The authors introduce geomathematics as an active research area to a wider audience. Chapter 1 presents an introduction to the Earth as a system to apply scientific methods. Emphasis is laid on transfers from virtual models to reality and vice versa. In the second chapter geomathematics is introduced as a new scientific area which nevertheless has its roots in antiquity. The modern conception of geomathematics is outlined from different points of view and its challenging nature is described as well as its interdisciplinarity. Geomathematics is shown as the bridge between the real world and the virtual world. The complex mathematical tools are shown from a variety of fields necessary to tackle geoscientific problems in the mathematical language. Chapter 3 contains some exemplary applications as novel exploration methods. Particular importance is laid on the change of language when it comes to translate measurements to mathematical models. New solution methods like the multiscale mollifier technique are presented. Further applications discussed are aspects of reflection seismics. Chapter 4 is devoted to the short description of recent activities in geomathematics. The Appendix (Chapter 5) is devoted to the GEM – International Journal on Geomathematics founded ten years ago. Besides a detailed structural analysis of the editorial goals an index of all papers published in former issues is given.
The authors introduce geomathematics as an active research area to a wider audience. Chapter 1 presents an introduction to the Earth as a system to apply scientific methods. Emphasis is laid on transfers from virtual models to reality and vice versa. In the second chapter geomathematics is introduced as a new scientific area which nevertheless has its roots in antiquity. The modern conception of geomathematics is outlined from different points of view and its challenging nature is described as well as its interdisciplinarity. Geomathematics is shown as the bridge between the real world and the virtual world. The complex mathematical tools are shown from a variety of fields necessary to tackle geoscientific problems in the mathematical language. Chapter 3 contains some exemplary applications as novel exploration methods. Particular importance is laid on the change of language when it comes to translate measurements to mathematical models. New solution methods like the multiscale mollifier technique are presented. Further applications discussed are aspects of reflection seismics. Chapter 4 is devoted to the short description of recent activities in geomathematics. The Appendix (Chapter 5) is devoted to the GEM – International Journal on Geomathematics founded ten years ago. Besides a detailed structural analysis of the editorial goals an index of all papers published in former issues is given.
Modal verbs in English communicate delicate shades of meaning, there being a large range of verbs both on the necessity side (must, have to, should, ought to, need, need to) and the possibility side (can, may, could, might, be able to). They therefore constitute excellent test ground to apply and compare different methodologies that can lay bare the factors that drive the speaker’s choice of modal verb. This book is not merely concerned with a purely grammatical description of the use of modal verbs, but aims at advancing our understanding of lexical and grammatical units in general and of linguistic methodologies to explore these. It thus involves a genuine effort to compare, assess and combine a variety of approaches. It complements the leading descriptive qualitative work on modal verbs by testing a diverse range of quantitative methods, while not ignoring qualitative issues pertaining to the semantics-pragmatics interface. Starting from a critical assessment of what constitutes the meaning of modal verbs, different types of empirical studies (usage-based, data-driven and experimental), drawing considerably on the same data sets, shows how method triangulation can contribute to an enhanced understanding. Due attention is also given to individual variation as well as the degree to which modals can predict L2 proficiency level.
Now in a revised and expanded fifth edition that reflects current research and best practices in direct assessment and intervention, this text addresses a perennial need for school practitioners and practitioners in training. Presented is a comprehensive, problem-solving-based approach for working with K–12 students who are struggling with reading, writing, or mathematics. The book provides a framework for evaluating the instructional environment as well as each student's context and unique learning needs; planning instructional modifications; and monitoring progress. The companion workbook, available separately, contains practice exercises and reproducible forms. New to This Edition *Revised throughout by new coauthor Nathan H. Clemens, while retaining the core elements of Edward S. Shapiro's approach. *New emphasis on the central role of language in reading, mathematics, and writing development and difficulties, and implications for working more effectively with linguistically and culturally diverse students. *Fresh perspectives on behaviors that facilitate learning, such as attention to task and following directions. *Updated and expanded coverage of key topics--universal screening; progress monitoring; intensive, individualized academic skills interventions; and more. See also Academic Skills Problems Fifth Edition Workbook, which provides the reproducible forms discussed in the text, practice exercises, and additional useful materials, in a convenient large-size format.
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