of their institutional missions and student populations. We believe community colleges need to develop their own models, rooted in their distinctive missions, to encourage student success. We illustrate this through our experience with a short-term research assistantship program. The program created a brief, but important, way to enhance the student–professor relationship and engage students in applied research practices. It also provided a resource to assist community college faculty in conducting their own, original research. We hope others will not only develop similar programs, but perhaps more importantly, that this article will spur bottom-up, creative thinking to engage time-constrained, community college students in meaningful ways.  相似文献   

3.
Abstract

In this article, we share a model of flipped instruction that allowed us to gain a window into our students’ mathematical thinking. We depict how that increased awareness of student thinking shaped our mathematics instruction in productive ways. Drawing on our experiences with students in our own classrooms, we show how flipped instruction can be used to design experiences that help students make sense of mathematics during class sessions.  相似文献   

4.
Abstract

The effects on student performance and student attitudes of varying the instructional locus of control between students and teachers were investigated. A 2 X 2 factorial design was used that included either teacher regulation or student regulation of 1) the setting of weekly learning goals, and 2) the evaluation of weekly work. After a 4-week period, a mathematics achievement test and a student attitude survey were administered. Results indicated that although teachers set more individual learning goals for students, students who set their own learning goals attained more of them. Students tended to evaluate their work more favorably than teachers, and work evaluations from both teachers and students were higher for students who initially set their own learning goals. In addition, students who were given the opportunity to set their own learning goals reported better goal-setting ability than those for whom goals were externally imposed by the teacher. As predicted, the self-regulated goal setting and evaluation were found to be significantly related to attitudes, but not to mathematics achievement.  相似文献   

5.
Abstract

As STEM educators, we know it is beneficial to train students to think critically and mathematically during their early mathematical lives. To this end, the author teaches the College Algebra/Precalculus course in a flipped classroom version of an inquiry-based learning style. However, the techniques described in this paper can be applied to a variety of freshman and sophomore mathematics courses (and above). In particular, in this model the students read the textbook before class and formulate questions, submitted prior to class via a learning management system, about the material to be covered in class the next day. During class they solve problems about that topic, and solutions are presented and discussed before the end of the period. After class, students complete standard homework about the topic, and are encouraged to bring any unresolved homework, worksheet, or reading questions for the next class period. This paper will discuss this method of engaging students, focusing on how student questions evolve during the semester, and student feedback.  相似文献   

6.
Abstract

We present a first-hand, longer-term account of one student’s (Christine’s) experiences in and after a mathematics inquiry course. In this course, students actively posed problems, conducted their own mathematical explorations, and wrote journal entries about their experiences. During the course, Christine found that inquiry helped her develop mathematical content knowledge and a deeper understanding of the nature of research. After the course, Christine became a mathematics education faculty member in a mathematics department and reports that the course impacted the way she teaches mathematics. This provides an illustrative case of the potential long-lasting benefits of an inquiry course.  相似文献   

7.
ABSTRACT

Educators in higher education commonly use peer and self evaluations to help assess student performance on group projects. Although these evaluations provide multiple benefits, many educators are wary of using them due to concerns about their quality. This study addresses three questions debated in the literature regarding the quality of these assessments. How much do students differentiate among peer contributions through their ratings? How reliable are peer ratings? How much agreement exists between peer and self ratings? Although these questions have been addressed to varying degrees in past work, their answers have been far from settled. While many studies focus on just one of the questions, this study’s data make it possible to address all three questions for the same group of students as well as examine each question by student performance level. The evaluations assessed in this study were completed by a large number of students under conditions associated with obtaining more valid and reliable ratings. Overall, the results provide support for using peer and self evaluations to help assess student contributions to group projects. Peer ratings were largely reliable as group members generally agreed on the scores given to their peers. In addition, most students differentiated among group member contributions through their ratings. Students also tended to rate themselves higher than their peers rated them. This study has implications for how peer and self evaluations can be most effectively used by educators to measure student performance in group work.  相似文献   

8.
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9.

