students on international comparisons of mathematics competency. Paradoxically, Chinese teachers receive far less education than U.S. teachers--11 to 12 years of schooling versus 16 to 18 years of schooling.Studies of U.S. teacher knowledge often document insufficient subject matter knowledge in mathematics. But, they give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education.This book describes the nature and development of the "profound understanding of fundamental mathematics" that elementary teachers need to become accomplished mathematics teachers, and suggests why such teaching knowledge is much more common in China than the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts.The studies described in this book suggest that Chinese teachers begin their teaching careers with a better understanding of elementary mathematics than that of most U.S. elementary teachers. Their understanding of the mathematics they teach and--equally important--of the ways that elementary mathematics can be presented to students, continues to grow throughout their professional lives.Teaching conditions in the United States, unlike those in China, militate against the development of elementary teachers' mathematical knowledge and its organization for teaching. The concluding chapter of the book suggests changes in teacher preparation, teacher support, and mathematics education research that might allow teachers in the United States to attain profound understanding of fundamental mathematics.

    But they don't boggle Socrates. The indomitable old Greek brings his unending questions to Desperate State University. With him come the same mind-opening and spirit-stretching challenge that disrupted ancient Athens.What is the purpose of education?Why do we make love?What good is money?Can computers think like people?Is there a difference between Capitalism and Communism?What is the greatest good?Is belief in God like belief in Santa Claus?In twelve short, Socratic dialogues Peter Kreeft explodes contemporary values like success, power and pleasure. And he bursts the modern bubbles of agnosticism and subjectivism. He leaves you richer, wiser and more able to discern what the best things in life actually are.

    Because they were given to "pioneers" dedicated to opening a new Waldorf school, these talks are often considered one of the best introductions to Waldorf education.Steiner shows the necessity for teachers to work on themselves first, in order to transform their own inherent gifts. He explains the need to use humor to keep their teaching lively and imaginative. Above all, he stresses the tremendous importance of doing everything in the knowledge that children are citizens of both the spiritual and the earthly worlds. And, throughout these lectures, he continually returns to the practical value of Waldorf education.These talks are filled with practical illustrations and revolve around certain themes--the need for observation in teachers; the dangers of stressing the intellect too early; children's need for teaching that is concrete and pictorial; the education of children's souls through wonder and reverence; the importance of first presenting the "whole," then the parts, to the children's imagination.Here is one of the best introductions to Waldorf education, straight from the man who started it all.German source: Die Kunst des Erziehens aus dem Erfassen der Menschenwesenhiet (GA 311).∞ ∞ ∞ SYNOPSIS OF THE LECTURESLECTURE 1: The need for a new art of education. The whole of life must be considered. Process of incarnation as a stupendous task of the spirit. Fundamental changes at seven and fourteen. At seven, the forming of the "new body" out of the "model body" inherited at birth. After birth, the bodily milk as sole nourishment. The teacher's task to give "soul milk" at the change of teeth and "spiritual milk" at puberty.LECTURE 2: In first epoch of life child is wholly sense organ. Nature of child's environment and conduct of surrounding adults of paramount importance. Detailed observation of children and its significance. In second epoch, seven to fourteen, fantasy and imagination as life blood of all education, e.g., in teaching of writing and reading, based on free creative activity of each teacher. The child as integral part of the environment until nine. Teaching about nature must be based on this. The "higher truths" in fairy tales and myths. How the teacher can guide the child through the critical moment of the ninth year.LECTURE 3: How to teach about plants and animals (seven to fourteen). Plants must always be considered, not as specimens, but growing in the soil. The plant belongs to the earth. This is the true picture and gives the child an inward joy. Animals must be spoken of always in connection with humans. All animal qualities and physical characteristics are to be found, in some form, in the human being. Humans as synthesis of the whole animal kingdom. Minerals should not be introduced until twelfth year. History should first be presented in living, imaginative pictures, through legends, myths, and stories. Only at eleven or twelve should any teaching be based on cause and effect, which is foreign to the young child's nature. Some thoughts on punishment, with examples.LECTURE 4: Development of imaginative qualities in the teacher. The story of the violet and the blue sky. Children's questions. Discipline dependent on the right mood of soul. The teacher's own preparation for this. Seating of children according to temperament. Retelling of stories. Importance of imaginative stories that can be recalled in later school life. Drawing of diagrams, from ninth year. Completion and metamorphosis of simple figures, to give children feeling of form and symmetry. Concentration exercises to awaken an active thinking as basis of wisdom for later life. Simple color exercises. A Waldorf school timetable. The "main lesson."LECTURE 5: All teaching matter must be intimately connected with life. In counting, each different number should be connected with the child or what the child sees in the environment. Counting and stepping in rhythm. The body counts. The head looks on. Counting with fingers and toes is good (also writing with the feet). The ONE is the whole. Other numbers proceed from it. Building with bricks is against the child's nature, whose impulse is to proceed from whole to parts, as in medieval thinking. Contrast atomic theory. In real life we have first a basket of apples, a purse of coins. In teaching addition, proceed from the whole. In subtraction, start with minuend and remainder; in multiplication, with product and one factor. Theorem of Pythagoras (eleven-twelve years). Details given of a clear, visual proof, based on practical thinking. This will arouse fresh wonder every time.LECTURE 6: In first seven years etheric body is an inward sculptor. After seven, child has impulse to model and to paint. Teacher must learn anatomy by modeling the organs. Teaching of physiology (nine to twelve years) should be based on modeling. Between seven and fourteen astral body gradually draws into physical body, carrying the breathing by way of nerves, as playing on a lyre. Importance of singing. Child's experience of well being like that of cows chewing the cud. Instrumental music from beginning of school life, wind or strings. Teaching of languages; up to nine through imitation, then beginnings of grammar, as little translation as possible. Vowels are expression of feeling, consonants are imitation of external processes. Each language expresses a different conception. Compare head, Kopf, testa. The parts of speech in relation to the life after death. If language is rightly taught, out of feeling, eurythmy will develop naturally, expressing inner and outer experiences in ordered movements--"visible speech." Finding relationship to space in gymnastics.LECTURE 7: Between seven and fourteen soul qualities are paramount. Beginnings of science teaching from twelfth year only, and connected with real phenomena of life. The problem of fatigue. Wrong conceptions of psychologists. The rhythmic system, predominant in second period, never tires. Rhythm and fantasy. Composition. Sums from real life, not abstractions. Einstein's theory. The kindergarten--imitation of life. Teachers' meetings, the heart of the school. Every child to be in the right class for its age. Importance of some knowledge of trades, e.g., shoemaking, handwork, and embroidery. Children's reports-- characterization, but no grading. Contact with the parents.QUESTIONS AND ANSWERS: The close relationship of Multiplication and Division. How to deal with both together. Transition from the concrete to the abstract in Arithmetic. Not before the ninth year. Healthiness of English weights and measures as related to real life. Decimal system as an intellectual abstraction.Drawing. Lines have no reality in drawing and painting, only boundaries. How to teach children to draw a tree in shading, speaking only of light and color. (Illustration). Line drawing belongs only to geometry.Gymnastics and Sport. Sport is of no educational value, but necessary as belonging to English life. Gymnastics should be taught by demonstration.Religious Instruction. Religion lessons in the Waldorf school given by Catholic priest and Protestant pastor. "Free" religion lessons provided for the other children. Plan of such teaching described, of which the fundamental aim is an understanding of Christianity. The Sunday services.Modern Language Lessons. Choice of languages must be guided by the demands of English life. These can be introduced at an early age. Direct method in language teaching.Closing words by Dr. Steiner on the seriousness of this first attempt to found a school in England.

