Karen Marrongellehttps://works.bepress.com/karen-marrongelle/Recent works by Karen Marrongelleen-usCopyright (c) 2019 All rights reserved.Fri, 01 Aug 2014 00:00:00 +00003600Research on calculus: What do we know and where do we need to go?https://works.bepress.com/karen-marrongelle/6/<div class="line" id="line-24"><span style="color: rgb(51, 51, 51); background-color: rgb(252, 252, 252); font-family: Georgia, serif; font-size: 17px;">In this introductory paper we take partial stock of the current state of field on calculus research, exemplifying both the promise of research advances as well as the limitations. We identify four trends in the calculus research literature, starting with identifying misconceptions to investigations of the processes by which students learn particular concepts, evolving into classroom studies, and, more recently research on teacher knowledge, beliefs, and practices. These trends are related to a model for the cycle of research and development aimed at improving learning and teaching. We then make use of these four trends and the model for the cycle of research and development to highlight the contributions of the papers in this issue. We conclude with some reflections on the gaps in literature and what new areas of calculus research are needed.</span></div>Chris Rasmussen et al.Fri, 01 Aug 2014 00:00:00 +0000https://works.bepress.com/karen-marrongelle/6/ArticlesScaling up professional development in an era of common state standardshttps://works.bepress.com/karen-marrongelle/7/<div class="line" id="line-24"><span style="color: rgb(64, 56, 56); font-family: Arial, Helvetica, sans-serif; font-size: 12.8px;">We describe the process and outcomes of a project aimed at bringing together a set of diverse experts to generate a set of design recommendations for what should be considered when creating, sustaining, and assessing professional development systems to support the Common Core State Standards in mathematics. Although the recommendations were generated in mathematics, the underlying guiding principles for professional development are generalizable to other disciplines. As such, we discuss implications for professional development more broadly.</span></div>Karen A. Marrongelle et al.Wed, 01 May 2013 00:00:00 +0000https://works.bepress.com/karen-marrongelle/7/ArticlesHaving Success with NSF: A Practical Guidehttps://works.bepress.com/karen-marrongelle/1/<div class="line" id="line-5"><span style="color: rgb(29, 38, 38); font-family: Lato, sans-serif; font-size: 14px;">This book is designed to help researchers achieve success in funding their National Science Foundation (NSF) research proposals. The book discusses aspects of the proposal submission and review process that are not typically communicated to the research community. Written by authors with successful track records in grant writing and years of experience as NSF Program Directors, this book provides an insider’s view of successful grantsmanship. Written in a practical approach, this book offers tips that will not be found in official paperwork and provides answers to questions frequently asked of NSF Program Directors. The purpose of the book is to improve your NSF grant-writing skills and improve your chances of funding.</span></div>Ping Li et al.Sat, 01 Dec 2012 00:00:00 +0000https://works.bepress.com/karen-marrongelle/1/BooksSupporting Implementation of the Common Core State Standards for Mathematics: Recommendations for Professional Developmenthttps://works.bepress.com/karen-marrongelle/14/In 2010, the National Governor’s Association and the Council of Chief State School Officers published the Common Core State Standards for Mathematics (CCSSM) and to date, 44 states, the District of Columbia, and the U.S. Virgin Islands have adopted the document. These content and practice standards, which specify what students are expected to understand and be able to do in K-12 mathematics, represent a significant departure from what mathematics is currently taught in most classrooms and how it is taught. Developing teachers’ capacity to enact these new standards in ways that support the intended student learning outcomes will require considerable changes in mathematics instruction in our nation’s classrooms. Such changes are likely to occur only through sustained and focused professional development opportunities for those who teach mathematics.
The recommendations that follow are intended to support large-scale, system-level implementation of professional development (PD) initiatives aligned with the CCSSM. They emerged from the work done under the auspices of a NSF-funded project, which provided the opportunity for experts from diverse fields to collaboratively address the challenge of providing high-quality mathematics PD at scale to support the implementation of the CCSSM. Over the course of the project, researchers and expert practitioners worked to integrate various perspectives on this challenge into a set of design recommendations for creating, sustaining, and assessing PD systems for practicing mathematics teachers. Generated from the coordination of research-based knowledge in different but related fields, these recommendations build on state-of-the-art research findings from mathematics education, PD, organizational theory, and policy.
