Download or read book Understanding Mathematics for Young Children written by Derek Haylock and published by SAGE. This book was released on 2017-02-08 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Having a deep understanding of the mathematical ideas and concepts taught in the classroom is vital as a nursery or primary school teacher. In order for children to get to grips with these concepts, trainee teachers need to be aware of how they come to interpret and understand them. Now in its 5th edition, this essential book helps trainee teachers develop their own knowledge of key mathematical ideas and concepts for the nursery and primary classroom. Now focusing specifically on ages 3-7, it also supports trainees with several age-appropriate classroom activities. As well as updates to further reading suggestions and research focuses, this revised edition includes new content on: Mastery in learning mathematics Simple fractions Roman numerals Money as a form of measurement

Download or read book Understanding Mathematics written by Keith Kressin and published by . This book was released on 1997-03 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive overview of elementary, middle, and high-school mathematics. Intended as a supplement to any math program, this book provides additional math explanation from basic to advanced levels. Emphasis is placed on why problems are solved in a certain manner. Tailored for those who need simplified, easy-to-read additional explanations of math concepts.

Download or read book Mine the Gap for Mathematical Understanding Grades 3 5 written by John SanGiovanni and published by Corwin Press. This book was released on 2016-09-16 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Being an effective math educator is one part based on the quality of the tasks we give, one part how we diagnose what we see, and one part what we do with what we find. Yet with so many students and big concepts to cover, it can be hard to slow down enough to look for those moments when students’ responses tell us what we need to know about next best steps. In this remarkable book, John SanGiovanni helps us value our students’ misconceptions and incomplete understandings as much as their correct ones—because it’s the gap in their understanding today that holds the secrets to planning tomorrow’s best teaching. SanGiovanni lays out 180 high-quality tasks aligned to the standards and big ideas of Grades 3-5 mathematics, including addition and subtraction of multi-digit whole numbers, multiplication and division of single and multi-digit whole numbers, foundational fraction concepts, foundational decimal concepts, and operations with fractions and decimals. The tasks are all downloadable so you can use or modify them for instruction and assessment. Each big idea offers a starting task followed by: what makes it a high-quality task what you might anticipate before students work with the task 4 student examples of the completed task showcasing a distinct "gap" commentary on what precisely counts for mathematical understanding and the next instructional steps commentary on the misconception or incomplete understanding so you learn why the student veered off course three additional tasks aligned to the mathematics topic and ideas about what students might do with these additional tasks. It’s time to break our habit of rushing into re-teaching for correctness and instead get curious about the space between right and wrong answers. Mine the Gap for Mathematical Understanding is a book you will return to again and again to get better at selecting tasks that will uncover students’ reasoning—better at discerning the quality and clarity of students’ understanding—and better at planning teaching based on the gaps you see.

Download or read book Understanding Mathematics in the Lower Primary Years written by Derek Haylock and published by SAGE. This book was released on 2003 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: New Edition of Best Seller! This is a fully revised and updated edition of the authors' successful and much-used book and was written for those who wish to have a clearer understanding of the mathematical ideas behind the material they use in the classroom.

Download or read book Understanding Mathematics for Young Children written by Derek Haylock and published by SAGE. This book was released on 2013-03-13 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lecturers, why waste time waiting for the post arrive? Request your e-inspection copy today! 'This book was a delight to read. The mathematical content is excellent and the approach to explaining complex concepts is exceptionally good!' -Dr Jennifer Way, University of Sydney 'I'm a really big fan of this book: it is the single most influential text in my experience of working with primary maths teachers in the last 12 years' - Andy Tynemouth, Every Child Counts National Adviser, Edge Hill University 'Every teacher of maths should read this book! It helped me realize why some children are struggling with doing simple word problems' -Amazon reader review If you are a teacher or student teacher in a nursery or primary school, you need a secure understanding of the mathematical ideas behind the material you will use in the classroom. To help young children develop their understanding of mathematics, you need to develop your own understanding of how mathematics is learnt. In this indispensible book, the authors help you to understand mathematical concepts and how children come to understand them, and also help develop your own confidence with mathematical activities. Each chapter of this book includes: -Real-life examples and illustrations from children and teachers in the classroom -The research behind some of the concepts and teaching approaches discussed -Pauses to reflect and discuss your own mathematical knowledge and experience -Age-appropriate classroom activities to try with your class or group.

