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Author : Ana C. Stephens
Publisher :
ISBN 13 :
Total Pages : 138 pages
Book Rating : 4.:/5 (89 download)
Download or read book Preservice Elementary Teachers' Conceptions of Algebra and Algebraic Equivalence written by Ana C. Stephens and published by . This book was released on 2004 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Rachael Mae Welder
Publisher :
ISBN 13 : 9781109929515
Total Pages : 161 pages
Book Rating : 4.9/5 (295 download)
Download or read book Preservice Elementary Teachers' Mathematical Content Knowledge of Prerequisite Algebra Concepts written by Rachael Mae Welder and published by . This book was released on 2007 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: The effects of an undergraduate mathematics content course for elementary education students on preservice teachers' common and specialized content knowledge of prerequisite algebra concepts was investigated, using a pre-experimental one-group pretest-posttest design. A quantitative, 51-item, multiple-choice instrument, developed specifically to measure both types of content knowledge with respect to prerequisite algebra concepts, was constructed from the Learning Mathematics for Teaching Project's Content Knowledge for Teaching Mathematics Measures question bank. This instrument was administered to all students enrolled in Mathematics for Elementary Teachers I (n = 48), at Montana State University, during the fall semester of 2006.
Author : Jia He
Publisher :
ISBN 13 : 9781339030951
Total Pages : 213 pages
Book Rating : 4.0/5 (39 download)
Download or read book Preservice Elementary Teachers' Conceptions of Mathematical Definitions written by Jia He and published by . This book was released on 2015 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 540 pages
Book Rating : 4.F/5 ( download)
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2005 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Steve Rhine
Publisher : IAP
ISBN 13 : 1641134135
Total Pages : 351 pages
Book Rating : 4.6/5 (411 download)
Download or read book How Students Think When Doing Algebra written by Steve Rhine and published by IAP. This book was released on 2018-11-01 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra is the gateway to college and careers, yet it functions as the eye of the needle because of low pass rates for the middle school/high school course and students’ struggles to understand. We have forty years of research that discusses the ways students think and their cognitive challenges as they engage with algebra. This book is a response to the National Council of Teachers of Mathematics’ (NCTM) call to better link research and practice by capturing what we have learned about students’ algebraic thinking in a way that is usable by teachers as they prepare lessons or reflect on their experiences in the classroom. Through a Fund for the Improvement of Post-Secondary Education (FIPSE) grant, 17 teachers and mathematics educators read through the past 40 years of research on students’ algebraic thinking to capture what might be useful information for teachers to know—over 1000 articles altogether. The resulting five domains addressed in the book (Variables & Expressions, Algebraic Relations, Analysis of Change, Patterns & Functions, and Modeling & Word Problems) are closely tied to CCSS topics. Over time, veteran math teachers develop extensive knowledge of how students engage with algebraic concepts—their misconceptions, ways of thinking, and when and how they are challenged to understand—and use that knowledge to anticipate students’ struggles with particular lessons and plan accordingly. Veteran teachers learn to evaluate whether an incorrect response is a simple error or the symptom of a faulty or naïve understanding of a concept. Novice teachers, on the other hand, lack the experience to anticipate important moments in the learning of their students. They often struggle to make sense of what students say in the classroom and determine whether the response is useful or can further discussion (Leatham, Stockero, Peterson, & Van Zoest 2011; Peterson & Leatham, 2009). The purpose of this book is to accelerate early career teachers’ “experience” with how students think when doing algebra in middle or high school as well as to supplement veteran teachers’ knowledge of content and students. The research that this book is based upon can provide teachers with insight into the nature of a student’s struggles with particular algebraic ideas—to help teachers identify patterns that imply underlying thinking. Our book, How Students Think When Doing Algebra, is not intended to be a “how to” book for teachers. Instead, it is intended to orient new teachers to the ways students think and be a book that teachers at all points in their career continually pull of the shelf when they wonder, “how might my students struggle with this algebraic concept I am about to teach?” The primary audience for this book is early career mathematics teachers who don’t have extensive experience working with students engaged in mathematics. However, the book can also be useful to veteran teachers to supplement their knowledge and is an ideal resource for mathematics educators who are preparing preservice teachers.
Author : Rosamund Sutherland
Publisher : Springer Science & Business Media
ISBN 13 : 0792364627
Total Pages : 277 pages
Book Rating : 4.7/5 (923 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 2001 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. The contributions represent 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 emphasises the situated nature of algebraic activity as opposed to being concerned with identifying students' conceptions in isolation from problem-solving activity. The chapters emerged from a working group of the International Group for the Psychology of Mathematics Education. The authors are drawn from an international community and the work highlights the differences in school algebra around the world. The group invited Nicolas Balacheff to write a provocative postscript and he suggests that `there is no possible entrance to the world of algebra without a strong push or guidance from the teacher, because there is no natural passage from the problématique accessible from the child's world to the mathematical problématique'.
