Computability theory is at the heart of theoretical computer science. Yet, ironically, many of its basic results were discovered by mathematical logicians prior to the development of the first stored-program computer. As a result, many texts on computability theory strike today's computer science students as far removed from their concerns. To remedy this, we base our approach to computability on the language of while-programs, a lean subset of PASCAL, and postpone consideration of such classic models as Turing machines, string-rewriting systems, and p. -recursive functions till the final chapter. Moreover, we balance the presentation of un solvability results such as the unsolvability of the Halting Problem with a presentation of the positive results of modern programming methodology, including the use of proof rules, and the denotational semantics of programs. Computer science seeks to provide a scientific basis for the study of information processing, the solution of problems by algorithms, and the design and programming of computers. The last 40 years have seen increasing sophistication in the science, in the microelectronics which has made machines of staggering complexity economically feasible, in the advances in programming methodology which allow immense programs to be designed with increasing speed and reduced error, and in the develop ment of mathematical techniques to allow the rigorous specification of program, process, and machine.
The study of formal languages and of related families of automata has long been at the core of theoretical computer science. Until recently, the main reasons for this centrality were connected with the specification and analy sis of programming languages, which led naturally to the following ques tions. How might a grammar be written for such a language? How could we check whether a text were or were not a well-formed program generated by that grammar? How could we parse a program to provide the structural analysis needed by a compiler? How could we check for ambiguity to en sure that a program has a unique analysis to be passed to the computer? This focus on programming languages has now been broadened by the in creasing concern of computer scientists with designing interfaces which allow humans to communicate with computers in a natural language, at least concerning problems in some well-delimited domain of discourse. The necessary work in computational linguistics draws on studies both within linguistics (the analysis of human languages) and within artificial intelligence. The present volume is the first textbook to combine the topics of formal language theory traditionally taught in the context of program ming languages with an introduction to issues in computational linguistics. It is one of a series, The AKM Series in Theoretical Computer Science, designed to make key mathematical developments in computer science readily accessible to undergraduate and beginning graduate students.
How might educational leaders and teachers improve literacy achievement in schools serving communities experiencing high levels of poverty? This question is the focus of this book. Drawing on long-term case studies of four primary schools located in these communities, this book describes the difference between what is commonly practiced and those practices that have a greater chance of supporting young people’s literacy learning. In this multi-layered analysis of the effects of policy on practice, the authors: discuss global concerns with literacy policy and testing in view of the growing gaps between rich and poor; examine the effects of the intensification of inequality and entrenched poverty, and the implications for schools; illustrate how deficit discourses pertaining to communities living in poverty are contested in schools; and describe the complexities of sustaining pedagogical and curriculum change to address the problem of unequal educational outcomes in literacy. This book grapples with some of the most debated questions regarding educational disadvantage, school change, leadership and literacy pedagogy that face educational researchers, policy-makers and practitioners internationally. As well as providing a critique of the risks of current policy rationales, it conveys some hopeful accounts of practice that provide leads for further development.
Empower students to be the change—join the teaching mathematics for social justice movement! We live in an era in which students have —through various media and their lived experiences— a more visceral experience of social, economic, and environmental injustices. However, when people think of social justice, mathematics is rarely the first thing that comes to mind. Through model lessons developed by over 30 diverse contributors, this book brings seemingly abstract high school mathematics content to life by connecting it to the issues students see and want to change in the world. Along with expert guidance from the lead authors, the lessons in this book explain how to teach mathematics for self- and community-empowerment. It walks teachers step-by-step through the process of using mathematics—across all high school content domains—as a tool to explore, understand, and respond to issues of social injustice including: environmental injustice; wealth inequality; food insecurity; and gender, LGBTQ, and racial discrimination. This book features: Content cross-referenced by mathematical concept and social issues Downloadable instructional materials for student use User-friendly and logical interior design for daily use Guidance for designing and implementing social justice lessons driven by your own students’ unique passions and challenges Timelier than ever, teaching mathematics through the lens of social justice will connect content to students’ daily lives, fortify their mathematical understanding, and expose them to issues that will make them responsive citizens and leaders in the future.
A very compelling set of fresh ideas are offered that prepare educators to turn the corner on advocating for social justice in the mathematics classroom. Each book is full of engaging activities, frameworks and standards that centers instruction on community, worldview, and the developmental needs of all students, a must needed resource to reboot our commitment to the next generation." Linda M. Fulmore TODOS: Mathematics For ALL Cave Creek, AZ Empower students to be the change—join the teaching mathematics for social justice movement! We live in an era in which students of all ages have—through media and their lived experiences— a more visceral experience of social injustices. However, when people think of social justice, mathematics rarely comes to mind. With a teacher-friendly design, this book brings upper elementary mathematics content to life by connecting it to student curiosity, empathy, and issues students see or experience. Tested in Grades 3-5 classrooms, the model lessons in this book walk teachers through the process of applying critical frameworks to instruction, using standards-based mathematics to explore, understand, and respond to social justice issues. Learn to plan instruction that engages students in mathematics explorations through age-appropriate, culturally relevant topics, such as valuing differences, health and pay inequality, bullying, voting rights, and environmental justice. Features include: Content cross-referenced by mathematical concept and social issues Connection to Learning for Justice’s social justice standards Downloadable instructional materials and lesson resources Guidance for lessons driven by students’ unique passions and challenges Connections between research and practice Written for teachers committed to developing equitable and just practices through the lens of mathematics content and practice standards as well as social justice standards, this book will help connect content to students’ daily lives, fortify their mathematical understanding, and expose them to issues that will support them in becoming active citizens and leaders.
This book offers an evidence-based guide to EAL for everyone who works with multilingual learners. It provides a concise, helpful introduction to the latest research underpinning three key areas of EAL practice: How children acquire additional languages How language works across the curriculum How you can establish outstanding EAL practice in your school. Other key features include case studies from experienced EAL specialists, extensive reading recommendations for teachers who want to build on their knowledge, and a detailed chapter on Ofsted based on interviews with senior inspectors. This book will prove an invaluable guide and support for everyone working with bilingual learners. In clear, short chapters it gives a thorough grounding in the evidence and principles needed to create outstanding EAL provision.
This handy reference is ideal for students and anyone in need of a comprehensive small format dictionary that provides the most current American English usage. Over 30,000 entries, covering basic vocabulary, offer clear, concise definitions. Includes a New Words Section.
Thank you for visiting our website. Would you like to provide feedback on how we could improve your experience?
This site does not use any third party cookies with one exception — it uses cookies from Google to deliver its services and to analyze traffic.Learn More.