nach oben

2016 | Buch

Kapitel lesen Erstes Kapitel lesen

Mathematics Education

A Spectrum of Work in Mathematical Sciences Departments

herausgegeben von: Jacqueline Dewar, Pao-sheng Hsu, Harriet Pollatsek

Verlag: Springer International Publishing

Buchreihe : Association for Women in Mathematics Series

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

Einloggen, um Zugang zu erhalten

Über dieses Buch

Many in the mathematics community in the U.S. are involved in mathematics education in various capacities. This book highlights the breadth of the work in K-16 mathematics education done by members of US departments of mathematical sciences. It contains contributions by mathematicians and mathematics educators who do work in areas such as teacher education, quantitative literacy, informal education, writing and communication, social justice, outreach and mentoring, tactile learning, art and mathematics, ethnomathematics, scholarship of teaching and learning, and mathematics education research. Contributors describe their work, its impact, and how it is perceived and valued. In addition, there is a chapter, co-authored by two mathematicians who have become administrators, on the challenges of supporting, evaluating, and rewarding work in mathematics education in departments of mathematical sciences.

This book is intended to inform the readership of the breadth of the work and to encourage discussion of its value in the mathematical community. The writing is expository, not technical, and should be accessible and informative to a diverse audience. The primary readership includes all those in departments of mathematical sciences in two or four year colleges and universities, and their administrators, as well as graduate students. Researchers in education may also find topics of interest. Other potential readers include those doing work in mathematics education in schools of education, and teachers of secondary or middle school mathematics as well as those involved in their professional development.

Inhaltsverzeichnis

Frontmatter

Benefitting the Readers of this Volume

Frontmatter

Chapter 1. Opening Lines: An Introduction to the Volume

Abstract

In this opening chapter, the editors set the stage for the wide-ranging description and discussion of work in mathematics education awaiting readers of this volume. They define how the phrase “work in mathematics education” is to be understood for this volume and explain how the 25 chapters are grouped according to intended beneficiaries of the work. The editors describe the genesis of the book: how the idea arose in June 2015 and how it was intended to be an extension of the conversation that would take place at the 2016 Joint Mathematics Meetings panel on “Work in Mathematics Education in Departments of Mathematical Sciences,” co-sponsored by the Association for Women in Mathematics (AWM) Education Committee and the American Mathematical Society Committee on Education. To entice the reader to explore the volume, the editors highlight some of the contents and note common themes and connections among the chapters. This chapter also summarizes the multi-stage process that brought the idea for this book to fruition so that the reader may understand the selection and peer review process. As many of the chapters do, this one closes with a final reflection by its authors on their involvement in this project.

Jacqueline Dewar, Pao-sheng Hsu, Harriet Pollatsek

Chapter 2. Communication, Culture, and Work in Mathematics Education in Departments of Mathematical Sciences

Abstract

Communication is much more than words—written, spoken, or unspoken. It is also in how a person participates in or orchestrates discussion (in a hallway or in a meeting). Conversation is shaped by what a person knows or anticipates about colleagues’ previous experiences and how to attend to that in the context of the goals of a given professional interaction. This chapter builds a foundation of ideas from discourse theory and intercultural competence development as aspects of communication. The presentation is grounded in two vignettes and several small examples of discourse about work in mathematics education. The ideas and vignettes provide touchstones for noticing and understanding what happens when people communicate across professional cultures within departments of mathematics.

Shandy Hauk, Allison F. Toney

Chapter 3. Valuing and Supporting Work in Mathematics Education: An Administrative Perspective

Abstract

In this chapter we reflect on the roles and responsibilities of academic leaders in encouraging faculty in mathematics departments to value contributions to mathematics teaching and learning. We discuss how academic leaders can and should use their perspective, position and influence to: encourage productive dialogue between practitioners of mathematics and mathematics education; use assessment of student learning as an opportunity to further this dialogue; and value and reward work in mathematics teaching and learning in the hiring, evaluation, tenure, promotion, and merit processes.