Download or read book Mine the Gap for Mathematical Understanding Grades K 2 written by John SanGiovanni and published by Corwin Press. This book was released on 2016-10-31 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Being an effective math educator is one part based on the quality of the tasks we give, one part how we diagnose what we see, and one part what we do with what we find. Yet with so many students and big concepts to cover, it can be hard to slow down enough to look for those moments when students’ responses tell us what we need to know about next best steps. In this remarkable book, John SanGiovanni helps us value our young learners’ misconceptions and incomplete understandings as much as their correct ones—because it’s the gap in their understanding today that holds the secrets to planning tomorrow’s best teaching. SanGiovanni lays out 160 high-quality tasks aligned to the standards and big ideas of grades K-2 mathematics, including counting and representing numbers, number relationships and comparison, addition and subtraction within 100 and 1000, money and time, and multiplication and division. The tasks are all downloadable so you can use or modify them for instruction and assessment. Each big idea offers a starting task followed by: what makes it a high-quality taskwhat you might anticipate before students work with the task 4 student examples of the completed task showcasing a distinct "gap" commentary on what precisely counts for mathematical understanding and the next instructional steps commentary on the misconception or incomplete understanding so you learn why the student veered off course three additional tasks aligned to the mathematics topic and ideas about what students might do with these additional tasks. It’s time to break our habit of rushing into re-teaching for correctness and instead get curious about the space between right and wrong answers. Mine the Gap for Mathematical Understanding is a book you will return to again and again to get better at selecting tasks that will uncover students’ reasoning—better at discerning the quality and clarity of students’ understanding—and better at planning teaching based on the gaps you see.

Download or read book Understanding Mathematics 3 written by C. Sailaja, Smita Ratish, Lata Wishram and published by Vikas Publishing House. This book was released on with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding Mathematics is a carefully written series of mathematics to help students encourage the study of mathematics in the best interactive form. It contains ample practice material, attractive illustrations and real-life examples for the students to relate the topics with their everyday life. Special care has been taken while teaching topics like geometry and probability to the students. Keeping in mind the development status and comprehension level of students, the text has been presented in a well graded manner.

Download or read book Understanding Mathematics for Young Children written by Derek Haylock and published by SAGE. This book was released on 2008-10-14 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'This book is the ideal way to dispel some of the fears which surround the subject area of mathematics and should be an essential part of the professional development library of every early years setting provider for children aged three and over' - Early Years Update 'A book that is both readable and rigorous. [Its] guidance will help teachers to make mathematics meaningful to young children. Throughout the book connections are made which relate language, symbols, concrete materials and pictures to the key ideas that are central to effective learning for the 21st century. This book will help teachers gain a depth of understanding that will make them confident in engaging children with real mathematical thinking' - Dr J.E. Anghileri, Senior Lecturer in Mathematics and Mathematics Education, Faculty of Education, University of Cambridge 'This is an updated version of a classic text which has been a best -seller among teachers and student teachers for many years. Being always strongly grounded in the classroom, it develops in a non-intimidating way teachers' own understanding of the mathematics they are teaching. Many insightful examples of children's thinking and appropriate activities help to illustrate the points. This is an essential book for teachers of Early Years and Key Stage 1' - Margaret Brown, Professor of Mathematics Education, King's College London, UK This is a fully revised version of the authors' successful and much-used book, Understanding Mathematics in the Lower Primary Years, updated to include the current Foundation Stage Curriculum and the new Primary Framework in England. The authors empower the reader to have a clearer understanding of the mathematical ideas behind the material they use in the classroom. They also show how children can be helped to develop an understanding of mathematics for themselves, rather than just learning recipes and routines with little meaning. Major themes are: - Understanding through making connections - Equivalence and transformation - Using and applying mathematics It is written for teachers and teacher trainees engaged in teaching mathematics to children aged 3 to 8 years. It is an essential student text and professional reference work for all teachers of children aged 3 to 8 years. Dr Derek Haylock is an education consultant and author, working in the field of mathematics education. His book Mathematics Explained for Primary Teachers has been a leader in the field for many years, with a third edition published in 2006. Dr Anne Cockburn is a Reader in the School of Education and Lifelong Learning at the University of East Anglia, Norwich. Watch the authors talking about their book here: YouTube

