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Author : Rand Corporation
Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.3/5 ( download)
Download or read book Algebraic Thinking Tools written by Rand Corporation and published by . This book was released on 1989 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Maria L. Blanton
Publisher :
ISBN 13 : 9780873536684
Total Pages : 102 pages
Book Rating : 4.5/5 (366 download)
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.
Author : Susan Jo Russell
Publisher : Heinemann Educational Books
ISBN 13 : 9780325041919
Total Pages : 0 pages
Book Rating : 4.0/5 (419 download)
Download or read book Connecting Arithmetic to Algebra written by Susan Jo Russell and published by Heinemann Educational Books. This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "To truly engage in mathematics is to become curious and intrigued about regularities and patterns, then describe and explain them. A focus on the behavior of the operations allows students starting in the familiar territory of number and computation to progress to true engagement in the discipline of mathematics." -Susan Jo Russell, Deborah Schifter, and Virginia Bastable Algebra readiness: it's a topic of concern that seems to pervade every school district. How can we better prepare elementary students for algebra? More importantly, how can we help all children, not just those who excel in math, become ready for later instruction? The answer lies not in additional content, but in developing a way of thinking about the mathematics that underlies both arithmetic and algebra. Connecting Arithmetic to Algebra invites readers to learn about a crucial component of algebraic thinking: investigating the behavior of the operations. Nationally-known math educators Susan Jo Russell, Deborah Schifter, and Virginia Bastable and a group of collaborating teachers describe how elementary teachers can shape their instruction so that students learn to: *notice and describe consistencies across problems *articulate generalizations about the behavior of the operations *develop mathematical arguments based on representations to explain why such generalizations are or are not true. Through such work, students become familiar with properties and general rules that underlie computational strategies-including those that form the basis of strategies used in algebra-strengthening their understanding of grade-level content and at the same time preparing them for future studies. Each chapter is illustrated by lively episodes drawn from the classrooms of collaborating teachers in a wide range of settings. These provide examples of posing problems, engaging students in productive discussion, using representations to develop mathematical arguments, and supporting both students with a wide range of learning profiles. Staff Developers: Available online, the Course Facilitator's Guide provides math leaders with tools and resources for implementing a Connecting Arithmetic to Algebra workshop or preservice course. For information on the PD course offered through Mount Holyoke College, download the flyer.
Author : N. Bednarz
Publisher : Springer Science & Business Media
ISBN 13 : 9400917325
Total Pages : 342 pages
Book Rating : 4.4/5 (9 download)
Download or read book Approaches to Algebra written by N. Bednarz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, except if those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an "arithmetic" of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano.
Author : Mark J. Driscoll
Publisher : Heinemann Educational Books
ISBN 13 :
Total Pages : 176 pages
Book Rating : 4.F/5 ( download)
Download or read book Fostering Algebraic Thinking written by Mark J. Driscoll and published by Heinemann Educational Books. This book was released on 1999 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fostering Algebraic Thinking is a timely and welcome resource for middle and high school teachers hoping to ease their students' transition to algebra.
Author : Dinah Zike
Publisher :
ISBN 13 : 9781882796274
Total Pages : 124 pages
Book Rating : 4.7/5 (962 download)
Download or read book Dinah Zike's Notebook Foldables for Spirals, Binders, & Composition Books written by Dinah Zike and published by . This book was released on 2008 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Rudy Rucker
Publisher : Courier Corporation
ISBN 13 : 0486492281
Total Pages : 337 pages
Book Rating : 4.4/5 (864 download)
Download or read book Mind Tools written by Rudy Rucker and published by Courier Corporation. This book was released on 2013-11-21 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: Boston: Houghton Mifflin, 1987.
Author : Thomas P. Carpenter
Publisher : Routledge
ISBN 13 : 1000089207
Total Pages : 260 pages
Book Rating : 4.0/5 ( download)
Download or read book Addition and Subtraction written by Thomas P. Carpenter and published by Routledge. This book was released on 2020-08-15 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: A hallmark of much of the research on children’s thinking in the 1970s had been the focus on explicit content domains. Much of this research had been represented by an eclectic collection of studies sampled from a variety of disciplines and content areas. However, in the few years before this publication, research in several content domains has begun to coalesce into a coherent body of knowledge. Originally published in 1982, the chapters in this work represent one of the first attempts to bring together the perspectives of a variety of different researchers investigating a specific, well defined content domain. This book presents theoretical views and research findings of a group of international scholars who are investigating the early acquisition of addition and subtraction skills by young children. Together, the contributors bring a blend of psychology, educational psychology, and mathematics education to this topic. Fields of interest such as information processing, artificial intelligence, early childhood, and classroom teaching and learning are included in this blend.
