mcdougal littell geometry for enjoyment challenge
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This book constitutes the thoroughly refereed post-workshop proceedings of the 8th International Workshop on Automated Deduction in Geometry, ADG 2010, held in Munich, Germany in July 2010. The 13 revised full papers presented were carefully selected during two rounds of reviewing and improvement from the lectures given at the workshop. Topics addressed by the papers are incidence geometry using some kind of combinatoric argument; computer algebra; software implementation; as well as logic and proof assistants.
This monograph reports on an analysis of a small part of the mathematics curriculum, the definitions given to quadrilaterals. This kind of research, which we call microcurricular analysis, is often undertaken by those who create curriculum, but it is not usually done systematically and it is rarely published. Many terms in mathematics education can be found to have different definitions in mathematics books. Among these are “natural number,” “parallel lines” and “congruent triangles,” “trapezoid” and “isosceles trapezoid,” the formal definitions of the trigonometric functions and absolute value, and implicit definitions of the arithmetic operations addition, subtraction, multiplication, and division. Yet many teachers and students do not realize there is a choice of definitions for mathematical terms. And even those who realize there is a choice may not know who decides which definition of any mathematical term is better, and under what criteria. Finally, rarely are the mathematical implications of various choices discussed. As a result, many students misuse and otherwise do not understand the role of definition in mathematics. We have chosen in this monograph to examine a bit of mathematics for its definitions: the quadrilaterals. We do so because there is some disagreement in the definitions and, consequently, in the ways in which quadrilaterals are classified and relate to each other. The issues underlying these differences have engaged students, teachers, mathematics educators, and mathematicians. There have been several articles and a number of essays on the definitions and classification of quadrilaterals. But primarily we chose this specific area of definition in mathematics because it demonstrates how broad mathematical issues revolving around definitions become reflected in curricular materials. While we were undertaking this research, we found that the area of quadrilaterals supplied grist for broader and richer discussions than we had first anticipated. The intended audience includes curriculum developers, researchers, teachers, teacher trainers, and anyone interested in language and its use.
Unmanned Aircraft Systems (UAS) have seen unprecedented levels of growth during the last decade in both military and civilian domains. It is anticipated that civilian applications will be dominant in the future, although there are still barriers to be overcome and technical challenges to be met. Integrating UAS into, for example, civilian space, navigation, autonomy, see-detect-and-avoid systems, smart designs, system integration, vision-based navigation and training, to name but a few areas, will be of prime importance in the near future. This special volume is the outcome of research presented at the International Symposium on Unmanned Aerial Vehicles, held in Orlando, Florida, USA, from June 23-25, 2008, and presents state-of-the-art findings on topics such as: UAS operations and integration into the national airspace system; UAS navigation and control; micro-, mini-, small UAVs; UAS simulation testbeds and frameworks; UAS research platforms and applications; UAS applications. This book aims at serving as a guide tool on UAS for engineers and practitioners, academics, government agencies and industry. Previously published in the Journal of Intelligent and Robotic Systems, 54 (1-3, 2009).
This book responds to the growing interest in the scholarship of mathematics teaching; over the last 20 years the importance of teachers' knowledge for effective teaching has been internationally recognised. For many mathematics teachers, the critical link between practice and knowledge is implied rather than explicitly understood or expressed. This means it can be difficult to assess and thus develop teachers' professional knowledge. The present book is based on two studies investigating exactly how teachers developed their pedagogical knowledge in mathematics from different sources. It describes: The findings in this book have significant implications for teachers, teacher educators, school administrators and educational researchers, as well as policy-makers and school practitioners worldwide.
In this study, I present an analysis of high school geometry curricula regarding mathematical proof opportunities. I examined eight high school level geometry textbooks, which were categorized into three main groups: technology-intensive, standards-based, and traditional curricula. I conceptualized 'ideal' proving activity combining two fundamentally different ways of knowing: a posteriori (or experimental/empirical) and a priori (or deductive/propositional). I argued that two major forces have given rise to such conception of proving: National Council of Teachers of Mathematics (NCTM)-led reform that favors a 'doing' perspective of mathematics and the availability of Dynamic Geometry Software (DGS), a genre of computer tools that allow experimentation, which enables such a vision. Using an analytical framework that maps onto this conception of proving, I investigated proof opportunities along two main dimensions: making mathematical generalizations and providing support to mathematical claims. I also examined the role of DGS within proving activity.