The recommendations take into account the important role teachers will play in making the standards a reality. A substantive body of research points to teachers as the most important factor in promoting mathematics learning, and the education of teachers has been deemed an essential aspect in promoting educational improvement. Thus, the recommendations proposed here make salient that attending to the PD of practicing mathematics teachers in light of the CCSSM is a requirement for the successful implementation of the new standards.
It is important to note that these recommendations are intended to build on, rather than replicate, the features of effective PD identified in prior research (e.g., Desimone, 2009; Elmore, 2002; Guskey & Yoon, 2009; Guskey, 2000). In particular, a recent report from the National Staff Development Council (Darling- Hammond et al., 2009) entitled, “Professional Learning in the Learning Profession: A Status Report on Teacher Development in the United States and Abroad” identified four basic, research-based principles for designing PD that we understand as common professional and research knowledge that serves as the foundation on which the current recommendations are built: 1) PD should be intensive, ongoing, and connected to practice; 2) PD should focus on student learning and address the teaching of specific content; 3) PD should align with school improvement priorities and goals; and 4) PD should build strong working relationships among teachers. We hope that the recommendations that follow, in conjunction with these four basic principles, can help districts and states in creating, sustaining, and assessing PD systems for practicing mathematics teachers that support their implementation of the CCSSM, and ultimately, the learning of all K-12 students.Sun, 01 Jan 2012 08:00:00 +0000https://works.bepress.com/karen-marrongelle/14/Technical ReportHow Students use Mathematical Resources in an Electrostatics Contexthttps://works.bepress.com/karen-marrongelle/8/We present evidence that although students’ mathematical skills in introductory calculus-based physics classes may not be readily applied in physics contexts, these students have strong mathematical resources on which to build effective instruction. Our evidence is based on clinical interviews of problem solving in electrostatics, which are analyzed using the framework of Sherin’s symbolic forms. We find that students use notions of “dependence” and “parts-of-a-whole” to successfully guide their work, even in novel situations. We also present evidence that students’ naive conceptions of the limit may prevent them from viewing integrals as sums.Sun, 01 Jun 2008 07:00:00 +0000https://works.bepress.com/karen-marrongelle/8/ArticlesEnhancing meaning in mathematics: Drawing on what students know about the physical worldhttps://works.bepress.com/karen-marrongelle/2/<div class="line" id="line-24">This book was commissioned in response to requests from teachers in grades K–12 for help in integrating communication strategies (e.g., reading, writing, listening, speaking,) into their mathematics teaching.</div>Karen A. MarrongelleFri, 07 Mar 2008 00:00:00 +0000https://works.bepress.com/karen-marrongelle/2/Book ChaptersUtilization of Revoicing Based on Learners‘ Thinking in an Inquiry-Oriented Differential Equations Classhttps://works.bepress.com/karen-marrongelle/15/Researchers of mathematics education are increasingly interested in a teacher's discursive moves, which refer to deliberate actions taken by a teacher to participate in or influence debate and discussion in the mathematics classroom. This study explored one teacher's discursive moves in an undergraduate inquiry-oriented mathematics class. The data for this study come from four class sessions in which students investigated initial value problems as represented by the phase portrait of a system of differential equations. Through the analysis and a review of the literature, we identified four categories of a teacher's discursive moves: revoicing, questioning/requesting, telling, and managing. This report focuses on the roles of revoicing as it relates to the development of mathematical ideas and student beliefs about themselves and mathematics. The results show that the teacher used revoicing in the following ways: revoicing as a binder, revoicing as a springboard, revoicing for ownership, revoicing as a means for socialization.Tue, 01 Jan 2008 08:00:00 +0000https://works.bepress.com/karen-marrongelle/15/ArticlesInduction of doctoral graduates in mathematics education into the professionhttps://works.bepress.com/karen-marrongelle/3/<div class="line" id="line-24"><span style="color: rgb(51, 51, 