Author : Anita Wah
Publisher : Henri Picciotto
ISBN 13 : 9781561072514
Total Pages : 540 pages
Book Rating : 4.0/5 (725 download)
Download or read book Algebra written by Anita Wah and published by Henri Picciotto. This book was released on 1994 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : National Council of Teachers of Mathematics
Publisher : National
ISBN 13 :
Total Pages : 56 pages
Book Rating : 4.F/5 ( download)
Download or read book Curriculum Focal Points for Prekindergarten Through Grade 8 Mathematics written by National Council of Teachers of Mathematics and published by National. This book was released on 2006 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence provides a rationale for focal points for each grade level, prekindergarten - 8.
Author : Anne Collins
Publisher : Stenhouse Publishers
ISBN 13 : 1625310676
Total Pages : 237 pages
Book Rating : 4.6/5 (253 download)
Download or read book Accessible Algebra written by Anne Collins and published by Stenhouse Publishers. This book was released on 2017 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible Algebra: 30 Modules to Promote Algebraic Reasoning, Grades 7-10 is for any pre-algebra or algebra teacher who wants to provide a rich and fulfilling experience for students as they develop new ways of thinking through and about algebra. The book includes 30 lessons that identifies a focal domain and standard in algebra, then lays out the common misconceptions and challenges students may face as they work to investigate and understand problems. Authors Anne Collins and Steven Benson conferred with students in real classrooms as the students explained what problem-solving strategies they were using or worked to ask the right questions that would lead them to a deeper understanding of algebra. Each scenario represents actual instances of an algebra classroom that demonstrate effective teaching methods, real-life student questions, and conversations about the problems at hand. Accessible Algebra works for students at every level. In each lesson there are sections on how to support struggling students, as well as ways to challenge students who may need more in-depth work. There are also numerous additional resources, including research articles and classroom vignettes.
Author : Rosamund Sutherland
Publisher : Springer Science & Business Media
ISBN 13 : 0306472236
Total Pages : 277 pages
Book Rating : 4.3/5 (64 download)
Download or read book Perspectives on School Algebra written by Rosamund Sutherland and published by Springer Science & Business Media. This book was released on 2006-02-16 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book confronts the issue of how young people can find a way into the world of algebra. It represents multiple perspectives which include an analysis of situations in which algebra is an efficient problem-solving tool, the use of computer-based technologies, and a consideration of the historical evolution of algebra. The book emphasizes the situated nature of algebraic activity as opposed to being concerned with identifying students' conceptions in isolation from problem-solving activity.
Author : Carolyn Kieran
Publisher : Springer
ISBN 13 : 3319683519
Total Pages : 443 pages
Book Rating : 4.3/5 (196 download)
Download or read book Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds written by Carolyn Kieran and published by Springer. This book was released on 2017-12-04 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights new developments in the teaching and learning of algebraic thinking with 5- to 12-year-olds. Based on empirical findings gathered in several countries on five continents, it provides a wealth of best practices for teaching early algebra. Building on the work of the ICME-13 (International Congress on Mathematical Education) Topic Study Group 10 on Early Algebra, well-known authors such as Luis Radford, John Mason, Maria Blanton, Deborah Schifter, and Max Stephens, as well as younger scholars from Asia, Europe, South Africa, the Americas, Australia and New Zealand, present novel theoretical perspectives and their latest findings. The book is divided into three parts that focus on (i) epistemological/mathematical aspects of algebraic thinking, (ii) learning, and (iii) teaching and teacher development. Some of the main threads running through the book are the various ways in which structures can express themselves in children’s developing algebraic thinking, the roles of generalization and natural language, and the emergence of symbolism. Presenting vital new data from international contexts, the book provides additional support for the position that essential ways of thinking algebraically need to be intentionally fostered in instruction from the earliest grades.
Author : Tana Hoban
Publisher : Harper Collins
ISBN 13 : 0688070345
Total Pages : 36 pages
Book Rating : 4.6/5 (88 download)
Download or read book Is It Red? Is It Yellow? Is It Blue? written by Tana Hoban and published by Harper Collins. This book was released on 1987-04-23 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: What color do you see? Red? Yellow? Blue? Here is a concept book young children can grow with, as they explore colors, sizes, shapes, and relationships with the master of the photo-concept book ' Tana Hoban.
