Download or read book Principles to Actions written by National Council of Teachers of Mathematics and published by National Council of Teachers of Mathematics, Incorporated. This book was released on 2014-02 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text offers guidance to teachers, mathematics coaches, administrators, parents, and policymakers. This book: provides a research-based description of eight essential mathematics teaching practices ; describes the conditions, structures, and policies that must support the teaching practices ; builds on NCTM's Principles and Standards for School Mathematics and supports implementation of the Common Core State Standards for Mathematics to attain much higher levels of mathematics achievement for all students ; identifies obstacles, unproductive and productive beliefs, and key actions that must be understood, acknowledged, and addressed by all stakeholders ; encourages teachers of mathematics to engage students in mathematical thinking, reasoning, and sense making to significantly strengthen teaching and learning.

Download or read book A Family s Guide written by Amy Mirra and published by . This book was released on 2004-01-01 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Family members play an important role in their children's attitudes toward, and success with, mathematics. This award-winning guide summarises what today's mathematics classroom is like, offers tips on how family members can help their children have a positive attitude and enjoy mathematics and presents practical ways to discuss and do maths at home together during everyday situations. Ideas are presented from the elementary and prekindergarten years all the way through high school. The guide is a great resource for family members or teachers and administrators who want ideas to share with family members during events such as Parent Teacher or Family Maths Nights. Reproducible take-home pages addressing questions commonly asked by family members are also included and can be used by teachers and administrators who want to send information home to family members.

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.

Download or read book Helping Children Learn Mathematics written by National Research Council and published by National Academies Press. This book was released on 2002-07-31 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.

Download or read book Early Algebra written by Carolyn Kieran and published by Springer. This book was released on 2016-07-11 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: This survey of the state of the art on research in early algebra traces the evolution of a relatively new field of research and teaching practice. With its focus on the younger student, aged from about 6 years up to 12 years, this volume reveals the nature of the research that has been carried out in early algebra and how it has shaped the growth of the field. The survey, in presenting examples drawn from the steadily growing research base, highlights both the nature of algebraic thinking and the ways in which this thinking is being developed in the primary and early middle school student. Mathematical relations, patterns, and arithmetical structures lie at the heart of early algebraic activity, with processes such as noticing, conjecturing, generalizing, representing, justifying, and communicating being central to students’ engagement.

Download or read book Open Middle Math written by Robert Kaplinsky and published by Taylor & Francis. This book was released on 2023-10-10 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an amazing resource for teachers who are struggling to help students develop both procedural fluency and conceptual understanding.. --Dr. Margaret (Peg) Smith, co-author of5 Practices for Orchestrating Productive Mathematical Discussions Robert Kaplinsky, the co-creator of Open Middle math problems, brings hisnew class of tasks designed to stimulate deeper thinking and lively discussion among middle and high school students in Open Middle Math: Problems That Unlock Student Thinking, Grades 6-12. The problems are characterized by a closed beginning,- meaning all students start with the same initial problem, and a closed end,- meaning there is only one correct or optimal answer. The key is that the middle is open- in the sense that there are multiple ways to approach and ultimately solve the problem. These tasks have proven enormously popular with teachers looking to assess and deepen student understanding, build student stamina, and energize their classrooms. Professional Learning Resource for Teachers: Open Middle Math is an indispensable resource for educators interested in teaching student-centered mathematics in middle and high schools consistent with the national and state standards. Sample Problems at Each Grade: The book demonstrates the Open Middle concept with sample problems ranging from dividing fractions at 6th grade to algebra, trigonometry, and calculus. Teaching Tips for Student-Centered Math Classrooms: Kaplinsky shares guidance on choosing problems, designing your own math problems, and teaching for multiple purposes, including formative assessment, identifying misconceptions, procedural fluency, and conceptual understanding. Adaptable and Accessible Math: The tasks can be solved using various strategies at different levels of sophistication, which means all students can access the problems and participate in the conversation. Open Middle Math will help math teachers transform the 6th -12th grade classroom into an environment focused on problem solving, student dialogue, and critical thinking.