51); font-family: Lato; font-size: 14px;">Mathematics education in the United States will be shaped at all levels by those who hold doctorates in the field. As professors, they influence the structure and content of university programs in mathematics education, where future teachers are prepared. As scholars, they engage in research and lead us to a deeper and better understanding of the field. This book is a detailed study of doctoral programs in mathematics education. It stems from a national conference sponsored by the National Science Foundation. It involved participants from across the United States, as well as Brazil, Japan, Norway, and Spain, and followed up the work of an earlier conference, published in </span><i style="color: rgb(51, 51, 51); font-family: Lato; font-size: 14px;">One Field, Many Paths: U.S. Doctoral Programs in Mathematics Education</i><span style="color: rgb(51, 51, 51); font-family: Lato; font-size: 14px;"> (Volume 9 in this series). - See more at: http://bookstore.ams.org/cbmath-15/#sthash.lqpxBwEc.dpuf</span></div>Robert E. Reys et al.Tue, 01 Jan 2008 00:00:00 +0000https://works.bepress.com/karen-marrongelle/3/Book ChaptersNo Research-based strategies for teaching: Linking student thinking with mathematical ideashttps://works.bepress.com/karen-marrongelle/4/<div class="line" id="line-24">The chapters in this volume convey insights from mathematics education research that have direct implications for anyone interested in improving teaching and learning in undergraduate mathematics. This synthesis of research on learning and teaching mathematics provides relevant information for any math department or individual faculty member who is working to improve introductory proof courses, the longitudinal coherence of precalculus through differential equations, students’ mathematical thinking and problem-solving abilities, and students’ understanding of fundamental ideas such as variable and rate of change. Other chapters include information about programs that have been successful in supporting students’ continued study of mathematics. The authors provide many examples and ideas to help the reader infuse the knowledge from mathematics education research into mathematics teaching practice.</div><div class="line" id="line-34"><br></div><div class="line" id="line-32">University mathematicians and community college faculty spend much of their time engaged in work to improve their teaching. Frequently, they are left to their own experiences and informal conversations with colleagues to develop new approaches to support student learning and their continuation in mathematics. Over the past 30 years, research in undergraduate mathematics education has produced knowledge about the development of mathematical understandings and models for supporting students’ mathematical learning. Currently, very little of this knowledge is affecting teaching practice. We hope that this volume will open a meaningful dialogue between researchers and practitioners toward the goal of realizing improvements in undergraduate mathematics curriculum and instruction.</div>Karen A. Marrongelle et al.Tue, 01 Jan 2008 00:00:00 +0000https://works.bepress.com/karen-marrongelle/4/Book ChaptersThe Function of Graphs and Gestures in Algorithmitizationhttps://works.bepress.com/karen-marrongelle/9/<div class="line" id="line-24"><span style="color: rgb(46, 46, 46); font-family: Arial, Helvetica, "Lucida Sans Unicode", "Microsoft Sans Serif", "Segoe UI Symbol", STIXGeneral, "Cambria Math", "Arial Unicode MS", sans-serif; font-size: 16px;">The purpose of this paper is to present evidence supporting the conjecture that graphs and gestures may function in different capacities depending on whether they are used to develop an algorithm or whether they extend or apply a previously developed algorithm in a new context. I illustrate these ideas using an example from undergraduate differential equations in which students move through a sequence of Realistic Mathematics Education (RME)-inspired instructional materials to create the Euler method algorithm for approximating solutions to differential equations. The function of graphs and gestures in the creation and subsequent use of the Euler method algorithm is explored. If students’ primary goal was algorithmatizing ‘from scratch’, they used imagery of graphing and gesturing as a tool for reasoning. However if students’ primary goal was to make predictions in a new context, they used their previously developed Euler algorithm to reason and used graphs and gestures to clarify their ideas.</span></div>Karen A. MarrongelleMon, 01 Jan 2007 00:00:00 +0000https://works.bepress.com/karen-marrongelle/9/Articles