Sousa discusses the cognitive mechanisms for learning mathematics and the environmental and developmental factors that contribute to mathematics difficulties. This award-winning text examines:Children's innate number sense and how the brain develops an understanding of number relationships Rationales for modifying lessons to meet the developmental learning stages of young children, preadolescents, and adolescents How to plan lessons in PreK-12 mathematics Implications of current research for planning mathematics lessons, including discoveries about memory systems and lesson timing Methods to help elementary and secondary school teachers detect mathematics difficulties Clear connections to the NCTM standards and curriculum focal points

    Topics include: Limits, Derivatives, and Integrations.

    Molinsky and Bill Bliss, is a dynamic, all-skills program that integrates conversation practice, reading, writing, and listening -- all in a light-hearted, fun, and easy-to-use format that has been embraced by students and teachers worldwide. This four-level program promotes native communication between students ... practicing speaking together "side by side." Features of the Third Edition Vocabulary Preview sections in every chapter introduce key words in a lively picture dictionary format. "How to Say It " lessons highlight communication strategies. Pronunciation exercises provide models for practicing authentic pronunciation, stress, and intonation. "Side by Side Gazette" "magazine-style" pages offer feature articles, fact files, vocabulary expansion, cross-cultural topics through photos, authentic listening activities, e-mail exchanges, and humorous cartoons for role-playing. All-new illustrations are lively, light-hearted, and richly detailed to offer students language practice that is contextualized and fun. The core components include Student Books, Teacher's Guides, Activity Workbooks, Activity & Test Prep Workbooks, Communication Games and Activity Masters, audio programs, combined split editions (Student Book and Workbook lessons combined), a testing program, and picture cards.

    Fully updated, the text engages the reader in its discussion of both technical and non-technical models of curriculum development.

    This brand new book from Ross Morrison McGill, bestselling author of 100 Ideas for Secondary Teachers: Outstanding Lessons and Teacher Toolkit, is packed full of practical ideas that will help teachers refine the key elements of their profession. Mark. Plan. Teach. shows how each stage of the teaching process informs the next, building a cyclical framework that underpins everything that teachers do.With teachers' workload at record levels and teacher recruitment and retention the number one issue in education, ideas that really work and will help teachers not only survive but thrive in the classroom are in demand. Every idea in Mark. Plan. Teach. can be implemented by all primary and secondary teachers at any stage of their career and will genuinely improve practice. The ideas have been tried and tested and are supported by evidence that explains why they work, including current educational research and psychological insights from Dr Tim O'Brien, leading psychologist and Visiting Fellow at UCL Institute of Education.Mark. Plan. Teach. will enable all teachers to maximise the impact of their teaching and, in doing so, save time, reduce workload and take back control of the classroom.

    No, hang on, let's make this interesting. Between zero and infinity. Even if you stick to the whole numbers, there are a lot to choose from - an infinite number in fact. Throw in decimal fractions and infinity suddenly gets an awful lot bigger (is that even possible?) And then there are the negative numbers, the imaginary numbers, the irrational numbers like pi which never end. It literally never ends.The world of numbers is indeed strange and beautiful. Among its inhabitants are some really notable characters - pi, e, the "imaginary" number i and the famous golden ratio to name just a few. Prime numbers occupy a special status. Zero is very odd indeed: is it a number, or isn't it?How Numbers Work takes a tour of this mind-blowing but beautiful realm of numbers and the mathematical rules that connect them. Not only that, but take a crash course on the biggest unsolved problems that keep mathematicians up at night, find out about the strange and unexpected ways mathematics influences our everyday lives, and discover the incredible connection between numbers and reality itself. ABOUT THE SERIESNew Scientist Instant Expert books are definitive and accessible entry points to the most important subjects in science; subjects that challenge, attract debate, invite controversy and engage the most enquiring minds. Designed for curious readers who want to know how things work and why, the Instant Expert series explores the topics that really matter and their impact on individuals, society, and the planet, translating the scientific complexities around us into language that's open to everyone, and putting new ideas and discoveries into perspective and context.

    Covering every aspect of the profession, this guide provides information, advice and useful tips on all the typical issues facing the new teacher during the school year, such as planning, controlling and teaching classes; coping with the administrative workload; developing positive relationships with students, colleagues and parents; and preparing for mentoring sessions, inspection and promotion.

    The following day, her story began appearing in Irish papers and soon after was splashed across the front page of the London Times, complete with a photo of Sarah and a caption calling her "brilliant." Just sixteen, she was a mathematician with an international reputation. IN CODE is a heartwarming story that will have readers cheering Sarah on. Originally published in England and cowritten with her mathematician father, David Flannery, IN CODE is "a wonderfully moving story about the thrill of the mathematical chase" (Nature) and "a paean to intellectual adventure" (Times Educational Supplement). A memoir in mathematics, it is all about how a girl next door, nurtured by her family, moved from the simple math puzzles that were the staple of dinnertime conversation to prime numbers, the Sieve of Eratosthenes, Fermat's Little Theorem, googols-and finally into her breathtaking algorithm. Parallel with each step is a modest girl's own self-discovery-her values, her burning curiosity, the joy of persistence, and, above all, her love for her family.

