Directions For Mathematics Research Experience For Undergraduates

Author: Rubinstein Yanir A
Publisher: World Scientific
ISBN: 9814630330
Format: PDF, ePub, Docs
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“The US National Science Foundation (NSF) Research Experiences for Undergraduates (REU) program in mathematics is now 25 years old, and it is a good time to think about what it has achieved, how it has changed, and where this idea will go next.”This was the premise of the conference held at Mt. Holyoke College during 21-22 June, 2013, and this circle of ideas is brought forward in this volume. The conference brought together diverse points of view, from NSF administrators, leaders of university-wide honors programs, to faculty who had led REUs, recent PhDs who are expected to lead them soon, and students currently in an REU themselves. The conversation was so varied that it justifies a book-length attempt to capture all that was suggested, reported, and said. Among the contributors are Ravi Vakil (Stanford), Haynes Miller (MIT), and Carlos Castillo-Chavez (Arizona, President's Obama Committee on the National Medal of Science 2010-2012).This book should serve not only as a collection of speakers' notes, but also as a source book for anyone interested in teaching mathematics and in the possibility of incorporating research-like experiences in mathematics classes at any level, as well as designing research experiences for undergraduates outside of the classroom.

Language and Mathematics Education

Author: Judit N. Moschkovich
Publisher: IAP
ISBN: 161735161X
Format: PDF
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Issues of language in mathematics learning and teaching are important for both practical and theoretical reasons. Addressing issues of language is crucial for improving mathematics learning and teaching for students who are bilingual, multilingual, or learning English. These issues are also relevant to theory: studies that make language visible provide a complex perspective of the role of language in reasoning and learning mathematics. What is the relevant knowledge base to consider when designing research studies that address issues of language in the learning and teaching of mathematics? What scholarly literature is relevant and can contribute to research? In order to address issues of language in mathematics education, researchers need to use theoretical perspectives that integrate current views of mathematics learning and teaching with current views on language, discourse, bilingualism, and second language acquisition. This volume contributes to the development of such integrated approaches to research on language issues in mathematics education by describing theoretical perspectives for framing the study of language issues and methodological issues to consider when designing research studies. The volume provides interdisciplinary reviews of the research literature from four very different perspectives: mathematics education (Moschkovich), CulturalHistoricalActivity Theory (Gutiérrez, SenguptaIrving, & Dieckmann), systemic functional linguistics (Schleppegrell), and assessment (SolanoFlores). This volume offers graduate students and researchers new to the study of language in mathematics education an introduction to resources for conceptualizing, framing, and designing research studies. For those already involved in examining language issues, the volume provides useful and critical reviews of the literature as well as recommendations for moving forward in designing research. Lastly, the volume provides a basis for dialogue across multiple research communities engaged in collaborative work to address these pressing issues.

New Directions in the Philosophy of Mathematics

Author: Thomas Tymoczko
Publisher: Princeton University Press
ISBN: 9780691034980
Format: PDF, Mobi
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The traditional debate among philosophers of mathematics is whether there is an external mathematical reality, something out there to be discovered, or whether mathematics is the product of the human mind. This provocative book, now available in a revised and expanded paperback edition, goes beyond foundationalist questions to offer what has been called a "postmodern" assessment of the philosophy of mathematics--one that addresses issues of theoretical importance in terms of mathematical experience. By bringing together essays of leading philosophers, mathematicians, logicians, and computer scientists, Thomas Tymoczko reveals an evolving effort to account for the nature of mathematics in relation to other human activities. These accounts include such topics as the history of mathematics as a field of study, predictions about how computers will influence the future organization of mathematics, and what processes a proof undergoes before it reaches publishable form. This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work.

Math Exchanges

Author: Kassia Omohundro Wedekind
Publisher: Stenhouse Publishers
ISBN: 1571108262
Format: PDF, Docs
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Traditionally, small-group math instruction has been used as a format for reaching children who struggle to understand. Math coach Kassia Omohundro Wedekind uses small-group instruction as the centerpiece of her math workshop approach, engaging all students in rigorous "math exchanges." The key characteristics of these mathematical conversations are that they are: 1) short, focused sessions that bring all mathematical minds together, 2) responsive to the needs of the specific group of mathematicians, and 3) designed for meaningful, guided reflection. As in reading and writing workshop, students in Kassia's math workshop are becoming self-directed and independent while participating in a classroom community of learners. Through the math exchanges, students focus on number sense and the big ideas of mathematics. Teachers guide the conversations with small groups of students, mediating talk and thinking as students share problem-solving strategies, discuss how math works, and move toward more effective and efficient approaches and greater mathematical understanding. Although grounded in theory and research, Math Exchanges is written for practicing teachers and answers such questions as the following: How can I use a math workshop approach and follow a certain textbook or set of standards? How should I form small groups? and How often should I meet with small groups? What should I focus on in small groups? How can I tell if my groups are making progress? What do small-group math exchanges look like, sound like, and feel like?

