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This fully up-dated second edition synthesizes the findings of the best of recent research from different parts of the world. Marilyn Nickson covers issues as diverse as pupils' understanding and handling of number, algebra, space and measurement, and their problem-solving ability, as well as the nature of assessment and the impact of ICT on the classroom. Each chapter provides both an overview of recent research and a detailed analysis of the most important findings. The research is carefully related to issues of pupils' progress in the subject, the differentiation of teaching and the role of gender.
This book offers a new conceptual framework for reflecting on the role of information and communication technology in mathematics education. Discussion focuses on how computers, writing and oral discourse transform education at an epistemological as well as a political level. Building on examples, research and theory, the authors propose that knowledge is not constructed solely by humans, but by collectives of humans and technologies of intelligence.
State-of-the-art analysis of geological structures has become increasingly quantitative but traditionally, graphical methods are used in teaching. This innovative lab book provides a unified methodology for problem-solving in structural geology using linear algebra and computation. Assuming only limited mathematical training, the book begins with classic orientation problems and progresses to more fundamental topics of stress, strain and error propagation. It introduces linear algebra methods as the foundation for understanding vectors and tensors, and demonstrates the application of geometry and kinematics in geoscience without requiring students to take a supplementary mathematics course. All algorithms are illustrated with a suite of online MATLAB functions, allowing users to modify the code to solve their own structural problems. Containing 20 worked examples and over 60 exercises, this is the ideal lab book for advanced undergraduates or beginning graduate students. It will also provide professional structural geologists with a valuable reference and refresher for calculations.
Explore and analyze the solutions of mathematical models from diverse disciplines As biology increasingly depends on data, algorithms, and models, it has become necessary to use a computing language, such as the user-friendly MapleTM, to focus more on building and analyzing models as opposed to configuring tedious calculations. Explorations of Mathematical Models in Biology with Maple provides an introduction to model creation using Maple, followed by the translation, analysis, interpretation, and observation of the models. With an integrated and interdisciplinary approach that embeds mathematical modeling into biological applications, the book illustrates numerous applications of mathematical techniques within biology, ecology, and environmental sciences. Featuring a quantitative, computational, and mathematical approach, the book includes: Examples of real-world applications, such as population dynamics, genetics, drug administration, interacting species, and the spread of contagious diseases, to showcase the relevancy and wide applicability of abstract mathematical techniques Discussion of various mathematical concepts, such as Markov chains, matrix algebra, eigenvalues, eigenvectors, first-order linear difference equations, and nonlinear first-order difference equations Coverage of difference equations to model a wide range of real-life discrete time situations in diverse areas as well as discussions on matrices to model linear problems Solutions to selected exercises and additional Maple codes Explorations of Mathematical Models in Biology with Maple is an ideal textbook for undergraduate courses in mathematical models in biology, theoretical ecology, bioeconomics, forensic science, applied mathematics, and environmental science. The book is also an excellent reference for biologists, ecologists, mathematicians, biomathematicians, and environmental and resource economists.
In the second book in the Uncomplicating Mathematics Series, professional developer Marian Small shows teachers how to uncomplicate the teaching of algebra by focusing on the most important ideas that students need to grasp. Organized by grade level around the Common Core State Standards for Mathematics, Small shares approaches that will lead to a deeper and richer understanding of algebra for both teachers and students. The book opens with a clear discussion of algebraic thinking and current requirements for algebraic understanding within standards-based learning environments. The book then launches with Kindergarten, where the first relevant standard is found in the operations and algebraic thinking domain, and ends with Grade 8, where the focus is on working with linear equations and functions. In each section the relevant standard is presented, followed by a discussion of important underlying ideas associated with that standard, as well as thoughtful, concept-based questions that can be used for classroom instruction, practice, or assessment. Underlying ideas include: Background to the mathematics of each relevant standard. Suggestions for appropriate representations for specific mathematical ideas. Suggestions for explaining ideas to students. Cautions about misconceptions or situations to avoid. The Common Core State Standards for Mathematics challenges students to become mathematical thinkers, not just mathematical “doers.” This resource will be invaluable for pre- and inservice teachers as they prepare themselves to understand and teach algebra with a deep level of understanding. “Uncomplicating Algebra is an excellent resource for teachers responsible for the mathematical education of K–8 students. It is also a valuable tool for the training of preservice teachers of elementary and middle school mathematics.” —Carole Greenes, associate vice provost for STEM education, director of the Practice Research and Innovation in Mathematics Education (PRIME) Center, professor of mathematics education, Arizona State University “The current climate in North America places a major emphasis on standards, including the Common Core State Standards for Mathematics in the U.S. In many cases, teachers are being asked to teach content with which they themselves struggle. In this book, Dr. Small masterfully breaks down the big ideas of algebraic thinking to assist teachers, math coaches, and preservice teachers—helping them to deepen their own understanding of the mathematics they teach. She describes common error patterns and examines algebraic reasoning from a developmental viewpoint, connecting the dots from kindergarten through grade 8. The book is clearly written, loaded with specific examples, and very timely. I recommend it strongly as a ‘must-read’ for all who are seeking to broaden their understanding of algebra and how to effectively teach this important content area to children.” —Daniel J. Brahier, director, Science and Math Education in ACTION, professor of mathematics education, School of Teaching and Learning, Bowling Green State University
Ce livre n'est pas un livre d'histoire, mais un événement historique : il se place au centre du grand tournant méthodologique du début du XXe siècle concernant le problème des rapports entre la géographie, la sociologie et l'histoire. Lucien Febvre établit un dialogue, d'abord sur les mérites et sur les erreurs des grands géographes et des grands sociologues du début du XXe siècle, auxquels on cherche à faire entendre raison. Dialogue sur les climats, leurs modifications, leur importance ; sur les montagnes, les plaines et les plateaux, qui sont des réalités moins simples qu'il ne paraît, sur les îles, les oasis, les « paysages ». Dialogue sur les moeurs des chasseurs, pêcheurs, pasteurs, cultivateurs, - sur les nomades et les sédentaires. Sur les États, les frontières « naturelles », les routes, les villes... Lucien Febvre établit un travail d'orientation, de réflexion critique sur l'énorme question des rapports du sol et des sociétés humaines, en transposant le problème dans le temps, pour se demander quelles déterminations - ou quelles prédéterminations - la terre habitable impose en ses diverses parties à l'Histoire. Toute la vie des hommes, toute l'activité multiple des hommes, des groupes humains, des sociétés humaines se trouve étudiée méthodiquement, rationnellement, en fonction du milieu géographique.
