Looking for a way to challenge your gifted students in math class? Look no further! Beyond Base Ten investigates the concept of place value and the representation of numbers by using place value and non-place-value systems. Number bases other than Base Ten are featured, especially through historical contexts of early civilizations that developed number systems different from the one we use today. Place value is a fundamental and powerful concept that is the foundation for the number system used by all cultures. Typical curriculum materials address this concept in a rote method. This unit goes beyond this and encourages students to analyze the structure of our number system and other systems; examine the historical foundations of place value systems (Babylonian and Mayan) and non-place-value systems (Roman and Greek) over thousands of years in different civilizations; analyze why Base Ten is the surviving number system; and investigate applications of other number bases in areas such as computers and electricity. Beyond Base Ten is perfect for any student who loves mathematics! Beyond Base Ten was developed by the Center for Gifted Education at The College of William and Mary. Grades 3-6

Looking for a way to challenge your gifted students in math class? Look no further! Beyond Base Ten investigates the concept of place value and the representation of numbers by using place value and non-place-value systems. Number bases other than Base Ten are featured, especially through historical contexts of early civilizations that developed number systems different from the one we use today.

The emergence of the National Council of Teachers of Mathematics Standards in 1989 sparked a sea change in thinking about the nature and quality of mathematics instruction in U.S. schools. Much is known about transmission forms of mathematics teaching and the influence of this teaching on students' learning, but there is still little knowledge about the alternative forms of instruction that have evolved from the recent widespread efforts to reform mathematics education. Beyond Classical Pedagogy: Teaching Elementary School Mathematics reports on the current state of knowledge about these new instructional practices, which differ in significant ways from the traditional pedagogy that has permeated mathematics education in the past. This book provides a research-based view of the nature of facilitative teaching in its relatively mature form, along with opposing views and critique of this form of pedagogy. The focus is on elementary school mathematics classrooms, where the majority of the reform-based efforts have occurred, and on the micro level of teaching (classroom interaction) as a source for revealing the complexity involved in teaching, teachers' learning, and the impact of both on children's learning. The work in elementary mathematics teaching is situated in the larger context of research on teaching. Research and insights from three disciplinary perspectives are presented: the psychological perspective centers on facilitative teaching as a process of teachers' learning; the mathematical perspective focuses on the nature of the mathematical knowledge teachers need in order to engage in this form of teaching; the sociological perspective attends to the interactive process of meaning construction as teachers and students create intellectual communities in their classrooms. The multidisciplinary perspectives presented provide the editors with the necessary triangulation to provide confirming evidence and rich detail about the nature of facilitative teaching. Audiences for this book include scholars in mathematics education and teacher education, teacher educators, staff developers, and classroom teachers. It is also appropriate as a text for graduate courses in mathematics education, teacher education, elementary mathematics teaching methods, and methods of research in mathematics education.

What happens when you want more in life than just running the bases? You hang out at home plate and stop playing the field. He's sexy and irresistible. I've done my best to ignore the magnetism that flows between us. I don't need complications in my life. I can't get wrapped up in his world, the last thing I need is to get attached to a professional athlete. I don't have time for heartbreak. Something about her pulls me in. I want to get to know her. I want a chance to show her I'm more than just my career, my paycheck. I'm the man for her. I know I am. No matter how much she resists this connection between us. It doesn't change the fact that she's my grand slam.

"Serving as a full-colour teacher reference resource, this title provides developmental activities to encourage the best use of maths manipulatives in the classroom. " - product description.

Polygons Galore! is a mathematics unit for high-ability learners in grades 3-5 focusing on 2-D and 3-D components of geometry by exploring polygons and polyhedra and their properties. The van Hiele levels of geometric understanding provide conceptual underpinnings for unit activities. The unit consists of nine lessons that include student discovery of properties of polygons and polyhedra, investigations for finding areas of triangles and quadrilaterals, study of the Platonic solids, and real-world applications of polygons and polyhedra. It also includes activities related to identifying, comparing, and analyzing polygons by using properties of the polygons; constructing meanings for geometric terms; developing strategies to find areas of specific polygons; identifying and building regular and nonregular polyhedra; and recognizing geometric ideas and relationships as applied in daily life and in other disciplines, such as art. Grades 3-5

Put math manipulatives to work in your classroom and make teaching and learning math both meaningful and productive. Mastering Math Manipulatives includes everything you need to integrate math manipulatives—both concrete and virtual—into math learning. Each chapter of this richly illustrated, easy-to-use guide focuses on a different powerful tool, such as base ten blocks, fraction manipulatives, unit squares and cubes, Cuisenaire Rods, Algebra tiles and two-color counters, geometric strips and solids, geoboards, and others, and includes a set of activities that demonstrate the many ways teachers can leverage manipulatives to model and reinforce math concepts for all learners. It features: · Classroom strategies for introducing math manipulatives, including commercial, virtual, and hand-made manipulatives, into formal math instruction. · Step-by-step instructions for over 70 activities that work with any curriculum, including four-color photos, printable work mats, and demonstration videos. · Handy charts that sort activities by manipulative type, math topic, domains aligned with standards, and grade-level appropriateness.