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 : Marian Small
Publisher : Teachers College Press
ISBN 13 : 0807773093
Total Pages : 177 pages
Book Rating : 4.8/5 (77 download)
Download or read book Uncomplicating Algebra to Meet Common Core Standards in Math, K-8 written by Marian Small and published by Teachers College Press. This book was released on 2014-12-04 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the second book in the Uncomplicating Mathematics Series, professional developer Marian Small shows teachers how to uncomplicate the teaching of algebra by focusing on the most important ideas that students need to grasp. Organized by grade level around the Common Core State Standards for Mathematics, Small shares approaches that will lead to a deeper and richer understanding of algebra for both teachers and students. The book opens with a clear discussion of algebraic thinking and current requirements for algebraic understanding within standards-based learning environments. The book then launches with Kindergarten, where the first relevant standard is found in the operations and algebraic thinking domain, and ends with Grade 8, where the focus is on working with linear equations and functions. In each section the relevant standard is presented, followed by a discussion of important underlying ideas associated with that standard, as well as thoughtful, concept-based questions that can be used for classroom instruction, practice, or assessment. Underlying ideas include: Background to the mathematics of each relevant standard. Suggestions for appropriate representations for specific mathematical ideas. Suggestions for explaining ideas to students. Cautions about misconceptions or situations to avoid. The Common Core State Standards for Mathematics challenges students to become mathematical thinkers, not just mathematical “doers.” This resource will be invaluable for pre- and inservice teachers as they prepare themselves to understand and teach algebra with a deep level of understanding. “Uncomplicating Algebra is an excellent resource for teachers responsible for the mathematical education of K–8 students. It is also a valuable tool for the training of preservice teachers of elementary and middle school mathematics.” —Carole Greenes, associate vice provost for STEM education, director of the Practice Research and Innovation in Mathematics Education (PRIME) Center, professor of mathematics education, Arizona State University “The current climate in North America places a major emphasis on standards, including the Common Core State Standards for Mathematics in the U.S. In many cases, teachers are being asked to teach content with which they themselves struggle. In this book, Dr. Small masterfully breaks down the big ideas of algebraic thinking to assist teachers, math coaches, and preservice teachers—helping them to deepen their own understanding of the mathematics they teach. She describes common error patterns and examines algebraic reasoning from a developmental viewpoint, connecting the dots from kindergarten through grade 8. The book is clearly written, loaded with specific examples, and very timely. I recommend it strongly as a ‘must-read’ for all who are seeking to broaden their understanding of algebra and how to effectively teach this important content area to children.” —Daniel J. Brahier, director, Science and Math Education in ACTION, professor of mathematics education, School of Teaching and Learning, Bowling Green State University
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.
Author : Kaye Stacey
Publisher : Springer Science & Business Media
ISBN 13 : 1402081316
Total Pages : 382 pages
Book Rating : 4.4/5 (2 download)
Download or read book The Future of the Teaching and Learning of Algebra written by Kaye Stacey and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kaye Stacey‚ Helen Chick‚ and Margaret Kendal The University of Melbourne‚ Australia Abstract: This section reports on the organisation‚ procedures‚ and publications of the ICMI Study‚ The Future of the Teaching and Learning of Algebra. Key words: Study Conference‚ organisation‚ procedures‚ publications The International Commission on Mathematical Instruction (ICMI) has‚ since the 1980s‚ conducted a series of studies into topics of particular significance to the theory and practice of contemporary mathematics education. Each ICMI Study involves an international seminar‚ the “Study Conference”‚ and culminates in a published volume intended to promote and assist discussion and action at the international‚ national‚ regional‚ and institutional levels. The ICMI Study running from 2000 to 2004 was on The Future of the Teaching and Learning of Algebra‚ and its Study Conference was held at The University of Melbourne‚ Australia fromDecember to 2001. It was the first study held in the Southern Hemisphere. There are several reasons why the future of the teaching and learning of algebra was a timely focus at the beginning of the twenty first century. The strong research base developed over recent decades enabled us to take stock of what has been achieved and also to look forward to what should be done and what might be achieved in the future. In addition‚ trends evident over recent years have intensified. Those particularly affecting school mathematics are the “massification” of education—continuing in some countries whilst beginning in others—and the advance of technology.
Author : National Research Council
Publisher : National Academies Press
ISBN 13 : 0309061474
Total Pages : 206 pages
Book Rating : 4.3/5 (9 download)
Download or read book The Nature and Role of Algebra in the K-14 Curriculum written by National Research Council and published by National Academies Press. This book was released on 1998-10-23 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.