Minerva Cordero, Maura B. Mast

Benefitting Pre-Service and In-Service Teachers and Graduate Student Instructors

Frontmatter

Chapter 4. Effects of a Capstone Course on Future Teachers (and the Instructor): How a SoTL Project Changed a Career

Abstract

In this chapter, I revisit my first scholarship of teaching and learning project as a 2000–2001 Carnegie Academy for the Scholarship of Teaching and Learning scholar. I describe my experience as a pure mathematician taking on a pedagogical research project and the effects of this project and of doing the scholarship of teaching and learning on my teaching and career. The project studied student development in a novel mathematics capstone course for future teachers. Student teams worked on semester-long mathematics research problems, while simultaneously completing a content-heavy course on how advanced mathematics informs the teaching of high school (and earlier) mathematical subjects. The course changed behaviors of the students by giving voice to students with prior negative classroom experiences. In addition, one student had a surprising change in attitude towards proof and its value to secondary mathematics teachers. Working through the context of the original study, I reflect on the effects of the course on the students and of the project on the next 15 years of my career.

Curtis D. Bennett

Chapter 5. By Definition: An Examination of the Process of Defining in Mathematics

Abstract

Our work as mathematics education researchers in a department of mathematical sciences rests upon a foundation of reflections on our own teaching practices and on the mathematical practices that our preservice mathematics teachers are expected to learn. In the nexus of these reflections sit issues relevant to the learning and teaching of mathematics, and the understanding of these issues requires sustained and systematic research that includes and goes beyond reflecting on practices. We present an example of a teaching episode focused on preparing secondary mathematics teachers to better understand mathematical definitions and the process of creating mathematical definitions. We then examine some historical developments in mathematical practice related to definitions and the defining process and relate these developments to challenges entailed in teaching practice. We conclude with examples of researchable areas embedded in these issues and comment on the impact of our work.

Elizabeth A. Burroughs, Maurice J. Burke

Chapter 6. Characterizing Mathematics Graduate Student Teaching Assistants’ Opportunities to Learn from Teaching

Abstract

Exemplary models to inform novice instruction and the development of graduate teaching assistants (TAs) exist. What is missing from the literature is the process of how graduate students in model professional development programs make sense of and enact the experiences offered. A first step to understanding TAs’ learning to teach is to characterize how and whether they link observations of student work to hypotheses about student thinking and then connect those hypotheses to future teaching actions. A reason to be interested in these connections is that their strength and coherence determine how well TAs can learn from experiences. We found TAs can connect observations and future teaching, but that the connections vary in quality. Our analysis suggests future revisions to TA development programs, which we discuss in the conclusion.

Yvonne Lai, Wendy M. Smith, Nathan P. Wakefield, Erica R. Miller, Julia St. Goar, Corbin M. Groothuis, Kelsey M. Wells

Chapter 7. Lessons Learned from a Math Teachers’ Circle

Abstract

In this chapter, we describe our experience running the Northern Colorado Math Teachers’ Circle (NoCOMTC), founded in 2011. The goal of the NoCOMTC is to improve middle school mathematics teachers’ mathematical and pedagogical content knowledge through interactive mathematical problem-solving professional development sessions. Our leadership team is an effective collaboration between university mathematics and mathematics education professors and middle and high school mathematics teachers. In this chapter, we describe our leadership team’s journey from founding the NoCOMTC through four academic years of monthly evening mathematics teachers’ circle sessions and three residential summer immersion workshops. We also discuss our recently initiated student circle program. We focus on aspects that were essential to forming and sustaining our program. In addition, we highlight lessons we have learned while planning and facilitating both mathematical problem-solving sessions and activities designed to help teachers’ implementation of problem solving.

Gulden Karakok, Katherine Morrison, Cathleen Craviotto

Chapter 8. Transforming Practices in Mathematics Teaching and Learning through Effective Partnerships

Abstract

This is the story of a partnership between a university professor of mathematics (the first author) and a high school mathematics teacher (the second author). It started in 2007 through the Teacher Partnership Program of the Association for Women in Mathematics. They describe a succession of joint projects designed to benefit students from middle school to college. The partnership began with informal visits to one another’s classrooms and engagement with a high school mathematics team. The association extended to include a research experiences for undergraduates program in 2009. In 2011 the collaboration continued in the STEM Accelerator Program at the College of Science at George Mason University (GMU). The GMU collaborative work included a summer camp for middle school girls called FOCUS and a transitional program for prospective and incoming college students called STEM Boot Camp. They describe these programs and say something about their impact on the student participants. The authors also reflect on what they have learned from the collaboration over the years and how their partnership has affected their professional lives.

