Volume 3 of Research in Collegiate Mathematics Education (RCME) presents state-of-the-art research on understanding, teaching and learning mathematics at the post-secondary level. This volume contains information on methodology and research concentrating on these areas of student learning: Problem Solving; Understanding Concepts; and Understanding Proofs.
The present volume of Research in Collegiate Mathematics Education, like previous volumes in this series, reflects the importance of research in mathematics education at the collegiate level. The editors in this series encourage communication between mathematicians and mathematics educators, and as pointed out by the International Commission of Mathematics Instruction (ICMI), much more work is needed in concert with these two groups. Indeed, editors of RCME are aware of this need and the articles published in this series are in line with that goal. Nine papers constitute this volume. The first two examine problems students experience when converting a representation from one particular system of representations to another. The next three papers investigate students learning about proofs. In the next two papers, the focus is instructor knowledge for teaching calculus. The final two papers in the volume address the nature of ``conception'' in mathematics. Whether they are specialists in education or mathematicians interested in finding out about the field, readers will obtain new insights about teaching and learning and will take away ideas that they can use.
The field of research in collegiate mathematics education has grown rapidly over the past 25 years. Many people are convinced that improvement in mathematics education can only come with a greater understanding of what is involved when a student tries to learn mathematics and how pedagogy can be more directly related to the learning process. Today there is a substantial body of work and a growing group of researchers addressing both basic and applied issues of mathematics education at the collegiate level. This second volume in Research in Collegiate Mathematics Education begins with a paper that attends to methodology and closes with a list of questions. The lead-off paper describes a distinctive approach to research on key concepts in the undergraduate mathematics curriculum. This approach is distinguished from others in several ways, especially its integration of research and instruction. The papers in this volume exhibit a large diversity in methods and purposes, ranging from historical studies, to theoretical examinations of the role of gender in mathematics education, to practical evaluations of particular practices and circumstances. As in RCME I, this volume poses a list of questions to the reader related to undergraduate mathematics education. The eighteen questions were raised at the first Oberwolfach Conference in Undergraduate Mathematics Education, which was held in the Fall of 1995, and are related to both research and curriculum. This series is published in cooperation with the Mathematical Association of America.
The sixth volume of Research in Collegiate Mathematics Education presents state-of-the-art research on understanding, teaching, and learning mathematics at the postsecondary level. The articles advance our understanding of collegiate mathematics education while being readable by a wide audience of mathematicians interested in issues affecting their own students. This is a collection of useful and informative research regarding the ways our students think about and learn mathematics.The volume opens with studies on students' experiences with calculus reform and on the effects of concept-based calculus instruction. The next study uses technology and the van Hiele framework to help students construct concept images of sequential convergence. The volume continues with studies ondeveloping and assessing specific competencies in real analysis, on introductory complex analysis, and on using geometry in teaching and learning linear algebra. It closes with a study on the processes used in proof construction and another on the transition to graduate studies in mathematics. Whether they are specialists in education or mathematicians interested in finding out about the field, readers will obtain new insights about teaching and learning and will take away ideas that they canuse. Information for our distributors: This series is published in cooperation with the Mathematical Association of America.
This fourth volume of Research in Collegiate Mathematics Education (RCME IV) reflects the themes of student learning and calculus. Included are overviews of calculus reform in France and in the U.S. and large-scale and small-scale longitudinal comparisons of students enrolled in first-year reform courses and in traditional courses. The work continues with detailed studies relating students' understanding of calculus and associated topics. Direct focus is then placed on instruction and student comprehension of courses other than calculus, namely abstract algebra and number theory. The volume concludes with a study of a concept that overlaps the areas of focus, quantifiers. The book clearly reflects the trend towards a growing community of researchers who systematically gather and distill data regarding collegiate mathematics' teaching and learning. This series is published in cooperation with the Mathematical Association of America.
The audience remains much the same as for the 1992 Handbook, namely, mathematics education researchers and other scholars conducting work in mathematics education. This group includes college and university faculty, graduate students, investigators in research and development centers, and staff members at federal, state, and local agencies that conduct and use research within the discipline of mathematics. The intent of the authors of this volume is to provide useful perspectives as well as pertinent information for conducting investigations that are informed by previous work. The Handbook should also be a useful textbook for graduate research seminars. In addition to the audience mentioned above, the present Handbook contains chapters that should be relevant to four other groups: teacher educators, curriculum developers, state and national policy makers, and test developers and others involved with assessment. Taken as a whole, the chapters reflects the mathematics education research community's willingness to accept the challenge of helping the public understand what mathematics education research is all about and what the relevance of their research fi ndings might be for those outside their immediate community.
