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Mathematics as a Constructive Activity

Mathematics as a Constructive Activity Author Anne Watson
ISBN-10 9781135630010
Release 2006-04-21
Pages 248
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This book explains and demonstrates the teaching strategy of asking learners to construct their own examples of mathematical objects. The authors show that the creation of examples can involve transforming and reorganizing knowledge and that, although this is usually done by authors and teachers, if the responsibility for making examples is transferred to learners, their knowledge structures can be developed and extended. A multitude of examples to illustrate this is provided, spanning primary, secondary, and college levels. Readers are invited to learn from their own past experience augmented by tasks provided in the book, and are given direct experience of constructing examples through a collection of many tasks at many levels. Classroom stories show the practicalities of introducing such shifts in mathematics education. The authors examine how their approach relates to improving the learning of mathematics and raise future research questions. *Based on the authors' and others' theoretical and practical experience, the book includes a combination of exercises for the reader, practical applications for teaching, and solid scholarly grounding. *The ideas presented are generic in nature and thus applicable across every phase of mathematics teaching and learning. *Although the teaching methods offered are ones that engage learners imaginatively, these are also applied to traditional approaches to mathematics education; all tasks offered in the book are within conventional mathematics curriculum content. Mathematics as a Constructive Activity: Learners Generating Examples is intended for mathematics teacher educators, mathematics teachers, curriculum developers, task and test designers, and classroom researchers, and for use as a text in graduate-level mathematics education courses.



Bringing Out the Algebraic Character of Arithmetic

Bringing Out the Algebraic Character of Arithmetic Author Analucia D. Schliemann
ISBN-10 9781136799624
Release 2013-05-13
Pages 160
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First Published in 2006. Routledge is an imprint of Taylor & Francis, an informa company.



The Mathematics that Every Secondary School Math Teacher Needs to Know

The Mathematics that Every Secondary School Math Teacher Needs to Know Author Alan Sultan
ISBN-10 9781135157821
Release 2010-09-13
Pages 760
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What knowledge of mathematics do secondary school math teachers need to facilitate understanding, competency, and interest in mathematics for all of their students? This unique text and resource bridges the gap between the mathematics learned in college and the mathematics taught in secondary schools. Written in an informal, clear, and interactive learner-centered style, it is designed to help pre-service and in-service teachers gain the deep mathematical insight they need to engage their students in learning mathematics in a multifaceted way that is interesting, developmental, connected, deep, understandable, and often, surprising and entertaining. Features include Launch questions at the beginning of each section, Student Learning Opportunities, Questions from the Classroom, and highlighted themes throughout to aid readers in becoming teachers who have great "MATH-N-SIGHT": M Multiple Approaches/Representations A Applications to Real Life T Technology H History N Nature of Mathematics: Reasoning and Proof S Solving Problems I Interlinking Concepts: Connections G Grade Levels H Honing of Mathematical Skills T Typical Errors This text is aligned with the recently released Common Core State Standards, and is ideally suited for a capstone mathematics course in a secondary mathematics certification program. It is also appropriate for any methods or mathematics course for pre- or in-service secondary mathematics teachers, and is a valuable resource for classroom teachers.



The Origins of Mathematical Knowledge in Childhood

The Origins of Mathematical Knowledge in Childhood Author Catherine Sophian
ISBN-10 9781351541749
Release 2017-09-25
Pages 216
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This book examines the origins and development of children's mathematical knowledge. It contrasts the widely held view that counting is the starting point for mathematical development with an alternative comparison-of-quantities position. According to the comparison-of-quantities position, the concept of number builds upon more basic concepts of equality, inequality, and less-than and greater-than relations, which derive from comparisons between unenumerated quantities such as lengths. The concept of number combines these basic comparative concepts with the concept of a unit of measure, which allows one quantity to be described as a multiple of another. Sophian examines these alternative accounts of children's developing mathematical knowledge in the light of research: on children's counting; on their reasoning about continuous quantities such as length and area; on the development of the concept of unit; on additive and multiplicative reasoning; and on knowledge about fractions. In the closing chapters, Sophian draws out the developmental and the educational implications of the research and theory presented. Developmentally, the comparison-of-quantities position undermines the idea that numerical knowledge develops through domain-specific learning mechanisms in that it links numerical development both to physical knowledge about objects, which is the starting point for the concept of unit, and to the acquisition of linguistic number terms. Instructionally, the comparison-of-quantities perspective diverges from the counting-first perspective in that it underscores the continuity between whole-number arithmetic and fraction learning that stems from the importance of the concept of unit for both. Building on this idea, Sophian advances three instructional recommendations: First, instruction about numbers should always be grounded in thinking about quantities and how numbers represent the relations between them; second, instruction in the early years should always be guided by a long-term perspective in which current objectives are shaped by an understanding of their role in the overall course of mathematics learning; and third, instruction should be directly toward promoting the acquisition of the most general mathematical knowledge possible. The Origins of Mathematical Knowledge in Childhood is intended for researchers, professionals, and graduate students in developmental psychology, educational psychology, and mathematics education, and as a supplementary text for advanced undergraduate courses in cognitive development, educational psychology, and mathematics education.