    Michael Guillen, known to millions as the science editor of ABC's Good Morning America, tells the fascinating stories behind five mathematical equations. As a regular contributor to daytime's most popular morning news show and an instructor at Harvard University, Dr. Michael Guillen has earned the respect of millions as a clear and entertaining guide to the exhilarating world of science and mathematics. Now Dr. Guillen unravels the equations that have led to the inventions and events that characterize the modern world, one of which -- Albert Einstein's famous energy equation, E=mc2 -- enabled the creation of the nuclear bomb. Also revealed are the mathematical foundations for the moon landing, airplane travel, the electric generator -- and even life itself. Praised by Publishers Weekly as "a wholly accessible, beautifully written exploration of the potent mathematical imagination," and named a Best Nonfiction Book of 1995, the stories behind The Five Equations That Changed the World, as told by Dr. Guillen, are not only chronicles of science, but also gripping dramas of jealousy, fame, war, and discovery. Dr. Michael Guillen is Instructor of Physics and Mathematics in the Core Curriculum Program at Harvard University.

    The text begins with basic skills related to personal experience and then carefully progresses to the more sophisticated reasoning skills required for abstract, academic contexts. Thinking Critically introduces students to the cognitive process while teaching them to develop their higher-order thinking and language abilities. A number of distinctive characteristics make the text an effective tool for both instructors and students. Exercises, discussion topics, and writing assignments encourage active participation, stimulating students to critically examine their own and others' thinking.

