Developing Essential Understanding Of Number And Numeration For Teaching Mathematics In Prekindergarten Grade 2

Author : Barbara J. Dougherty
Publisher : Unknown
Page : 60 pages
File Size : 53,7 Mb
Release : 2010
Category : Number concept
ISBN : 0873536290

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Developing Essential Understanding of Number and Numeration for Teaching Mathematics in Prekindergarten--grade 2 by Barbara J. Dougherty Pdf

How do composing and decomposing numbers connect with the properties of addition? Focus on the ideas that you need to thoroughly understand in order to teach with confidence. The mathematical content of this book focuses on essential knowledge for teachers about numbers and number systems. It is organised around one big idea and supported by smaller, more specific, interconnected ideas (essential understandings). Gaining this understanding is essential because numbers and numeration are building blocks for other mathematical concepts and for thinking quantitatively about the real-world. Essential Understanding series topics include: Number and Numeration for Grades Pre-K-2 Addition and Subtraction for Grades Pre-K-2 Geometry for Grades Pre-K-2 Reasoning and Proof for Grades Pre-K-8 Multiplication and Division for Grades 3-5 Rational Numbers for Grades 3-5 Algebraic Ideas and Readiness for Grades 3-5 Geometric Shapes and Solids for Grades 3-5 Ratio, Proportion and Proportionality for Grades 6-8 Expressions and Equations for Grades 6-8 Measurement for Grades 6-8 Data Analysis and Statistics for Grades 6-8 Function for Grades 9-12 Geometric Relationships for Grades 9-12 Reasoning and Proof for Grades 9-12 Statistics for Grades 9-12

Author : Janet H. Caldwell
Publisher : National Council of Teachers of English
Page : 85 pages
File Size : 53,5 Mb
Release : 2011
Category : Addition
ISBN : 0873536649

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Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in Prekindergarten-grade 2 by Janet H. Caldwell Pdf

What is the relationship between addition and subtraction? How do you know whether an algorithm will always work? Can you explain why order matters in subraction but not in addition or why it is false to assert that the sum of any two whole numbers is greater than either number? It is organised around two big ideas and supported by smaller, more specific, interconnected ideas (essential understandings). Gaining an understanding about addition and subtraction is essential as they are the foundation for students’ later learning of multiplication and division. Essential Understanding Series topics include: Number and Numeration for Grades Pre-K-2 Addition and Subtraction for Grades Pre-K-2 Geometry for Grades Pre-K-2 Reasoning and Proof for Grades Pre-K-8 Multiplication and Division for Grades 3-5 Rational Numbers for Grades 3-5 Algebraic Ideas and Readiness for Grades 3-5 Geometric Shapes and Solids for Grades 3-5 Ratio, Proportion and Proportionality for Grades 6-8 Expressions and Equations for Grades 6-8 Measurement for Grades 6-8 Data Analysis and Statistics for Grades 6-8 Function for Grades 9-12 Geometric Relationships for Grades 9-12 Reasoning and Proof for Grades 9-12 Statistics for Grades 9-12

Author : Barbara J. Dougherty,Karen S. Karp
Publisher : Unknown
Page : 128 pages
File Size : 45,8 Mb
Release : 2019
Category : Number concept
ISBN : 0873539168

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Putting Essential Understanding of Number and Numeration Into Practice in Pre-K--grade 2 by Barbara J. Dougherty,Karen S. Karp Pdf

Author : Barbara J. Dougherty,Karen S. Karp
Publisher : National Council of Teachers of English
Page : 128 pages
File Size : 42,9 Mb
Release : 2019
Category : Number concept
ISBN : 0873537165

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Putting Essential Understanding of Number and Numeration Into Practice in Pre-K--Grade 2 by Barbara J. Dougherty,Karen S. Karp Pdf

Author : Janet H. Caldwell,Beth McCord Kobett,Karen S. Karp
Publisher : Unknown
Page : 152 pages
File Size : 49,7 Mb
Release : 2014
Category : Addition
ISBN : 0873537300

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Putting Essential Understanding of Addition and Subtraction Into Practice in Prekindergarten-grade 2 by Janet H. Caldwell,Beth McCord Kobett,Karen S. Karp Pdf

Do your students have the incorrect idea that addition “makes numbers bigger” and subtraction “makes numbers smaller”? Do they believe that subtraction is always “taking away”? What tasks can you offer - what questions can you ask - to determine what your students know or don’t know - and move them forward in their thinking? This book focuses on the specialized pedagogical content knowledge that you need to teach addition and subtraction effectively in prekindergarten–grade 2. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with these computations - not only in their current work, but also in higher-level mathematics and a myriad of real-world contexts. Explore rich, research-based strategies and tasks that show how students are reasoning about and making sense of addition and subtraction. Use the opportunities that these and similar tasks provide to build on their understanding while identifying and correcting misunderstandings that may be keeping them from taking the next steps in learning. You have essential understanding. It’s time to put it into practice in your teaching. The Putting Essential Understanding into Practice Series moves NCTM’s Essential Understanding Series into the classroom. The new series details and explores best practices for teaching the essential ideas that students must grasp about fundamental topics in mathematics - topics that are challenging to learn and teach but are critical to the development of mathematical understanding. Classroom vignettes and samples of student work bring each topic to life, and questions for reader reaction open it up for hands-on exploration. Each volume underscores connections with the Common Core State Standards for Mathematics while highlighting the knowledge of learners, curriculum, instructional strategies, and assessment that pedagogical content knowledge entails. Resources and tasks are available at nctm.org/more4U.