Padmanabhan Seshaiyer, Kristin Kappmeyer

Chapter 9. Developing Collaborations Among Mathematicians, Teachers, and Mathematics Educators

Abstract

Mathematics education is a discipline in the overlap between mathematics and education, and solving problems in mathematics education requires expertise from both domains. Scholarly work in mathematics education is accomplished either by individual scholars who have expertise in both areas or as a collaboration among scholars who collectively have the necessary kinds of expertise. Illustrative Mathematics, an example of an organization that supports such collaborations, is described as one model for supporting scholarly work in mathematics education. Reasons why departments of mathematical sciences should actively support such scholarship are explored.

Kristin Umland, Ashli Black

Benefitting STEM Majors

Frontmatter

Chapter 10. Finding Synergy Among Research, Teaching, and Service: An Example from Mathematics Education Research

Abstract

Being a faculty member in higher education involves the balance and integration of various roles and demands. In this chapter I present my own story, as a mathematics education researcher in the teaching and learning of undergraduate mathematics focusing on linear algebra. Using my experience as an example, I describe how synergy among research, teaching, and service can impact career goals and institutional needs.

Megan Wawro

Chapter 11. Communicating Mathematics Through Writing and Speaking Assignments

Abstract

This chapter contains examples of writing and speaking assignments in mathematics courses at all levels, from a first-year seminar to a graduate course for teachers of mathematics. Courses in chaos theory, differential equations, history of mathematics, and mathematical modeling are illustrated as case studies for implementing writing and speaking assignments. These assignments are described, along with grading guides and reflections on the impact of these forms of assessment.

Suzanne Sumner

Chapter 12. Real Clients, Real Problems, Real Data: Client-Driven Statistics Education

Abstract

In this chapter we describe two client-focused educational experiences at Harvey Mudd College that offer students the opportunity to work on real problems for real clients using real data. The first is the Harvey Mudd College Clinic capstone program, in which teams of students spend an academic year working on a project for an external sponsor. The second is a course project in an upper level statistics elective in which the students analyze data provided by a campus partner. For both of these, we describe their structure, recent projects, as well as student and client feedback. We also offer our reflections on how providing these educational experiences has influenced us personally and professionally.

Talithia D. Williams, Susan E. Martonosi

Chapter 13. A Montessori-Inspired Career in Mathematics Curriculum Development: GeoGebra, Writing-to-Learn, Flipped Learning

Abstract

With an overview of Montessori education, I set the stage for curriculum materials aimed at improving undergraduate mathematics education. I describe four ways to enhance student learning with the dynamical mathematics software GeoGebra: classroom demonstrations, student activities with instructor-created applets, student activities with applets that students create by following podcast instructions, and student-created applets that more advanced students generate independently to solve problems. I discuss two types of writing-to-learn assignments: guided reflection and journaling. I also describe collaborative classroom activities, including associated video lessons that I constructed to implement a flipped or blended learning environment. Connections are made between current mathematics education research findings, Montessori principles and the curriculum materials that I designed. The chapter closes with a reflection on my career path. I discuss my passion for mathematics and social justice, how this led to professional opportunities in mathematics education including a project in the scholarship of teaching and learning, and how my work in mathematics education is useful as I assume leadership as chair of my department.

Kathy A. Tomlinson

Chapter 14. “The Wild Side of Math”: Experimenting with Group Theory

Abstract

Group theory has traditionally been taught to mathematics majors using the “theorem-proof-example” format. Although this method of presentation is satisfying to a mathematician, many students have difficulty learning the concepts of group theory this way. More than 20 years ago, I transformed my abstract algebra classroom into an active learning environment by using the software package Exploring Small Groups. In this chapter, I describe my approach, illustrating it with a specific example, and discuss its impact on my students, my career and other mathematicians.