“Andrew Smart deftly shows why it’s time for us to think deeply about thinking machines before they begin thinking deeply about us.” —Douglas Rushkoff, author, Escaping the Growth Trap,Present Shock, and Program or Be Programmed “Provocative and cool.” —Cory Doctorow “Forget the Turing test—will the supersmart AIs that we hear so much about these days pass the acid test? In this playful, informative, and prescient book, Andrew Smart brings psychedelics into dialogue with neuroscience in order to challenge the whiz-bang computational views of human and machine sentience that dominate the headlines. Giving robots LSD sounds like a joke, but Smart is dead serious in his critique of the hidden and sometimes dangerous biases that underlie both popular and scientific fantasies of digital minds.” —Erik Davis, host of “Expanding Mind” and author, Techgnosis: Myth, Magic, and Mysticism in the Age of Information “Philosophy, psychedelics, robots, and the future; consciousness and intelligence, what else do you desire? Here you will see why those machines that reach singularity will be smarter than us and take over the world—and shall need to be conscious…and maybe they can only be conscious if they are human enough. The thesis of the book, and the path shown us by Smart, leads to a great trip, of imagination and philosophy, of maths and neuroscience.” —Dr. Tristan Bekinschtein, Lecturer, Department of Psychology, University of Cambridge Can we build a robot that trips on acid? This is not a frivolous question, according to neuroscientist Andrew Smart. If we can’t, he argues, we haven’t really created artificial intelligence. In an exposition reminiscent of crossover works such as Gödel, Escher, Bach and Fermat’s Last Theorem, Andrew Smart weaves together Mangarevan binary numbers, the discovery of LSD, Leibniz, computer programming, and much more to connect the vast but largely forgotten world of psychedelic research with the resurgent field of AI and the attempt to build conscious robots. A book that draws on the history of mathematics, philosophy, and digital technology, Beyond Zero and One challenges fundamental assumptions underlying artificial intelligence. Is the human brain based on computation? Can information alone explain human consciousness and intelligence? Smart convincingly makes the case that true intelligence, and artificial intelligence, requires an appreciation of what is beyond the computational.

Multiple-choice testing is an educational reality. Rather than complain about the negative impact these tests may have on teaching and learning, why not use them to better understand your students' true mathematical knowledge and comprehension? Maryann Wickett and Eunice Hendrix-Martin show teachers how to move beyond the student's answer--right or wrong--to uncover understanding and/or misconceptions. By asking a few simple follow-up questions, teachers can learn a great deal about student understanding and make better, more informed instructional decisions. The Beyond the Bubble books (grades 2-3 and grades 4-5) are each divided into five strands--number, measurement, algebra, geometry, and probability--with six problems per strand. Each problem includes an overview of the objective of the test question, a sample question, typical of those found on standardized tests, strategies students employ to solve the problem, conversation starters, student work, student-teacher conversations, and instructional strategies to advance student learning. Teachers will also find suggestions for differentiation, reproducible of sample questions, and a comprehensive list of additional resources. With dozens of sample test questions and numerous student samples, Beyond the Bubble shows educators how to use multiple choice tests to provide more purposeful, focused mathematics instruction for all of their students.

Written by a teacher with many years' experience of teaching mathematics to primary school dyslexic and dyspraxic children with a wide range of abilities, this book is designed to be a practical teaching guide. It offers detailed guidance and specific teaching suggestions to all specialist teachers, support teachers, classroom teachers and parents who either directly teach mathematics to dyslexic and dyspraxic children or who support the mathematics teaching programmes of dyslexic or dyspraxic children. Although the book has grown out of teaching experience it is also informed by widely acknowledged contemporary and international research, which explores the cognitive aspects of learning mathematics and tries to understand why it is that some children fail to learn mathematics. Many of the teaching principles described in the text have specific and quite far-reaching implications. The theoretical arguments should therefore also be of interest to special needs co-ordinators, heads of maths departments, head teachers or other professionals who are responsible for designing or modifying the maths learning programmes of children with special learning and maths difficulties. In more general terms, the book hopes to contribute to the broad discussion of the cognitive features and educational needs of dyslexic and dyspraxic children.