Author : Carne Barnett-Clarke
Publisher : National Council of Teachers of English
Page : 83 pages
File Size : 47,5 Mb
Release : 2010
Category : Mathematics
ISBN : 0873536304

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Developing Essential Understanding of Rational Numbers for Teaching Mathematics in Grades 3/5 by Carne Barnett-Clarke Pdf

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.

Author : Monica Neagoy
Publisher : Corwin Press
Page : 210 pages
File Size : 50,5 Mb
Release : 2012-04-20
Category : Education
ISBN : 9781452283630

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Planting the Seeds of Algebra, PreK–2 by Monica Neagoy Pdf

Help young minds explore algebraic concepts Algebra is the gateway to higher education, and preparing students to grasp algebraic concepts increases their opportunities to succeed. This book shows teachers how to create a strong foundation in algebra for very young children. Using in-depth math "explorations," the author unpacks—step by step—the hidden connections to higher algebra. Each exploration contains an elegantly simple grade-banded lesson (on addition, subtraction, patterns, and odd and even numbers), followed by a discussion of the algebra connections in the lesson, as well as suggestions for additional problems to explore. Throughout, readers will find: Clear explanations of algebraic connections Specific strategies for teaching the key ideas of algebra Lesson modifications for older or younger students An array of age-appropriate problems, games, and lessons Planting the seeds of Algebra, PreK–2 helps teachers foster mathematical habits of mind in students such as critical thinking, problem solving, adaptability, agility, communication, curiosity, and imagination. Growth in these ways of thinking and doing will transfer to other areas of education and life—raising the bar and challenging students to aspire.

Author : Albert Dean Otto
Publisher : National Council of Teachers of English
Page : 84 pages
File Size : 47,9 Mb
Release : 2011
Category : Division
ISBN : 0873536673

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Developing Essential Understanding of Multiplication and Division for Teaching Mathematics in Grades 3-5 by Albert Dean Otto Pdf

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.

Author : Monica Neagoy
Publisher : Corwin Press
Page : 249 pages
File Size : 42,5 Mb
Release : 2014-12-23
Category : Education
ISBN : 9781412996617

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Planting the Seeds of Algebra, 3-5 by Monica Neagoy Pdf

'Planting the Seeds of Algebra, 3-5' will empower teachers with theoretical and practical knowledge about both the content and pedagogy of algebraic instruction, and shows them the different faces of algebra as it appears in the early grades.

Author : Robert Reys,Mary Lindquist,Diana V. Lambdin,Nancy L. Smith
Publisher : John Wiley & Sons
Page : 432 pages
File Size : 44,5 Mb
Release : 2014-10-20
Category : Education
ISBN : 9781118654101

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Helping Children Learn Mathematics by Robert Reys,Mary Lindquist,Diana V. Lambdin,Nancy L. Smith Pdf

The 11th Edition of Helping Children Learn Mathematics is designed to help those who are or will be teachers of mathematics in elementary schools help children develop understanding and proficiency with mathematics so they can solve problems. This text is built around three main themes; helping children make sense of mathematics, incorporating practical experiences and using research to guide teaching. It also integrates connections and implications from the Common Core Standards: Mathematics (CCSS-M).

Author : Meletiou-Mavrotheris, Maria
Publisher : IGI Global
Page : 330 pages
File Size : 54,5 Mb
Release : 2015-07-13
Category : Education
ISBN : 9781466687158

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Integrating Touch-Enabled and Mobile Devices into Contemporary Mathematics Education by Meletiou-Mavrotheris, Maria Pdf

Despite increased interest in mobile devices as learning tools, the amount of available primary research studies on their integration into mathematics teaching and learning is still relatively small due to the novelty of these technologies. Integrating Touch-Enabled and Mobile Devices into Contemporary Mathematics Education presents the best practices in mathematics education research and teaching practice by providing an account of current and future trends and issues in mobile mathematics learning and associated technologies and educational methodologies. This edited volume approaches a broad audience including researchers and practitioners interested in the exploitation of mobile technologies in mathematics teaching and learning, as well as mathematics teachers at all levels. This premier reference source compiles the best practices and recommended processes for effectively utilizing the vast capabilities of mobile technologies in the mathematics classroom through a collection of chapters covering topics including, but not limited to, touch-enabled virtual mapping, perceptual learning technologies, mobile teaching, statistics apps for mobile devices, smartphones for the visually impaired, pedagogical and instructional design, and touch screen interfaces in algebraic instruction.