Ellen J. Maycock

Chapter 15. A Departmental Change: Professional Development Through Curricular Innovation

Abstract

Roosevelt University is a private, comprehensive master’s institution with a social justice mission. Faculty are expected to cultivate excellent teaching, create significant amounts of research, and perform much service work. It is challenging to find time for all three when they are approached as distinct tasks. The mathematics department has developed creative activities that integrate all of these professional responsibilities resulting in a significant change in departmental culture. Faculty have added large- and small-scale projects to courses. They are now working with more students on undergraduate research and have created a venue, the Math x-Position, to showcase student work. This was all accomplished by ongoing faculty mentoring, combining teaching and research, and by fostering a safe environment for innovation.

Steve Cohen, Bárbara González-Arévalo, Melanie Pivarski

Chapter 16. SMP: Building a Community of Women in Mathematics

Abstract

On the surface, the Carleton College Summer Mathematics Program for Women Undergraduates (SMP) looks like many other summer programs: students spend several weeks engaging with mathematics with peers from a variety of institutions. However, SMP offers both formal and informal mentoring activities that go far beyond one summer, providing support to participants through critical stages of their mathematical careers. The result is a strong community of successful women in mathematics.

Pamela A. Richardson

Benefitting Students in General Education Courses

Frontmatter

Chapter 17. Creating and Sustaining a First-Year Course in Quantitative Reasoning

Abstract

In 2009, the Louisiana Board of Regents ceased to require that all undergraduate students receive credit for either a version of college algebra or calculus. By that time, many universities across the nation had well-established quantitative reasoning (QR) courses. Since the Department of Mathematics at the University of Louisiana at Lafayette has been active in mathematics reform, it was natural for the department to expand first-year course offerings by creating a QR course. This chapter describes the development and implementation of this course, which was first offered in Spring 2013. It also gives details about continuing challenges and the resources created to support course instructors and students. Of particular concern was whether students in the QR course would progress through their mathematics courses at the same rate as students with similar background who take college algebra. Data collected on student progress suggest that this is the case. The chapter discusses campus reactions to the new course and closes with a brief reflection on how working to develop the QR course fit into the careers of the developers.

Kathleen Lopez, Melissa Myers, Christy Sue Langley, Diane Fisher

Chapter 18. A Story of Teaching Using Inquiry

Abstract

This chapter tells my story of learning how to teach mathematics using inquiry and becoming a facilitator of professional development (PD) workshops on inquiry-based learning (IBL) for teachers of kindergarten to graduate school. I am an associate professor at Westfield State University in Massachusetts and an integral part of the project “Discovering the Art of Mathematics” (DAoM). In this chapter, I describe a salsa rueda activity used to teach mathematics via inquiry to liberal arts students who often are not interested in or even fear mathematics. I present a vignette of a PD workshop activity designed to teach participants in an inquiry-based way how to teach using inquiry. The chapter also summarizes results of students’ beliefs and attitudes surveys as evidence of the effectiveness of IBL. I close with plans for future work and a reflection on the challenges I face as I step into a leadership role.

Christine von Renesse

Chapter 19. An Ethnomathematics Course and a First-Year Seminar on the Mathematics of the Pre-Columbian Americas

Abstract

As mathematicians know—but, unfortunately, many students don’t—mathematics can be both fun and culturally relevant. One way to reach more students is to teach ethnomathematics, i.e., mathematical thinking found among such non-Western peoples as the Maasai of Kenya and Tanzania, and the ancient Maya. This chapter describes, and provides a rationale for, two different courses in ethnomathematics: an undergraduate ethnomathematics course for non-STEM students, and a first-year seminar on the mathematics of pre-Columbian Americans. Also included are aspects of the development and structure of the courses, examples of ethnomathematics topics, and lists of projects. Feedback from students, alumni, and colleagues regarding the value of such courses is provided.

Ximena Catepillán

Chapter 20. First-Year Seminar Writing for Quantitative Literacy

Abstract

This chapter describes a series of writing assignments from two distinct first-year seminars at Worcester State University. Both of these seminars focus on building quantitative literacy skills. Students research and write about a variety of topics related to globalization, population growth, human rights and climate change. The impact of these seminars for the students, institution, department, and instructor is discussed.