    I just wish I had known all of this twelve years ago...'When you speak to the likes of Dylan Wiliam, Doug Lemov, Daisy Christodoulou, Kris Boulton and the Bjorks, you are bound to learn a thing or two. But when he started his Mr Barton Maths Podcast, Craig Barton wasn't expecting to have his whole outlook on teaching and learning turned upside down. How I Wish I'd Taught Maths is the story of an experienced and successful maths teacher's journey into the world of research, and what it looks like in the classroom.Along the way we meet practical, easy-to-implement strategies including Supercharged Worked Examples, Silent Teacher, SSDD problems, low-stakes quizzes, diagnostic questions, Purposeful Practice, self-explanations, harnessing the power of the hypercorrection effect, how to (and how not to) teach problem-solving and much more. No matter your experience, teaching style or favourite number, every maths teacher will find something to think about in this book.

    The author explains what a classroom number talk is; how to follow students’ thinking and pose the right questions to build understanding; how to prepare for and design purposeful number talks; and how to develop grade-level specific thinking strategies for the operations of addition, subtraction, multiplication, and division. Number Talks includes connections to NCTM’s Principles and Standards for School Mathematics as well as reference tables to help you quickly and easily locate strategies, number talks, and video clips. Includes a Facilitator’s Guide and DVD.

    Former co-teacher and national presenter Anne Beninghof shares stories, and real-life co-taught lesson examples that emphasize creative yet time-efficient instructional strategies that lend themselves beautifully to the co-taught classroom. Teachers and instructional leaders at all levels and in a wide variety of content areas will find this book replete with valuable co-teaching guidance so that success is guaranteed.Offers tips for effective teaching strategies for every type of team teaching situation imaginable Includes guidelines for successful team-teaching with specialists in technology; literacy; occupational/physical therapy; special education; speech-language therapy; ELL; gifted The author is an internationally recognized consultant and trainer This user-friendly, comprehensive book is filled with concrete ideas teachers can implement immediately in the classroom to boost student learning and engagement.

    Teaching Music with Passion is a one-of-a-kind, collective masterpiece of thoughts, ideas and suggestions about the noble profession of music education. Both inspirational and instructional, it will surely change the way you teach (and think) about music. Filled with personal experiences, anecdotes and wonderful quotations, this book is an easy-to-read, essential treasure! "One of the most 'real' writings I have read during my 35 years in music education." Mel Clayton, President, MENC: The National Association for Music Education Click here for a YouTube video on Teaching Music with Passion

    Of course, it’s not all cooking; we’ll also run the New York and Chicago marathons, pay visits to Cinderella and Lewis Carroll, and even get to the bottom of a tomato’s identity as a vegetable. This is not the math of our high school classes: mathematics, Cheng shows us, is less about numbers and formulas and more about how we know, believe, and understand anything, including whether our brother took too much cake.At the heart of How to Bake Pi is Cheng’s work on category theory—a cutting-edge “mathematics of mathematics.” Cheng combines her theory work with her enthusiasm for cooking both to shed new light on the fundamentals of mathematics and to give readers a tour of a vast territory no popular book on math has explored before. Lively, funny, and clear, How to Bake Pi will dazzle the initiated while amusing and enlightening even the most hardened math-phobe.

    Fully revised to meet the needs of the wide range of students beginning engineering courses, this edition has an extended Foundation section including new chapters on graphs, trigonometry, binomial series and functions and a CD-ROM

    This book is about making those encounters as compelling as we can make them." -Harvey "Smokey" Daniels and Steven ZemelmanWe are specialists to the bone-in science, math, social studies, art, music, business, and foreign language. But now, the Common Core and state standards require us to help our students better understand the distinctive texts in our subject areas. "Nobody's making us into reading teachers," write Smokey Daniels and Steve Zemelman, "but we must become teachers of disciplinary thinking through our students' reading."If this shift sounds like a tough one, Subjects Matter, Second Edition is your solution. Smokey and Steve, two of America's most popular educators, share exactly what you need to help students read your nonfiction content closely and strategically: 27 proven teaching strategies that help meet-and exceed-the standards how-to suggestions for engaging kids with content through wide, real-world reading a lively look at using "boring" textbooks motivating instruction that's powered by student collaboration specifics for helping struggling readers succeed.Subjects Matter, Second Edition enables deep, thoughtful learning for your students, while keeping the irreverent, inspiring heart that's made the first edition indispensable. You'll discover fresh and re-energized lessons, completely updated research, and vibrant vignettes from new colleagues and old friends who have as much passion for their subjects as you do."We'll be using methods particular to our fields as well as engaging reading materials that help students understand and remember our content better," write Smokey and Steve. "We can realize that vision of the light going on in kids' heads and maybe fill them with enthusiasm about the amazing subject matter that we have to offer. Sound good? Let's get to work." Read a sample chapter from Subjects Matter, Second Edition.