Research Directions in Distributed Parameter Systems

Author: Ralph C. Smith
Publisher: SIAM
ISBN: 9780898717525
Format: PDF, ePub, Mobi
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Written by the plenary speakers for the Conference on Future Directions in Distributed Parameter Systems (October 2000), the volume addresses the state of the art, open questions, and important research directions in applications modeled by partial differential equations and delay systems. Topics include electromagnetic theory for dielectric and conductive materials, flow control, cardiovascular and respiratory models, homogenization and systems theory, optimal and geometric control, reduced-order models for large-scale systems, smart materials, and nondestructive evaluation and structural health monitoring for systems, including nuclear power plants.

Reaching Students

Author: Nancy Kober
Publisher: National Academies Press
ISBN: 0309300460
Format: PDF
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The undergraduate years are a turning point in producing scientifically literate citizens and future scientists and engineers. Evidence from research about how students learn science and engineering shows that teaching strategies that motivate and engage students will improve their learning. So how do students best learn science and engineering? Are there ways of thinking that hinder or help their learning process? Which teaching strategies are most effective in developing their knowledge and skills? And how can practitioners apply these strategies to their own courses or suggest new approaches within their departments or institutions? Reaching Students strives to answer these questions. Reaching Students presents the best thinking to date on teaching and learning undergraduate science and engineering. Focusing on the disciplines of astronomy, biology, chemistry, engineering, geosciences, and physics, this book is an introduction to strategies to try in your classroom or institution. Concrete examples and case studies illustrate how experienced instructors and leaders have applied evidence-based approaches to address student needs, encouraged the use of effective techniques within a department or an institution, and addressed the challenges that arose along the way. The research-based strategies in Reaching Students can be adopted or adapted by instructors and leaders in all types of public or private higher education institutions. They are designed to work in introductory and upper-level courses, small and large classes, lectures and labs, and courses for majors and non-majors. And these approaches are feasible for practitioners of all experience levels who are open to incorporating ideas from research and reflecting on their teaching practices. This book is an essential resource for enriching instruction and better educating students.

Discipline Based Education Research

Author: Committee on the Status, Contributions, and Future Directions of Discipline-Based Education Research
Publisher: National Academies Press
ISBN: 0309254124
Format: PDF, ePub, Docs
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The National Science Foundation funded a synthesis study on the status, contributions, and future direction of discipline-based education research (DBER) in physics, biological sciences, geosciences, and chemistry. DBER combines knowledge of teaching and learning with deep knowledge of discipline-specific science content. It describes the discipline-specific difficulties learners face and the specialized intellectual and instructional resources that can facilitate student understanding. Discipline-Based Education Research is based on a 30-month study built on two workshops held in 2008 to explore evidence on promising practices in undergraduate science, technology, engineering, and mathematics (STEM) education. This book asks questions that are essential to advancing DBER and broadening its impact on undergraduate science teaching and learning. The book provides empirical research on undergraduate teaching and learning in the sciences, explores the extent to which this research currently influences undergraduate instruction, and identifies the intellectual and material resources required to further develop DBER. Discipline-Based Education Research provides guidance for future DBER research. In addition, the findings and recommendations of this report may invite, if not assist, post-secondary institutions to increase interest and research activity in DBER and improve its quality and usefulness across all natural science disciples, as well as guide instruction and assessment across natural science courses to improve student learning. The book brings greater focus to issues of student attrition in the natural sciences that are related to the quality of instruction. Discipline-Based Education Research will be of interest to educators, policy makers, researchers, scholars, decision makers in universities, government agencies, curriculum developers, research sponsors, and education advocacy groups.

Handbook of Research on the Psychology of Mathematics Education

Author: Angel Gutiérrez
Publisher: Sense Publishers
ISBN: 9077874194
Format: PDF, ePub
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This volume is a compilation of the research produced by the International Group for the Psychology of Mathematics Education (PME) since its creation, 30 years ago. It has been written to become an essential reference for mathematics education research in the coming years