Download or read book Big Ideas Math written by Ron Larson and published by . This book was released on 2018 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book Second Handbook of Research on Mathematics Teaching and Learning written by Frank K. Lester and published by IAP. This book was released on 2007-02-01 with total page 1380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The audience remains much the same as for the 1992 Handbook, namely, mathematics education researchers and other scholars conducting work in mathematics education. This group includes college and university faculty, graduate students, investigators in research and development centers, and staff members at federal, state, and local agencies that conduct and use research within the discipline of mathematics. The intent of the authors of this volume is to provide useful perspectives as well as pertinent information for conducting investigations that are informed by previous work. The Handbook should also be a useful textbook for graduate research seminars. In addition to the audience mentioned above, the present Handbook contains chapters that should be relevant to four other groups: teacher educators, curriculum developers, state and national policy makers, and test developers and others involved with assessment. Taken as a whole, the chapters reflects the mathematics education research community's willingness to accept the challenge of helping the public understand what mathematics education research is all about and what the relevance of their research fi ndings might be for those outside their immediate community.

Download or read book Unpacking Fractions written by Monica Neagoy and published by ASCD. This book was released on 2017-03-10 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: For years, the teaching and learning of fractions has been associated with rote memorization. But this mechanical approach to instruction—which strips students of an ability to reason or make sense of math—has resulted in a failure of understanding. Author Monica Neagoy, drawing on decades of research studies, evidence from teacher practice, and 25 years of experience working around the world with teachers, students, and parents, addresses seven big ideas in the teaching and learning of fractions in grades 2–6. Each idea is supported by a vignette from a real classroom, common misconceptions, a thorough unpacking of productive mathematical thinking, and several multistep and thought-provoking problems for teachers to explore. She offers three fundamental reasons why it’s imperative for us to take a closer look at how we teach fractions: 1. Fractions play a key role in students’ feelings about mathematics. 2. Fractions are fundamental to school math and daily life. 3. Fractions are foundational to success in algebra. While a solid grounding in algebra is necessary for a STEM career, the worthy goal of “algebra for all” will not be possible until “fractions for all” is a reality. Unpacking Fractions provides teachers with concrete strategies for achieving that reality—in short, helping all students gain the knowledge they need to feel at ease with fractions.

Download or read book Silent Voices written by Adam J. Berinsky and published by Princeton University Press. This book was released on 2013-12-03 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past century, opinion polls have come to pervade American politics. Despite their shortcomings, the notion prevails that polls broadly represent public sentiment. But do they? In Silent Voices, Adam Berinsky presents a provocative argument that the very process of collecting information on public preferences through surveys may bias our picture of those preferences. In particular, he focuses on the many respondents who say they "don't know" when asked for their views on the political issues of the day. Using opinion poll data collected over the past forty years, Berinsky takes an increasingly technical area of research--public opinion--and synthesizes recent findings in a coherent and accessible manner while building on this with his own findings. He moves from an in-depth treatment of how citizens approach the survey interview, to a discussion of how individuals come to form and then to express opinions on political matters in the context of such an interview, to an examination of public opinion in three broad policy areas--race, social welfare, and war. He concludes that "don't know" responses are often the result of a systematic process that serves to exclude particular interests from the realm of recognized public opinion. Thus surveys may then echo the inegalitarian shortcomings of other forms of political participation and even introduce new problems altogether.

Download or read book Math Exchanges written by Kassia Omohundro Wedekind and published by Stenhouse Publishers. This book was released on 2011 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditionally, small-group math instruction has been used as a format for reaching children who struggle to understand. Math coach Kassia Omohundro Wedekind uses small-group instruction as the centerpiece of her math workshop approach, engaging all students in rigorous "math exchanges." The key characteristics of these mathematical conversations are that they are: 1) short, focused sessions that bring all mathematical minds together, 2) responsive to the needs of the specific group of mathematicians, and 3) designed for meaningful, guided reflection. As in reading and writing workshop, students in math workshop become self-directed and independent while participating in a classroom community of learners. Through the math exchanges, students focus on number sense and the big ideas of mathematics. Teachers guide the conversations with small groups of students, mediating talk and thinking as students share problem-solving strategies, discuss how math works, and move toward more effective and efficient approaches and greater mathematical understanding. Although grounded in theory and research, Math Exchanges: Guiding Young Mathematicians in Small Group Meetings is written for practicing teachers and answers such questions as the following: How can I use a math workshop approach and follow a certain textbook or set of standards? How should I form small groups? How often should I meet with small groups? What should I focus on in small groups? How can I tell if my groups are making progress? What do small-group math exchanges look like, sound like, and feel like?