Download or read book How We Understand Mathematics written by Jacek Woźny and published by Springer. This book was released on 2018-04-25 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume examines mathematics as a product of the human mind and analyzes the language of "pure mathematics" from various advanced-level sources. Through analysis of the foundational texts of mathematics, it is demonstrated that math is a complex literary creation, containing objects, actors, actions, projection, prediction, planning, explanation, evaluation, roles, image schemas, metonymy, conceptual blending, and, of course, (natural) language. The book follows the narrative of mathematics in a typical order of presentation for a standard university-level algebra course, beginning with analysis of set theory and mappings and continuing along a path of increasing complexity. At each stage, primary concepts, axioms, definitions, and proofs will be examined in an effort to unfold the tell-tale traces of the basic human cognitive patterns of story and conceptual blending. This book will be of interest to mathematicians, teachers of mathematics, cognitive scientists, cognitive linguists, and anyone interested in the engaging question of how mathematics works and why it works so well.

Download or read book Developing Essential Understanding of Rational Numbers for Teaching Mathematics in Grades 3 5 written by Carne Barnett-Clarke and published by National Council of Teachers of English. This book was released on 2010 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is the relationship between fractions and rational numbers? Can you explain why the product of two fractions between 0 and 1 is less than either factor? How are rational numbers related to irrational numbers, which your students will study in later grades? How much do you know… and how much do you need to know? Helping your upper elementary school students develop a robust understanding of rational numbers requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about rational numbers. It is organised around four big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to rational numbers, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls and dispel misconceptions. You will also learn to develop appropriate tasks, techniques and tools for assessing students’ understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently.

Download or read book Problem Solving in Mathematics Grades 3 6 written by Alfred S. Posamentier and published by Corwin Press. This book was released on 2009-03-18 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Demonstrates problem solving strategies with solutions and teaching notes and allows the teacher to create a collection of problems to fit a particular grade level."-Janice L. Richardson, Associate Professor and Education Coordinator, Department of MathematicsElon UniversityHelp students succeed as problem solvers in and out of the classroom! Problem solving skills are critical to students' success in mathematics, but the techniques can't be caught; they must be taught. Based on the premise that educators must take a deliberate approach to the teaching of problem solving skills, this book helps teachers engage students in the process. Problem Solving in Mathematics, Grades 3-6 stresses the importance of problem solving in mathematics and presents nine strategies that students can use to solve problems, such as working backwards, finding a pattern, making a drawing, or solving a simpler equivalent problem. Each chapter demonstrates how teachers can:Apply the strategies to problems at different grade levels Incorporate these strategies into a mathematics program Understand how each strategy can be applied to real-life situations Make each strategy an integral part of students' thinking processesWith helpful teaching notes, sample problems for students that fit into any mathematics curriculum, and step-by-step solutions to sample problems, this book is perfect for teachers who want their students to succeed in mathematics!

Download or read book Knowing and Teaching Elementary Mathematics written by Liping Ma and published by Routledge. This book was released on 2010-03-26 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author’s work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work.