Often, mathematics teachers do not incorporate whole-class discourse of students’ various ideas and solution methods into their teaching practice. Particularly complex is the in-the-moment decision-making that is necessary to build on students’ thinking and develop their collective construction of mathematics. This study explores the decision-making patterns of five experienced Dutch mathematics teachers during their novice attempts at orchestrating whole-class discourse concerning students’ various solution methods. Our goal has been to unpack the complexity of their in-the-moment decision-making during whole-class discourse through lesson observations and stimulated recall interviews. We investigated teacher decision-making adopting a model that combines two perspectives, namely (1) we explored student-teacher interaction with regard to building on student thinking and (2) we explored how the teachers based decisions during such interaction upon their own personal conceptions and interpretation of student thinking. During these novice attempts at orchestrating whole-class discourse, the teachers created many situations for students to articulate their thinking. We found that at certain instances, teachers’ in-the-moment decision-making resulted in opportunities to build on student thinking that were not completely seized. During such instances, the teachers’ decision-making was shaped by the teachers’ own conceptions of the relevant mathematics and by teacher conceptions that centered around student understanding and mathematical goals. Our findings suggest that teachers might be supported in their novice attempts at whole-class discourse by explicit discussion of the mathematics and of their conceptions with regard to student understanding and mathematical goals.

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10.
Dominic Klyve 《PRIMUS》2017,27(4-5):548-557
Abstract

This paper describes efforts by the author to engage and motivate students in undergraduate research by giving them a large audience and engaging the media in disseminating their work. I provide an introduction to public relations from the point of view of a mathematics professor, and describe some lessons I have learned in my own attempts to engage newsprint, radio, and television sources in stories about undergraduate research in mathematics. After describing some partially successful early attempts, the paper discusses a recent event in which undergraduate research in mathematics became, briefly, a “hot news item” in Central Washington. The paper concludes with some thoughts about the benefits of this type of work to our students and our profession.  相似文献   

11.
Robert W. Bell 《PRIMUS》2017,27(3):406-417
Abstract

Mentoring undergraduate students in research is both rewarding and challenging. In this paper we present how we established a summer Research Experience for Undergraduates (REU) program in the mathematical sciences at Michigan State University. A goal of our REU is to include students who are at an early stage of their study of mathematics. We share our experiences in recruiting students, designing research projects, and mentoring our participants. We discuss the challenges we faced and the solutions we found while working with a diverse group of undergraduate students from across the nation.  相似文献   

12.
Abstract

There is evidence that many students leave university without effective learning strategies and skills that would facilitate their learning in the future. For example, they can complete their university courses without developing information skills or a love of learning, with only a limited repertoire of learning strategies, and with no intention of engaging in further learning. While these findings indicate a need for universities to review the structure of courses and the way that they are taught and assessed, it is not necessary to wait for this to happen. Within existing course structures, universities can help prepare students for lifelong learning by teaching them learning strategies. This is best done if the strategies are taught by university teachers in the context of their regular coursework. We have confirmed in our research and professional development projects that this can be done. In an experimental study, we investigated the effects of explicidy teaching students learning strategies in the context of their regular coursework. This research indicated that students who were taught learning strategies in the context of their regular coursework used them effectively and achieved better results than students who were taught in the conventional way. In a professional development project, we taught university teachers from a variety of subject areas to teach learning strategies to students in their own courses. These teachers were successful in helping students develop a repertoire of effective learning strategies and display greater commitment to their learning.  相似文献   

13.
abstract

In the context of our work as literacy specialists, we taught teachers to use sentence frames to support ELL students’ writing. We then studied the impact of their instruction on students. Our analysis of student writing samples revealed no groupwide developmental trends so we posed deeper questions about their work using the data analysis methods learned through the action research process. We report our findings about the relationship between student writing development and language instruction. We discuss our learning as well as implications for our work supporting teacher instruction.  相似文献   

14.
M. Greene 《PRIMUS》2017,27(7):646-668
Abstract

This paper aims to illustrate a design cycle of inquiry-based mathematics activities. We highlight a series of questions that we use when creating inquiry-based materials, testing and evaluating those materials, and revising the materials following this evaluation. These questions highlight the many decisions necessary to find just the right tasks for our students. Throughout the paper the use of multiple representations (graphical, numerical, symbolic, and narrative) and the distinction between facts, skills, methods, and conceptual understanding is explained and illustrated with examples. Additionally, we present evidence of student learning through excerpts from student journals and exam analysis.  相似文献   

15.
John P. D’Angelo 《PRIMUS》2017,27(8-9):778-791
Abstract

We offer many specific detailed examples, several of which are new, that instructors can use (in lecture or as student projects) to revitalize the role of complex variables throughout the curriculum. We conclude with three primary recommendations: revise the syllabus of Calculus II to allow early introductions of complex numbers and linear algebra, include complex variables and some infinite-dimensional linear maps in linear algebra courses, and spice up complex variable courses by better connecting them with the mathematics used in engineering in physics.  相似文献   