This report is a resource for those who teach mathematics and statistics to PreK-12 mathematics teachers, both future teachers and those who already teach in our nation's schools. The report makes recommendations for the mathematics that teachers should know and how they should come to know that mathematics. It urges greater involvement of mathematicians and statisticians in teacher education so that the nation's mathematics teachers have the knowledge, skills, and dispositions needed to provide students with a mathematics education that ensures high school graduates are college- and career-ready as envisioned by the Common Core State Standards. This report draws on the experience and knowledge of the past decade to: Update the 2001 Mathematical Education of Teachers report's recommendations for the mathematical preparation of teachers at all grade levels: elementary, middle, and high school. Address the professional development of teachers of mathematics. Discuss the mathematical knowledge needed by teachers at different grade levels and by others who teach mathematics such as elementary mathematics specialists, special education teachers, and early childhood educators. Each of the MET II writers is a mathematician, statistician, or mathematics educator with substantial expertise and experience in mathematics education. Among them are principal investigators for Math Science Partnerships as well as past presidents and chairs of the American Statistical Association, Association of Mathematics Teacher Educators, Association of State Supervisors of Mathematics, Conference Board of the Mathematical Sciences, and National Council of Teachers of Mathematics. The audience for this report includes all who teach mathematics to teachers--mathematicians, statisticians, and mathematics educators--and all who are responsible for the mathematical education of teachers--department chairs, educational administrators, and policy-makers at the national, state, school-district, and collegiate levels.
The purpose of this handbook is to help launch institutional transformations in mathematics departments to improve student success. We report findings from the Student Engagement in Mathematics through an Institutional Network for Active Learning (SEMINAL) study. SEMINAL's purpose is to help change agents, those looking to (or currently attempting to) enact change within mathematics departments and beyond—trying to reform the instruction of their lower division mathematics courses in order to promote high achievement for all students. SEMINAL specifically studies the change mechanisms that allow postsecondary institutions to incorporate and sustain active learning in Precalculus to Calculus 2 learning environments. Out of the approximately 2.5 million students enrolled in collegiate mathematics courses each year, over 90% are enrolled in Precalculus to Calculus 2 courses. Forty-four percent of mathematics departments think active learning mathematics strategies are important for Precalculus to Calculus 2 courses, but only 15 percnt state that they are very successful at implementing them. Therefore, insights into the following research question will help with institutional transformations: What conditions, strategies, interventions and actions at the departmental and classroom levels contribute to the initiation, implementation, and institutional sustainability of active learning in the undergraduate calculus sequence (Precalculus to Calculus 2) across varied institutions?
The definitive guide to the basic principles and latest advances in Nutritional Genomics Though still in its infancy, nutritional genomics, or "nutrigenomics," has revealed much about the complex interactions between diet and genes. But it is in its potential applications that nutrigenomics promises to revolutionize the ways we manage human health and combat disease in the years ahead. Great progress already has been made in modeling "personalized" nutrition for optimal health and longevity as well as in genotype-based dietary interventions for the prevention, mitigation, or possible cure of a variety of chronic diseases and some types of cancer. Topics covered include: * Nutrients and gene expression * The role of metabolomics in individualized health * Molecular mechanisms of longevity regulation and calorie restriction * Green tea polyphenols and soy peptides in cancer prevention * Maternal nutrition and fetal gene expression * Genetic susceptibility to heterocyclic amines from cooked foods * Bioinformatics and biocomputation in nutrigenomics * The pursuit of optimal diets Written by an all-star team of experts from around the globe, this volume provides an integrated overview of the cutting-edge field of nutritional genomics. The authors and editors lead an in-depth discussion of the fundamental principles and scientific methodologies that serve as the foundation for nutritional genomics and explore important recent advances in an array of related disciplines. Each self-contained chapter builds upon its predecessor, leading the reader seamlessly from basic principles to more complex scientific findings and experimental designs. Scientific chapters are carefully balanced with those addressing the social, ethical, regulatory, and commercial implications of nutrigenomics.