Download or read book Understanding Analysis written by Stephen Abbott and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This elementary presentation exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions.

Download or read book Developing Essential Understanding of Algebraic Thinking for Teaching Mathematics in Grades 3 5 written by Maria L. Blanton and published by . This book was released on 2011 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like algebra at any level, early algebra is a way to explore, analyse, represent and generalise mathematical ideas and relationships. This book shows that children can and do engage in generalising about numbers and operations as their mathematical experiences expand. The authors identify and examine five big ideas and associated essential understandings for developing algebraic thinking in grades 3-5. The big ideas relate to the fundamental properties of number and operations, the use of the equals sign to represent equivalence, variables as efficient tools for representing mathematical ideas, quantitative reasoning as a way to understand mathematical relationships and functional thinking to generalise relationships between covarying quantities. The book examines challenges in teaching, learning and assessment and is interspersed with questions for teachers’ reflection.

Download or read book Developing Essential Understanding of Multiplication and Division for Teaching Mathematics in Grades 3 5 written by Albert Dean Otto and published by National Council of Teachers of English. This book was released on 2011 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unpacking"" the ideas related to multiplication and division is a critical step in developing a deeper understanding. To those without specialised training, many of these ideas might appear to be easy to teach. But those who teach in grades 3-5 are aware of their subtleties and complexities. This book identifies and examines two big ideas and related essential understandings for teaching multiplication and division in grades 3–5. Big Idea 1 captures the notion that multiplication is usefully defined as a scalar operation. Problem situations modelled by multiplication have an element that represents the scalar and an element that represents the quantity to which the scalar applies. Big Idea 2 relates to the algorithms that problem solvers have invented - some of which have become “standard” - for multiplying and dividing. The authors examine the ways in which counting, adding and subtracting lead to multiplication and division, as well as the role that these operations play in algebraic expressions and other advanced topics. The book examines challenges in teaching, learning and assessment and is interspersed with questions for teachers’ reflection.

Download or read book Visible Learning for Mathematics Grades K 12 written by John Hattie and published by Corwin Press. This book was released on 2016-09-15 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Selected as the Michigan Council of Teachers of Mathematics winter book club book! Rich tasks, collaborative work, number talks, problem-based learning, direct instruction...with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one—it’s about when—and show you how to design high-impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school. That’s a high bar, but with the amazing K-12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in "visible" learning because the effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students. Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: Surface learning phase: When—through carefully constructed experiences—students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings. Deep learning phase: When—through the solving of rich high-cognitive tasks and rigorous discussion—students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency. Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations. To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K-12 through intentionally designed guided, collaborative, and independent learning.

Download or read book The Daily 5 written by Gail Boushey and published by Stenhouse Publishers. This book was released on 2014 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Daily 5, Second Edition retains the core literacy components that made the first edition one of the most widely read books in education and enhances these practices based on years of further experience in classrooms and compelling new brain research. The Daily 5 provides a way for any teacher to structure literacy (and now math) time to increase student independence and allow for individualized attention in small groups and one-on-one. Teachers and schools implementing the Daily 5 will do the following: Spend less time on classroom management and more time teaching Help students develop independence, stamina, and accountability Provide students with abundant time for practicing reading, writing, and math Increase the time teachers spend with students one-on-one and in small groups Improve schoolwide achievement and success in literacy and math. The Daily 5, Second Edition gives teachers everything they need to launch and sustain the Daily 5, including materials and setup, model behaviors, detailed lesson plans, specific tips for implementing each component, and solutions to common challenges. By following this simple and proven structure, teachers can move from a harried classroom toward one that hums with productive and engaged learners. What's new in the second edition: Detailed launch plans for the first three weeks Full color photos, figures, and charts Increased flexibility regarding when and how to introduce each Daily 5 choice New chapter on differentiating instruction by age and stamina Ideas about how to integrate the Daily 5 with the CAFE assessment system New chapter on the Math Daily 3 structure