16.
Abstract

School–university partnerships also known as professional development school (PDS) partnerships provide potential for universities and schools to establish partnerships that can benefit university faculty, school teachers, university students, and school students. This study examines the impact of a PDS partnership in which the author served as a school-based mathematics coach for two years in a high-need elementary school. Data sources included interviews, surveys, and field notes from classroom observations. Inductive qualitative analyses which were situated in a multi-level framework for researching professional development found that teachers posed more cognitively demanding mathematical tasks and high-level questions in year two compared to year one of this project. Further, student achievement was noted on both state-wide and district-created assessments. Also teachers reported that the school-based approach to professional development led to some teachers taking on more informal leadership roles to support their colleagues’ mathematics instruction. Implications for school-based learning opportunities across the world include the need to establish specific university–school partnerships, and carefully designing research studies to examine the impact of these learning opportunities.  相似文献   

17.
Mehdi Razzaghi 《PRIMUS》2017,27(4-5):517-525
Abstract

Undergraduate research has become the centerpiece of many institutions of higher education’s efforts to attract and recruit high school graduates. Since 1987, throughout my tenure at Bloomsburg University, I have involved over 20 students in my research. In my experience, there is clear evidence that students of mathematics substantially benefit if they engage in research during their undergraduate studies. Whether the student plans to apply for employment after graduation or continue with graduate studies, the undergraduate research experience has a tremendous effect on the student’s success. In this paper, I will provide some personal insight on my experience in working with undergraduate students. In most cases, my experience has been in working with one student on a long term (one semester or mostly year-long) research problems. I will discuss my approach to identifying students, the type of projects, providing guidance, and finally the challenges that we face in supervising undergraduate research. To exemplify, emphasis will be placed on the status of a recent 1-year research project, which was funded by the Pennsylvania State System of Higher Education, and a senior undergraduate student worked on it for one year.  相似文献   

18.
David White 《PRIMUS》2019,29(9):997-1038
Abstract

In an increasingly data-driven world, facility with statistics is more important than ever for our students. At institutions without a statistician, it often falls to the mathematics faculty to teach statistics courses. This paper presents a model that a mathematician asked to teach statistics can follow. This model entails connecting with faculty from numerous departments on campus to develop a list of topics, building a repository of real-world datasets from these faculty, and creating projects where students interface with these datasets to write lab reports aimed at consumers of statistics in other disciplines. The end result is students who are well prepared for interdisciplinary research, who are accustomed to coping with the idiosyncrasies of real data, and who have sharpened their technical writing and speaking skills.  相似文献   

19.
Abstract

This paper discusses the use of comics in teaching mathematics in the secondary mathematics classroom. We explicate how the use of comics in teaching mathematics can prepare students for the twenty-first century competencies. We developed an alternative teaching package using comics for two lower secondary mathematics topics. This alternative teaching package consists of (1) several sets of comic strips expounding all related mathematical concepts in a lively way; (2) tiered practice questions for learning reinforcement; and (3) a set of proposed lesson outlines with suggestions on how to use the comics for mathematics teaching. We also report how one of the teachers in our study used this teaching package in her mathematics lessons. Her lessons were video-recorded and 11 students were interviewed to help us understand how the mathematics comics lessons were enacted and the students’ perception of comics as instruction. We identified instances in which the teacher tweaked the provided resource to further enhance student learning and incorporated elements of the twenty-first century competencies during her lessons. Through selected student interviews, we also identified instances in which students commented on their gain from the new approach from the perspective of the twenty-first century competencies.  相似文献   

20.
Abstract

This paper links educational psychology research about curiosity to teacher moves that are effective in an inquiry-based mathematics classroom. Three vignettes will show explicit teacher moves (staging disagreement, intriguing anecdotes, and creating a safe space) for different audiences (math majors, mathematics for liberal arts students, and future elementary school teachers) and tie them to particular studies about curiosity. The goal is to deepen our thinking about inquiry-based teaching by considering curiosity as one of the starting points of inquiry. Educational psychologists have found ample evidence that curiosity improves learning. We claim that curiosity and inquiry are deeply connected in a curiosity–inquiry cycle and become most active in a classroom that exhibits a culture of asking questions.  相似文献   

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