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Helping students think more critically, communicate ideas more effectively, and work more cooperatively with others are goals widely recognized as indispensable to a proper education. Adventures in Reasoning: Communal Inquiry Through Fantasy Role-Play provides middle school, high school, and even post-secondary teachers with a method to cultivate these crucial skill sets in a way that is engaging, academically rigorous, and also fun. The role-playing approach draws upon the pioneering notion of the community of inquiry as a vehicle for enhancing student learning and development through discussing philosophical concepts and issues. Students create characters that they then use to explore a rich fantasy world filled with practical and conceptual challenges specifically designed to enhance a wide range of cognitive and communication abilities. Drawing together the appeal of fantasy narratives with the rigor of communal inquiry, Adventures in Reasoning provides educators with a rich array of tools through which to engage students’ interests, capture their curiosity, and cultivate crucial cognitive and social skills. Some additional key features of this book include: step-by-step instructions on how to implement fantasy-gaming in the classroom tips on how to assess students’ critical and creative reasoning skills easy to understand rules for fantasy role-playing detailed adventure quests provided that target a wide array of skill sets overview of the pedagogical benefits of introducing philosophy and communal inquiry to middle and high school students lots of advice and suggestions on how to facilitate an effective community of inquiry and how to accommodate different class sizes and student abilities recommendations on how to use fantasy role-playing as a type of service learning in college classrooms
Eight fascinating examples show how understanding of certain topics in advanced mathematics requires nothing more than arithmetic and common sense. Covers mathematical applications behind cell phones, computers, cell growth, and other areas.
Eight fascinating examples show how understanding of certain topics in advanced mathematics requires nothing more than arithmetic and common sense. Covers mathematical applications behind cell phones, computers, cell growth, and other areas.
Lost in a fantasy world, Nikki has only logic and science to help her find her way home. Logic to the Rescue is designed to teach kids critical thinking. A combination of fiction and non-fiction, it weaves examples of logical fallacies into a fictional sword-and-sorcery fantasy. Simple examples for testing a hypothesis and setting up experiments in chemistry, physics, and biology are integrated into the plot. The Logic to the Rescue series is a useful addition to a home library for kids ages 10 to 14. The series is designed to kick-start kids' interest in logic, critical thinking, and science through the use of an engrossing story. Mystics and Medicine is the fourth book in the series.
This collection of essays examines the key achievements and likely developments in the area of automated reasoning. In keeping with the group ethos, Automated Reasoning is interpreted liberally, spanning underpinning theory, tools for reasoning, argumentation, explanation, computational creativity, and pedagogy. Wider applications including secure and trustworthy software, and health care and emergency management. The book starts with a technically oriented history of the Edinburgh Automated Reasoning Group, written by Alan Bundy, which is followed by chapters from leading researchers associated with the group. Mathematical Reasoning: The History and Impact of the DReaM Group will attract considerable interest from researchers and practitioners of Automated Reasoning, including postgraduates. It should also be of interest to those researching the history of AI.
In the 20th century philosophy of mathematics has to a great extent been dominated by views developed during the so-called foundational crisis in the beginning of that century. These views have primarily focused on questions pertaining to the logical structure of mathematics and questions regarding the justi?cation and consistency of mathematics. Paradigmatic in this - spect is Hilbert’s program which inherits from Frege and Russell the project to formalize all areas of ordinary mathematics and then adds the requi- ment of a proof, by epistemically privileged means (?nitistic reasoning), of the consistency of such formalized theories. While interest in modi?ed v- sions of the original foundational programs is still thriving, in the second part of the twentieth century several philosophers and historians of mat- matics have questioned whether such foundational programs could exhaust the realm of important philosophical problems to be raised about the nature of mathematics. Some have done so in open confrontation (and hostility) to the logically based analysis of mathematics which characterized the cl- sical foundational programs, while others (and many of the contributors to this book belong to this tradition) have only called for an extension of the range of questions and problems that should be raised in connection with an understanding of mathematics. The focus has turned thus to a consideration of what mathematicians are actually doing when they produce mathematics. Questions concerning concept-formation, understanding, heuristics, changes instyle of reasoning, the role of analogies and diagrams etc.
This book offers a deeper insight into what mathematics is, tapping every child's intuitive ideas of logic and natural enjoyment of games. Simple-looking games and puzzles quickly lead to deeper insights, which will eventually connect with significant formal mathematical ideas as the child grows. This book is addressed to leaders of math circles or enrichment programs, but its activities can fit into regular math classes, homeschooling venues, or situations in which students are learning mathematics on their own. The mathematics contained in the activities can be enjoyed on many levels.
1. This book is above all addressed to mathematicians. It is intended to be a textbook of mathematical logic on a sophisticated level, presenting the reader with several of the most significant discoveries of the last ten or fifteen years. These include: the independence of the continuum hypothe sis, the Diophantine nature of enumerable sets, the impossibility of finding an algorithmic solution for one or two old problems. All the necessary preliminary material, including predicate logic and the fundamentals of recursive function theory, is presented systematically and with complete proofs. We only assume that the reader is familiar with "naive" set theoretic arguments. In this book mathematical logic is presented both as a part of mathe matics and as the result of its self-perception. Thus, the substance of the book consists of difficult proofs of subtle theorems, and the spirit of the book consists of attempts to explain what these theorems say about the mathematical way of thought. Foundational problems are for the most part passed over in silence. Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life. 2. The first two chapters are devoted to predicate logic. The presenta tion here is fairly standard, except that semantics occupies a very domi nant position, truth is introduced before deducibility, and models of speech in formal languages precede the systematic study of syntax.
Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs.Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics. Reviews prior mathematical work with “Preview Activities” at the start of each section. Includes “Activities” throughout that relate to the material contained in each section. Focuses on Congruence Notation and Elementary Number Theorythroughout.For professionals in the sciences or engineering who need to brush up on their advanced mathematics skills. Mathematical Reasoning: Writing and Proof, 2/E Theodore Sundstrom