     Involved Parents = Better Students How do you ensure your child gets the best education possible when U.S. schools have become overburdened, test-driven institutions that rank only average worldwide? Decades of research confirm that when parents engage with their children’s learning, kids do better in school—and life. This straight-talking guide helps you:• understand the critical role you play in your child’s education, • connect with educators in respectful ways, • encourage a love of reading in your kids, • minimize homework meltdowns and disorganization, • support students who struggle academically, • help children navigate social situations and bullying, and • fuel your child’s mind and body for learning. Parent involvement looks different for every family and every child. Packed with real stories and tested strategies, The Parent Backpack demystifies our complex education system and gives you the insights you need to help your kids thrive.

    Featuring more than 150 activities, this guide teaches the styles, works, and techniques of the great masters—Van Gogh, Michelangelo, Rembrandt, and more—through innovative, hands-on, open-ended activities for children Kindergarten through Middle School (ages 6 to 13).

    Good stories are full of life: they engage our emotions and have subtlety and nuance, but they lack rigor and the truths they tell are elusive and subject to debate. As ways of understanding the world around us, numbers and stories seem almost completely incompatible. Once Upon a Number shows that stories and numbers aren't as different as you might imagine, and in fact they have surprising and fascinating connections. The concepts of logic and probability both grew out of intuitive ideas about how certain situations would play out. Now, logicians are inventing ways to deal with real world situations by mathematical means -- by acknowledging, for instance, that items that are mathematically interchangeable may not be interchangeable in a story. And complexity theory looks at both number strings and narrative strings in remarkably similar terms. Throughout, renowned author John Paulos mixes numbers and narratives in his own delightful style. Along with lucid accounts of cutting-edge information theory we get hilarious anecdotes and jokes; instructions for running a truly impressive pyramid scam; a freewheeling conversation between Groucho Marx and Bertrand Russell (while they're stuck in an elevator together); explanations of why the statistical evidence against OJ Simpson was overwhelming beyond doubt and how the Unabomber's thinking shows signs of mathematical training; and dozens of other treats. This is another winner from America's favorite mathematician.

    Fascinating facts about God's world that gives us thousands of pieces of evidence to prove that He created and sustains the universe.

    This classic volume uses simple, conversational language to discuss such matters as the nature of God, sin, salvation, the Christian life, the church, prayer and the Second Coming. Widely used by teachers and parents, this valuable book contains eighty-six sections, each followed by discussion questions, a suggested reading, a hymn, and a prayer.

    New nature games--favorites from the field--and Cornell's typically insightful commentary make the second edition of this special classic even more valuable to nature lovers world-wide. The Sharing Nature movement that Cornell pioneered has now expanded to countries all over the globe. Recommended by Boy Scouts of America, American Camping Association, National Audubon Society and many others.

    This frustration led to Foster's first book, George Washington's World (1941). In her unique approach, Foster weaves a story of the world around her central character; rather than focusing exclusively on geo-political events, as most textbooks do; she includes stories of scientific discovery and invention, music, literature, art, and religion. She has a keen intuition for stories that will especially delight and amuse her youthful audience. In Augustus Caesar's World, Foster traces the seven major civilizations Rome, Greece, Israel, Egypt, China, India, and Persia from 4500 B.C. to the time of Augustus Caesar in 44 B.C. and culminating in 14 A.D. Within this timeframe readers will learn not only the stories of Julius Caesar, Cleopatra, and Marc Antony, but also the historian Livy and how Virgil came to write the Aeneid. Foster will then take her readers all over the world to learn what was happening at this same time in China, Persia, India and so on. Foster's detailed pen and ink drawings are fresh and appealing, and her illustrated timelines give a clear sense of chronology, enriching the engaging text. An all-time customer favorite!

    Ending the Homework Hassle

    Thirty years and nine children later, Cindy has become a popular blogger, podcaster, and award winning teacher. This is her story. It's a story of big families and cross-country moves, and small-town living. It's about great books and morning times and nursery rhymes. It's the story of a dedicated mother's journey toward the Truth and the family she brought along with her.

    Just open the door and step outside. A fun, hands on approach to getting involved in nature, The Kids' Outdoor Adventure Book is a year-round how-to activity guidebook for getting kids outdoors and exploring nature, be it catching fireflies in the cool summer evenings; making birdfeeders in the fall from peanut butter, pine cones, and seed; building a snowman in 3 feet of fresh winter snow; or playing duck, duck, goose with friends in a meadow on a warm spring day. The Kids' Outdoor Adventure Book includes 448 things to do in nature for kids of all ages--more than one activity for every single day of the year. Each of the year's four seasons includes fifty checklist items, fifty challenge items, three each of projects, destinations, garden recipes, and outdoor games. Throughout the book, you'll also find fascinating facts, useful tips and tricks, and plenty of additional resources to turn to. Complete with whimsical, vibrant illustrations, this book is a must for parents and their kids.