Download or read book International Handbook of Mathematics Teacher Education Volume 2 written by and published by BRILL. This book was released on 2019-12-16 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition of the International Handbook of Mathematics Teacher Education builds on and extends the topics/ideas in the first edition while maintaining the themes for each of the volumes. Collectively, the authors look back beyond and within the last 10 years to establish the state-of-the-art and continuing and new trends in mathematics teacher and mathematics teacher educator education, and look forward regarding possible avenues for teachers, teacher educators, researchers, and policy makers to consider to enhance and/or further investigate mathematics teacher and teacher educator learning and practice, in particular. The volume editors provide introductions to each volume that highlight the subthemes used to group related chapters, which offer meaningful lenses to see important connections within and across chapters. Readers can also use these subthemes to make connections across the four volumes, which, although presented separately, include topics that have relevance across them since they are all situated in the common focus regarding mathematics teachers. Volume 2, Tools and Processes in Mathematics Teacher Education, describes and analyze various promising tools and processes, from different perspectives, aimed at facilitating the mathematics teacher learning and development. It provides insights of how mathematics teacher educators think about and approach their work with teachers. Thus, as the second volume in the series, it broadens our understanding of the mathematics teacher and their learning and teaching.

Download or read book Math Running Records in Action written by Nicki Newton and published by Routledge. This book was released on 2016-06-17 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this new book from popular consultant and bestselling author Dr. Nicki Newton, you’ll discover how to use Math Running Records to assess students’ basic fact fluency and increase student achievement. Like a GPS, Math Running Records pinpoint exactly where students are in their understanding of basic math facts and then outline the next steps toward comprehensive fluency. This practical book introduces a research-based framework to assess students’ thinking and move them toward becoming confident, proficient, flexible mathematicians with a robust sense of numbers. Topics include: Learning how often to administer Math Running Records and how to strategically introduce them into your existing curriculum; Analyzing, and interpreting Math Running Records for addition, subtraction, multiplication, and division; Using the data gathered from Math Running Records to implement evidence-based, research-driven instruction. Evaluating students’ speed, accuracy, flexibility, and efficiency to help them attain computational fluency; Each chapter offers a variety of charts and tools that you can use in the classroom immediately, and the strategies can easily be adapted for students at all levels of math fluency across grades K-8. Videos of sample running records are also available for download at https://guidedmath.wordpress.com/math-running-records-videos. Blackline masters are available on the Running Records Dropbox at https://bit.ly/3gnggIq

Download or read book The Pythagorean Proposition written by Elisha Scott Loomis and published by . This book was released on 1927 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Learning to Think Spatially written by National Research Council and published by National Academies Press. This book was released on 2005-02-03 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learning to Think Spatially examines how spatial thinking might be incorporated into existing standards-based instruction across the school curriculum. Spatial thinking must be recognized as a fundamental part of Kâ€"12 education and as an integrator and a facilitator for problem solving across the curriculum. With advances in computing technologies and the increasing availability of geospatial data, spatial thinking will play a significant role in the information-based economy of the twenty-first century. Using appropriately designed support systems tailored to the Kâ€"12 context, spatial thinking can be taught formally to all students. A geographic information system (GIS) offers one example of a high-technology support system that can enable students and teachers to practice and apply spatial thinking in many areas of the curriculum.

Download or read book Compendium for Research in Mathematics Education written by Jinfa Cai and published by National Council of Teachers of English. This book was released on 2017 with total page 1008 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, a comprehensive survey and critical analysis of today's issues in mathematics education, distills research to build knowledge and capacity in the field. The compendium is a valuable new resource that provides the most comprehensive evidence about what is known about research in mathematics education. The 38 chapters present five sections that address research about (1) foundations, (2) methods, (3) mathematical processes and content, (4) students, teachers, and learning environments, and (5) futuristic issues. Each chapter offers a synthesis of research with an eye to the historical development of a research topic and, in particular, historical milestones of the research about the topic.