Algebra in the early grades

Algebra in the early grades Author James J. Kaput
ISBN-10 UOM:39015074229801
Release 2008
Pages 526
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This volume is the first to offer a comprehensive, research-based, multi-faceted look at issues in early algebra. In recent years, the National Council for Teachers of Mathematics has recommended that algebra become a strand flowing throughout the K-12 curriculum, and the 2003 RAND Mathematics Study Panel has recommended that algebra be "the initial topical choice for focused and coordinated research and development [in K-12 mathematics]." The book provides a rationale for a stronger and more sustained approach to algebra in school, as well as concrete examples of how algebraic reasoning may be developed in the early grades. It is organized around three themes: *The Nature of Early Algebra *Students' Capacity for Algebraic Thinking *Issues of Implementation: Taking Early Algebra to the Classrooms The contributors to this landmark volume have been at the forefront of an effort to integrate algebra into the existing early grades mathematics curriculum. They include scholars who have been developing the conceptual foundations for such changes as well as researchers and developers who have led empirical investigations in school settings. Algebra in the Early Gradesaims to bridge the worlds of research, practice, design, and theory for educators, researchers, students, policy makers, and curriculum developers in mathematics education.



Journal for Research in Mathematics Education

Journal for Research in Mathematics Education Author
ISBN-10 STANFORD:36105131501897
Release 2009
Pages
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Journal for Research in Mathematics Education has been writing in one form or another for most of life. You can find so many inspiration from Journal for Research in Mathematics Education also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Journal for Research in Mathematics Education book for free.



Raising Achievement in Secondary Mathematics

Raising Achievement in Secondary Mathematics Author Anne Watson
ISBN-10 033521861X
Release 2006
Pages 191
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A guide to teaching lower attaining students in secondary mathematics offers an alternative view of attainment and capability, arguing that teaching should be based on a learner's proficiency, rather than on knowledge deficits.



Amongst Mathematicians

Amongst Mathematicians Author Elena Nardi
ISBN-10 9780387371436
Release 2007-11-19
Pages 341
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This book offers a unique perspective on ways in which mathematicians: perceive their students' learning; teach; reflect on their teaching practice. Elena Nardi achieves this by employing two fictional, yet entirely data-grounded, characters to create a conversation on these important issues. The construction of these characters is based on large bodies of data including intense focused group interviews with mathematicians and extensive analyses of students' written work, collected and analyzed over a substantial period.



Making the Connection

Making the Connection Author Marilyn Paula Carlson
ISBN-10 0883851830
Release 2008
Pages 319
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The chapters in this volume convey insights from mathematics education research that have direct implications for anyone interested in improving teaching and learning in undergraduate mathematics. This synthesis of research on learning and teaching mathematics provides relevant information for any math department or individual faculty member who is working to improve introductory proof courses, the longitudinal coherence of precalculus through differential equations, students' mathematical thinking and problem-solving abilities, and students' understanding of fundamental ideas such as variable and rate of change. Other chapters include information about programs that have been successful in supporting students' continued study of mathematics. The authors provide many examples and ideas to help the reader infuse the knowledge from mathematics education research into mathematics teaching practice. University mathematicians and community college faculty spend much of their time engaged in work to improve their teaching. Frequently, they are left to their own experiences and informal conversations with colleagues to develop new approaches to support student learning and their continuation in mathematics. Over the past 30 years, research in undergraduate mathematics education has produced knowledge about the development of mathematical understandings and models for supporting students' mathematical learning. Currently, very little of this knowledge is affecting teaching practice. We hope that this volume will open a meaningful dialogue between researchers and practitioners toward the goal of realizing improvements in undergraduate mathematics curriculum and instruction.