Author : Judith A. Muschla
Publisher : John Wiley & Sons
ISBN 13 : 111810613X
Total Pages : 338 pages
Book Rating : 4.1/5 (181 download)
Download or read book The Algebra Teacher's Guide to Reteaching Essential Concepts and Skills written by Judith A. Muschla and published by John Wiley & Sons. This book was released on 2011-11-15 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Easy to apply lessons for reteaching difficult algebra concepts Many students have trouble grasping algebra. In this book, bestselling authors Judith, Gary, and Erin Muschla offer help for math teachers who must instruct their students (even those who are struggling) about the complexities of algebra. In simple terms, the authors outline 150 classroom-tested lessons, focused on those concepts often most difficult to understand, in terms that are designed to help all students unravel the mysteries of algebra. Also included are reproducible worksheets that will assist teachers in reviewing and reinforcing algebra concepts and key skills. Filled with classroom-ready algebra lessons designed for students at all levels The 150 mini-lessons can be tailored to a whole class, small groups, or individual students who are having trouble This practical, hands-on resource will help ensure that students really get the algebra they are learning
Author : Audrey C. Rule
Publisher :
ISBN 13 :
Total Pages : 15 pages
Book Rating : 4.:/5 (16 download)
Download or read book Algebra Rules Object Boxes as an Authentic Assessment Task of Preservice Elementary Teacher Learning in a Mathematics Methods Course written by Audrey C. Rule and published by . This book was released on 2007 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this study was to describe elementary preservice teachers' difficulties with understanding algebraic generalizations that were set in an authentic context. Fifty-eight preservice teachers enrolled in an elementary mathematics methods course participated in the study. These students explored and practiced with authentic, hands-on materials called "object boxes," then created sets of their own object box materials. Each algebra rules object box contained materials to illustrate and describe four different algebraic generalizations, or "rules." The variables "n" and "z" were used in each of the generalizations. For each generalization, there was a set of objects attached to a piece of mat board that showed three cases of the generalization for different values of "n." Two sets of cards accompanied these objects, giving word problems, defining variables, stating equations, and explaining the algebraic generalizations. Students matched word problems to the object sets, defined variables and checked their work, then wrote algebraic generalizations for the object sets and used the reverse sides of the equation cards to check their work. Projects were graded with a rubric. Students were then surveyed about their difficulties. Results of the analysis showed that students were able to make an assortment of authentic materials in a variety of contexts and enjoyed the creative aspects of the project, but found the algebraic content challenging. The most common mathematical difficulties were being able to define the variable, and identify the pattern. Examples of effective student materials are provided. (Contains 4 tables and 16 figures.) [This paper was presented at the: (1) Annual Conference of the New York State Association of Teacher Educators (NYSATE) (Saratoga Springs, New York, April 28) [Conference presentation title: Preservice Elementary Candidate Assessment of Algebraic Understanding for Accreditation]; and (2) Annual Conference of the Association of Mathematics Teachers of New York State (AMTNYS) (Saratoga Springs, New York, October 26-28) [Conference presentation title: Using Hands-On Materials to Write Algebraic Generalizations (Grades 5-8)].].
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 : Carole Anne Hayata
Publisher :
ISBN 13 :
Total Pages : 144 pages
Book Rating : 4.:/5 (855 download)
Download or read book The Development of Algebraic Reasoning in Undergraduate Elementary Preservice Teachers written by Carole Anne Hayata and published by . This book was released on 2012 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Lyn D. English
Publisher : Routledge
ISBN 13 : 1135192839
Total Pages : 830 pages
Book Rating : 4.1/5 (351 download)
Download or read book Handbook of International Research in Mathematics Education written by Lyn D. English and published by Routledge. This book was released on 2010-04-02 with total page 830 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition continues the mission of bringing together important new mathematics education research that makes a difference in both theory and practice. It updates and extends the Handbook’s original key themes and issues for international research in mathematics education for the 21st century, namely: priorities in international mathematics education research lifelong democratic access to powerful mathematical ideas advances in research methodologies influences of advanced technologies. Each of these themes is examined in terms of learners, teachers, and learning contexts, with theory development being an important component of all these aspects. This edition also examines other catalysts that have gained increased import in recent years including a stronger focus on the teacher and teacher practice, a renewed interest in theory development, an increased focus on the mathematics needed in work place settings, and a proliferation of research designs and methodologies that have provided unprecedented opportunities for investigating (and ultimately improving) mathematical teaching and learning. This edition includes ten totally new chapters; all other chapters are thoroughly revised and updated.
Author : Thomas P. Carpenter
Publisher : Heinemann Educational Books
ISBN 13 :
Total Pages : 166 pages
Book Rating : 4.F/5 ( download)
Download or read book Thinking Mathematically written by Thomas P. Carpenter and published by Heinemann Educational Books. This book was released on 2003 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the authors reveal how children's developing knowledge of the powerful unifying ideas of mathematics can deepen their understanding of arithmetic