With the 1989 release of Everybody Counts by the Mathematical Sciences Education Board (MSEB) of the National Research Council and the Curriculum and Evaluation Standards for School Mathematics by the National Council of Teachers of Mathematics (NCTM), the "standards movement" in K-12 education was launched. Since that time, the MSEB and the NCTM have remained committed to deepening the public debate, discourse, and understanding of the principles and implications of standards-based reform. One of the main tenets in the NCTM Standards is commitment to providing high-quality mathematical experiences to all students. Another feature of the Standards is emphasis on development of specific mathematical topics across the grades. In particular, the Standards emphasize the importance of algebraic thinking as an essential strand in the elementary school curriculum. Issues related to school algebra are pivotal in many ways. Traditionally, algebra in high school or earlier has been considered a gatekeeper, critical to participation in postsecondary education, especially for minority students. Yet, as traditionally taught, first-year algebra courses have been characterized as an unmitigated disaster for most students. There have been many shifts in the algebra curriculum in schools within recent years. Some of these have been successful first steps in increasing enrollment in algebra and in broadening the scope of the algebra curriculum. Others have compounded existing problems. Algebra is not yet conceived of as a K-14 subject. Issues of opportunity and equity persist. Because there is no one answer to the dilemma of how to deal with algebra, making progress requires sustained dialogue, experimentation, reflection, and communication of ideas and practices at both the local and national levels. As an initial step in moving from national-level dialogue and speculations to concerted local and state level work on the role of algebra in the curriculum, the MSEB and the NCTM co-sponsored a national symposium, "The Nature and Role of Algebra in the K-14 Curriculum," on May 27 and 28, 1997, at the National Academy of Sciences in Washington, D.C.
This eBook deals with 12 solved problems dealing with the General Energy equation, finding pipe losses (major + minor losses), pump heads as well as the pressures and velocities associated with Type I, II and III systems. It also considers the power and efficiency of the device in question and the energy this transfers to the fluid and pump selection. This eBook is a general second half of a typical fluid mechanics course focusing on a practical approach to the solution of fluid dynamic problems. Give it a try!
This book promotes the experimental mathematics approach in the context of secondary mathematics curriculum by exploring mathematical models depending on parameters that were typically considered advanced in the pre-digital education era. This approach, by drawing on the power of computers to perform numerical computations and graphical constructions, stimulates formal learning of mathematics through making sense of a computational experiment. It allows one (in the spirit of Freudenthal) to bridge serious mathematical content and contemporary teaching practice. In other words, the notion of teaching experiment can be extended to include a true mathematical experiment. When used appropriately, the approach creates conditions for collateral learning (in the spirit of Dewey) to occur including the development of skills important for engineering applications of mathematics. In the context of a mathematics teacher education program, the book addresses a call for the preparation of teachers capable of utilizing modern technology tools for the modeling-based teaching of mathematics with a focus on methods conducive to the improvement of the whole STEM education at the secondary level. By the same token, using the book’s pedagogy and its mathematical content in a pre-college classroom can assist teachers in introducing students to the ideas that develop the foundation of engineering profession.
Pourquoi tout employé tend à s’élever jusqu’à son niveau d’incompétence Le principe de Peter est un best-seller international qui répond à la question que tout le monde se pose depuis la nuit des temps : pourquoi y a-t-il tant de gens incompétents dans leur travail et pourquoi leur nombre ne cesse d’augmenter? Dans cet ouvrage, Laurence J. Peter et Raymond Hull exposent, non sans humour, leur principe selon lequel, dans une hiérarchie, chacun sera inévitablement promu jusqu’à atteindre son niveau d’incompétence. Grâce à ce livre au ton satirique d’Oscar Wilde, à la justesse psychologique de Sigmund Freud et au sens aigu de l’observation d’Émile Durkheim, vous serez un expert en «hiérarchologie» et vous apprendrez à reconnaître lorsqu’une personne est arrivée à son seuil d’incompétence, à éviter que cela vous arrive et à mieux comprendre les limites de vos chefs... ou même les vôtres!