Author : Max Ray
Publisher : Heinemann Educational Books
ISBN 13 : 9780325050904
Total Pages : 0 pages
Book Rating : 4.0/5 (59 download)
Download or read book Powerful Problem Solving written by Max Ray and published by Heinemann Educational Books. This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: How can we break the cycle of frustrated students who "drop out of math" because the procedures just don't make sense to them? Or who memorize the procedures for the test but don't really understand the mathematics? Max Ray-Riek and his colleagues at the Math Forum @ Drexel University say "problem solved," by offering their collective wisdom about how students become proficient problem solvers, through the lens of the CCSS for Mathematical Practices. They unpack the process of problem solving in fresh new ways and turn the Practices into activities that teachers can use to foster habits of mind required by the Common Core: communicating ideas and listening to the reflections of others estimating and reasoning to see the "big picture" of a problem organizing information to promote problem solving using modeling and representations to visualize abstract concepts reflecting on, revising, justifying, and extending the work. Powerful Problem Solving shows what's possible when students become active doers rather than passive consumers of mathematics. Max argues that the process of sense-making truly begins when we create questioning, curious classrooms full of students' own thoughts and ideas. By asking "What do you notice? What do you wonder?" we give students opportunities to see problems in big-picture ways, and discover multiple strategies for tackling a problem. Self-confidence, reflective skills, and engagement soar, and students discover that the goal is not to be "over and done," but to realize the many different ways to approach problems. Read a sample chapter.
Author : Beth McCord Kobett
Publisher : Corwin Press
ISBN 13 : 1544374925
Total Pages : 189 pages
Book Rating : 4.5/5 (443 download)
Download or read book Strengths-Based Teaching and Learning in Mathematics written by Beth McCord Kobett and published by Corwin Press. This book was released on 2020-02-27 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is a game changer! Strengths-Based Teaching and Learning in Mathematics: 5 Teaching Turnarounds for Grades K- 6 goes beyond simply providing information by sharing a pathway for changing practice. . . Focusing on our students’ strengths should be routine and can be lost in the day-to-day teaching demands. A teacher using these approaches can change the trajectory of students’ lives forever. All teachers need this resource! Connie S. Schrock Emporia State University National Council of Supervisors of Mathematics President, 2017-2019 NEW COVID RESOURCES ADDED: A Parent’s Toolkit to Strengths-Based Learning in Math is now available on the book’s companion website to support families engaged in math learning at home. This toolkit provides a variety of home-based activities and games for families to engage in together. Your game plan for unlocking mathematics by focusing on students’ strengths. We often evaluate student thinking and their work from a deficit point of view, particularly in mathematics, where many teachers have been taught that their role is to diagnose and eradicate students’ misconceptions. But what if instead of focusing on what students don’t know or haven’t mastered, we identify their mathematical strengths and build next instructional steps on students’ points of power? Beth McCord Kobett and Karen S. Karp answer this question and others by highlighting five key teaching turnarounds for improving students’ mathematics learning: identify teaching strengths, discover and leverage students’ strengths, design instruction from a strengths-based perspective, help students identify their points of power, and promote strengths in the school community and at home. Each chapter provides opportunities to stop and consider current practice, reflect, and transfer practice while also sharing · Downloadable resources, activities, and tools · Examples of student work within Grades K–6 · Real teachers’ notes and reflections for discussion It’s time to turn around our approach to mathematics instruction, end deficit thinking, and nurture each student’s mathematical strengths by emphasizing what makes them each unique and powerful.
Author : Center for Science, Mathematics, and Engineering Education
Publisher : National Academies Press
ISBN 13 : 0309522455
Total Pages : 206 pages
Book Rating : 4.3/5 (95 download)
Download or read book The Nature and Role of Algebra in the K-14 Curriculum written by Center for Science, Mathematics, and Engineering Education and published by National Academies Press. This book was released on 1998-10-07 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the 1989 release of Everybody Counts by the Mathematical Sciences Education Board (MSEB) of the National Research Council and the Curriculum and Evaluation Standards for School Mathematics by the National Council of Teachers of Mathematics (NCTM), the "standards movement" in K-12 education was launched. Since that time, the MSEB and the NCTM have remained committed to deepening the public debate, discourse, and understanding of the principles and implications of standards-based reform. One of the main tenets in the NCTM Standards is commitment to providing high-quality mathematical experiences to all students. Another feature of the Standards is emphasis on development of specific mathematical topics across the grades. In particular, the Standards emphasize the importance of algebraic thinking as an essential strand in the elementary school curriculum. Issues related to school algebra are pivotal in many ways. Traditionally, algebra in high school or earlier has been considered a gatekeeper, critical to participation in postsecondary education, especially for minority students. Yet, as traditionally taught, first-year algebra courses have been characterized as an unmitigated disaster for most students. There have been many shifts in the algebra curriculum in schools within recent years. Some of these have been successful first steps in increasing enrollment in algebra and in broadening the scope of the algebra curriculum. Others have compounded existing problems. Algebra is not yet conceived of as a K-14 subject. Issues of opportunity and equity persist. Because there is no one answer to the dilemma of how to deal with algebra, making progress requires sustained dialogue, experimentation, reflection, and communication of ideas and practices at both the local and national levels. As an initial step in moving from national-level dialogue and speculations to concerted local and state level work on the role of algebra in the curriculum, the MSEB and the NCTM co-sponsored a national symposium, "The Nature and Role of Algebra in the K-14 Curriculum," on May 27 and 28, 1997, at the National Academy of Sciences in Washington, D.C.