Author : Susan Scharton
Publisher : Math Solutions
Page : 184 pages
File Size : 40,7 Mb
Release : 2005
Category : Education
ISBN : 0941355608

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Teaching Number Sense, Grade 2 by Susan Scharton Pdf

The teaching number sense series focuses on the critical role that number sense plays in students' developing mathematical understanding. Number sense encompasses a wide range of abilities, including being able to make reasonable estimates and to think and reason flexibly.

Author : Rina Zazkis,John Mason,Igor' Kontorovich
Publisher : Taylor & Francis
Page : 229 pages
File Size : 53,7 Mb
Release : 2021-05-23
Category : Education
ISBN : 9780429757969

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The Learning and Teaching of Number by Rina Zazkis,John Mason,Igor' Kontorovich Pdf

Numbers are the backbones of mathematics. From 1 to infinity, numbers accompany and underlie the learning of mathematics and research. While perceived as familiar and understood, numbers present fascinating and often mysterious patterns, relationships and pedagogical issues. The Learning and Teaching of Number explores how mathematics education research has addressed issues related to the structure of numbers and number operations and provides a classroom context. It invites readers to explore less-travelled paths through a well-trodden terrain of number. This fascinating book combines mathematical content with pedagogical ideas and research results. Focusing on number, the book illustrates central ideas related to numbers via a variety of tasks at different levels of complexity. The Learning and Teaching of Number will allow the reader to examine and develop personal understanding of number sets and the relationships among them; enhance personal understanding of familiar topics associated with number operations; engage in a variety of tasks and strengthen personal problem-solving skills; enrich their repertoire of mathematical tasks and pedagogical actions; and consider research ideas and results related to teaching numbers, number operations and number relationships. This is a valuable resource for teacher education courses, graduate programs in mathematics education and professional development programs. Teacher trainers and maths teachers will find their personal understanding of numbers and relationships enriched and will draw connections between research and classroom pedagogy which will extend and enhance their teaching.

Author : Joanne Elizabeth Lobato,Amy B. Ellis,Randall Inners Charles
Publisher : National Council of Teachers of English
Page : 0 pages
File Size : 55,8 Mb
Release : 2010
Category : Curriculum planning
ISBN : 0873536223

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Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning for Teaching Mathematics in Grades 6-8 by Joanne Elizabeth Lobato,Amy B. Ellis,Randall Inners Charles Pdf

"A series for teaching mathematics."--P. [1] of cover.

Author : Association of Mathematics Teacher Educators (AMTE)
Publisher : IAP
Page : 199 pages
File Size : 53,9 Mb
Release : 2020-02-01
Category : Mathematics
ISBN : 9781641139984

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Standards for Preparing Teachers of Mathematics by Association of Mathematics Teacher Educators (AMTE) Pdf

Also available in a black + white version AMTE, in the Standards for Preparing Teachers of Mathematics (SPTM), puts forward a national vision of initial preparation for all Pre-K–12 teachers who teach mathematics. SPTM contains critical messages for all who teach mathematics, including elementary school teachers teaching all disciplines, middle and high school mathematics teachers who may teach mathematics exclusively, special education teachers, teachers of emergent multilingual students, and other teaching professionals and administrators who have responsibility for students’ mathematical learning. SPTM has broad implications for teacher preparation programs, in which stakeholders include faculty and administrators in both education and mathematics at the university level; teachers, principals, and district leaders in the schools with which preparation programs partner; and the communities in which preparation programs and their school partners are situated. SPTM is intended as a national guide that articulates a vision for mathematics teacher preparation and supports the continuous improvement of teacher preparation programs. Such continuous improvement includes changes to preparation program courses and structures, partnerships involving schools and universities and their leaders, the ongoing accreditation of such programs regionally and nationally, and the shaping of state and national mathematics teacher preparation policy. SPTM is also designed to inform assessment practices for mathematics teacher preparation programs, to influence policies related to preparation of teachers of mathematics, and to promote national dialogue around preparing teachers of mathematics. The vision articulated in SPTM is aspirational in that it describes a set of high expectations for developing a well-prepared beginning teacher of mathematics who can support meaningful student learning. The vision is research-based and establishes a set of goals for the continued development and refinement of a mathematics teacher preparation program and a research agenda for the study of the effects of such a program. SPTM contains detailed depictions of what a well-prepared beginning teacher knows and is able to do related to content, pedagogy, and disposition, and what a strong preparation program entails with respect to learning experiences, assessments, and partnerships. Stakeholders in mathematics teacher preparation will find messages related to their roles. Standards for Preparing Teachers of Mathematics includes standards and indicators for teacher candidates and for the design of teacher preparation programs. SPTM outlines assessment practices related to overall quality, program effectiveness, and candidate performance. SPTM describes specific focal practices by grade band and provides guidance to stakeholders regarding processes for productive change.