For the Learning of Mathematics

For the Learning of Mathematics Author
ISBN-10 CORNELL:31924099653218
Release 2007
Pages
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For the Learning of Mathematics has been writing in one form or another for most of life. You can find so many inspiration from For the Learning of Mathematics also informative, and entertaining. Click DOWNLOAD or Read Online button to get full For the Learning of Mathematics book for free.



Creating contexts for learning and self authorship

Creating contexts for learning and self authorship Author Marcia B. Baxter Magolda
ISBN-10 0826513433
Release 1999-11-01
Pages 345
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In her thoughtful and innovative new book, Marcia B. Baxter Magolda writes of "bridging the worlds between educator and students." There is perhaps no task more fundamental to effective teaching and learning. All too often a distinct gap develops or cannot be overcome between instructor and student, one that leaves each struggling to understand the other's position. The professional quest for principles of structure and process that can help close this divide is both evolving and unending. This book is intended to help college faculty create conditions in which students learn to construct knowledge in their disciplines and achieve self-authorship. A significant, and often overlooked, dimension mediating learning and self-authorship centers on learners' ways of knowing, or their assumptions about the nature, limits, and certainty of knowledge. A learner who assumes that all knowledge is certain expects to hear answers from an authority figure; in contrast, a learner who views knowledge as relative expects to explore multiple viewpoints. By taking a constructive-developmental approach, Baxter Magolda demonstrates how students' ability to construct knowledge is intertwined with the development of their assumptions about knowledge itself and their role in creating it. She shows how the structure of constructive-developmental teaching hinges on three principles: validating students' ability to know, situating learning in students' experience, and defining learning as teachers and students mutually constructing meaning. Unlike most of the literature on the subject, this book takes abstract pedagogical principles and translates them into practical methods. By observing four semester-length college courses in mathematics, zoology, human development, and education and intensively interviewing students and their instructors, Baxter Magolda provides much-needed, concrete principles that will lead to valuable improvements in the classroom environment. With an enhanced level of understanding of the teaching-learning relationship, professors will be able to teach better, and students will be able to learn better, thus preparing them to meet the demands inherent in adulthood and preparing them to take an active role in creating a better society. Those actively involved in higher education, whether college faculty or students in graduate programs, as well as anyone focused on education in general will find much of interest in this book.



Modelling and Applications in Mathematics Education

Modelling and Applications in Mathematics Education Author Peter L. Galbraith
ISBN-10 0387298223
Release 2007-12-05
Pages 524
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The book aims at showing the state-of-the-art in the field of modeling and applications in mathematics education. This is the first volume to do this. The book deals with the question of how key competencies of applications and modeling at the heart of mathematical literacy may be developed; with the roles that applications and modeling may play in mathematics teaching, making mathematics more relevant for students.



Current Index to Journals in Education

Current Index to Journals in Education Author
ISBN-10 MINN:31951P00746696L
Release 1998-10
Pages
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Current Index to Journals in Education has been writing in one form or another for most of life. You can find so many inspiration from Current Index to Journals in Education also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Current Index to Journals in Education book for free.



Classics In Mathematics Education Research

Classics In Mathematics Education Research Author Thomas P. Carpenter
ISBN-10 0873535650
Release 2004-05-01
Pages 226
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Classics In Mathematics Education Research has been writing in one form or another for most of life. You can find so many inspiration from Classics In Mathematics Education Research also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Classics In Mathematics Education Research book for free.



The Australian Mathematics Teacher

The Australian Mathematics Teacher Author
ISBN-10 UOM:39015053957307
Release 1998
Pages
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The Australian Mathematics Teacher has been writing in one form or another for most of life. You can find so many inspiration from The Australian Mathematics Teacher also informative, and entertaining. Click DOWNLOAD or Read Online button to get full The Australian Mathematics Teacher book for free.



Research in the Schools

Research in the Schools Author
ISBN-10 UVA:X006063040
Release 1996
Pages
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UME Trends

UME Trends Author
ISBN-10 CORNELL:31924074847330
Release 1990
Pages
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UME Trends has been writing in one form or another for most of life. You can find so many inspiration from UME Trends also informative, and entertaining. Click DOWNLOAD or Read Online button to get full UME Trends book for free.