Maria G. Fung

Chapter 21. Tactile Mathematics

Abstract

Tactile mathematics, defined as recognizing deep mathematical concepts through engagement with physical objects, can be used to help students discover mathematics for themselves. This paper discusses the design of tactile learning activities, the insertion of such activities into existing courses, and special considerations for courses to be taught almost entirely with tactile activities. We explain a specific example activity for a group theory course. A collection of mathematics faculty members experienced in tactile learning contribute their thoughts on the implementation of largely tactile mathematics courses. We end with the role of tactile mathematics in the author’s career.

Carolyn Yackel

Chapter 22. Incorporating Writing into Statistics

Abstract

This chapter describes the work of a statistician who, after a career outside the academy, became a teacher of statistics in an urban university. To determine if the inclusion of write-to-learn activities improved her working adult students’ ability to communicate the results of hypothesis tests in context, the author reviewed the literature on using writing-to-learn and conducted a research study on incorporating such activities in an introductory statistics course. Students’ perceptions of the write-to-learn activities were also obtained. The study showed that the write-to-learn activities helped students become better at communicating statistical results in context, and students had positive impressions of the writing activities, claiming that the writing activities were helpful in their learning. Suggestions are offered on how to best incorporate write-to-learn activities in an introductory statistics class.

Katherine G. Johnson

Chapter 23. An Infusion of Social Justice into Teaching and Learning

Abstract

We present a narrative account of the effects of adopting a social justice perspective on one mathematician’s career path. We offer geographic and institutional context, explore interpretations of “social justice” and its intersections with mathematics, and describe implications for teaching and professional learning. We illustrate our explorations of this perspective in teaching first-year seminars, number theory for in-service teachers, mathematics for pre-service teachers, as well as some standard mathematics courses such as abstract algebra and linear algebra. The chapter ends with some reflections on the author’s professional development.

Priscilla Bremser

Benefitting the Public and the Larger Mathematical Community

Frontmatter

Chapter 24. Popular Culture in Teaching, Scholarship, and Outreach: The Simpsons and Futurama

Abstract

Subject to thoughtful analysis of the benefits and challenges, popular culture can be an ideal source of fun ways to connect students and the general public to mathematics. My colleague Andrew Nestler and I created, class-tested, and widely shared activities related to the Twentieth Century Fox television show The Simpsons. The scholarship of teaching and learning (SoTL) provides us with an analytic framework to develop, improve, and share our activities. We designed the activities to introduce or review important mathematical concepts and engage students. Later I expanded my interest into Futurama, another Twentieth Century Fox television show. I will describe informal outreach activities connected to both programs, including our educational website Simpsonsmath.com and my interactive lecture that audiences have accessed worldwide from a Futurama DVD. I will summarize the reception of my work by departmental colleagues, the institution, and the mathematical community. I will reflect on how this work has affected students and general audiences. I will also consider the direct and indirect impacts on my career and the unique challenges and rewards of working with popular culture in teaching, scholarship, and outreach.

Sarah J. Greenwald

Chapter 25. Transforming Post-Secondary Education in Mathematics

Abstract

In this chapter I introduce and describe the work of mathematicians and mathematics educators in the group Transforming Post-Secondary Education in Mathematics (TPSE Math or TPSE, for short). TPSE aims to coordinate and drive constructive change in education in the mathematical sciences at 2- and 4-year colleges and universities across the nation. It seeks to build on the successes of the entire mathematical sciences community.

This chapter reviews the events that led to the founding of TPSE Math and articulates its vision and mission. In its first phase with national events, TPSE found broad consensus within the mathematical sciences community on the challenges facing the community. Learning from educational transformations in other scientific fields, and with the support of the Mathematical Advisory Group of 34 mathematical sciences department chairs and leaders, TPSE moves into a second phase, focused on action. This chapter is a snapshot in time; TPSE’s continuing activities will be documented and disseminated. The chapter concludes with a reflection on the impact that my involvement in this work has had on my career.

Tara Holm

Backmatter

Titel: Mathematics Education
herausgegeben von: Jacqueline Dewar
Pao-sheng Hsu
Harriet Pollatsek
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-44950-0
Print ISBN: 978-3-319-44949-4
DOI: https://doi.org/10.1007/978-3-319-44950-0