The Role Of Mental Computation And Estimation In Elementary School

Author : Peter McCarthy
Publisher : Unknown
Page : 460 pages
File Size : 41,9 Mb
Release : 2007
Category : Mental arithmetic
ISBN : 049427929X

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The Role of Mental Computation and Estimation in Elementary School by Peter McCarthy Pdf

The study sought to investigate how Grade 3 students from two separate schools learned mathematics. The study explores the role of mental computation when students are engaged in sharing their invented strategies. I observed students sharing ideas and teachers implementing mental computation lessons over fifteen sessions. Interviews with students and teachers, copies of students' journal on mental math strategies were used to collect additional data. The findings were organized around descriptive moments; as I described how students were absorbed in mathematical conversation when they were invited to think mathematically and also encouraged to use their own strategies. I drew on the epistemology of constructivism in problem solving, to understand how students develop conceptual understanding of mathematics when given the opportunity to explain their own strategies. Students' cooperation in sharing their inventions was observed in class and group discussions, as well as in pairs with classmates. It was at these levels where the students: (a) eagerly invented numerous strategies for solving addition, subtraction and multiplication problems; (b) made sound arguments in support of their ideas when discussing problem solving strategies; (c) were cooperative in presenting their strategies; (d) learned from each other by listening to one another's explanations; (e) learned from correcting their errors; and (f) used their cognitive backgrounds as useful heuristics in their discussions. The students expressed their satisfaction and enjoyment during their collaborative learning and social interactions. The teachers used questioning strategies, among other teaching principles, to help students to complete their presentations. These included leading questions, probing and follow-ups, checklisting and student-specific questioning strategies. The study informs teachers about how mental mathematics lessons were implemented in the two Grade 3 classrooms to help the students understand mathematics. Teachers should be given courses, workshops and supportive programs on implementing mental computation lessons. This will give teachers the necessary experiences to increase their understanding of how students improve their understanding of mathematics when they are encouraged to share their inventions in class. The study provides a useful template for future studies in all subject areas of mathematics related to mental computation and estimation at all grade levels.

Author : Charalampos Lemonidis
Publisher : Routledge
Page : 291 pages
File Size : 55,6 Mb
Release : 2015-12-01
Category : Education
ISBN : 9781317382843

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Mental Computation and Estimation by Charalampos Lemonidis Pdf

Mental calculations and estimations are basic, everyday skills that are essential for real-life arithmetic operations and number sense. This book presents a much needed overview and analysis of mental computation and estimation, drawing on contemporary research and empirical studies that were conducted on students, teachers and adults to cover all aspects of this complex field. Mental Computation and Estimation analyses the implications that are involved in the research, teaching and learning of mathematics and delivers effective practices that will enhance everyday learning for students. Focusing on a range of international research and studies from the School of Nature and Life Mathematics in Greece, it answers a number of important questions including: What mental calculations and estimations are, why they are important and what other mathematical concepts and cognitive behaviors are they related to? What strategies are used on mental additions, subtractions, multiplications and divisions and how are multiplication tables learned? What are the new trends in the teaching of mental calculation and estimation? An invaluable resource for all those involved in the practice and research of mathematics education, Mental Computation and Estimation will also be a useful tool for researchers, policy makers and developers of educational programs.

Author : Charalampos Lemonidis
Publisher : Routledge
Page : 242 pages
File Size : 41,7 Mb
Release : 2015-12-01
Category : Education
ISBN : 9781317382850

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Mental Computation and Estimation by Charalampos Lemonidis Pdf

Mental calculations and estimations are basic, everyday skills that are essential for real-life arithmetic operations and number sense. This book presents a much needed overview and analysis of mental computation and estimation, drawing on contemporary research and empirical studies that were conducted on students, teachers and adults to cover all aspects of this complex field. Mental Computation and Estimation analyses the implications that are involved in the research, teaching and learning of mathematics and delivers effective practices that will enhance everyday learning for students. Focusing on a range of international research and studies from the School of Nature and Life Mathematics in Greece, it answers a number of important questions including: What mental calculations and estimations are, why they are important and what other mathematical concepts and cognitive behaviors are they related to? What strategies are used on mental additions, subtractions, multiplications and divisions and how are multiplication tables learned? What are the new trends in the teaching of mental calculation and estimation? An invaluable resource for all those involved in the practice and research of mathematics education, Mental Computation and Estimation will also be a useful tool for researchers, policy makers and developers of educational programs.

Author : Anonim
Publisher : Unknown
Page : 264 pages
File Size : 53,5 Mb
Release : 1986
Category : Estimation theory
ISBN : UOM:39015036972522

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Estimation and Mental Computation by Anonim Pdf

Author : Harold L. Schoen
Publisher : Unknown
Page : 266 pages
File Size : 41,8 Mb
Release : 1986
Category : Mathematics
ISBN : UOM:39015011608828

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Estimation and Mental Computation by Harold L. Schoen Pdf

Author : Robert Reys,Mary Lindquist,Diana V. Lambdin,Nancy L. Smith
Publisher : John Wiley & Sons
Page : 432 pages
File Size : 41,9 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 : Shannon W. Dingman,Laura B. Kent,Kim K. McComas,Cynthia C. Orona
Publisher : BRILL
Page : 140 pages
File Size : 47,6 Mb
Release : 2019-08-26
Category : Education
ISBN : 9789004412651

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The Language of Mathematics Education by Shannon W. Dingman,Laura B. Kent,Kim K. McComas,Cynthia C. Orona Pdf

The Language of Mathematics Education: An Expanded Glossary of Key Terms and Concepts in Mathematics Teaching and Learning offers mathematics teachers, mathematics education professionals and students a valuable resource in which common terms are defined and expounded upon in short essay format. The shared vocabulary and terminology relating to mathematics teaching and learning, and used by mathematics educators is an essential component of work conducted in the field. The authors provide an overview of more than 100 terms commonly used in mathematics teaching and learning. Each term is defined and is followed by a short overview of the concept under discussion that includes several bibliographic references the reader can use for further investigation. In addition to terms specific to the domain of mathematics education, select key terms common across all fields of education (e.g., curriculum, epistemology, metacognition) are included. The goal for this book is to serve as a resource for those entering the field as they navigate the language and terminology of mathematics education and as an asset for more established professionals who wish to gain additional insights into these ideas.

Author : John A. Van de Walle
Publisher : Longman Publishing Group
Page : 550 pages
File Size : 44,6 Mb
Release : 1994
Category : Mathematics
ISBN : UCSC:32106018113511

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Elementary School Mathematics by John A. Van de Walle Pdf

Elementary School Mathematics: Teaching Developmentally, Second Edition, provides detailed, comprehensive coverage of the teaching of mathematics in grades K-8. Firmly grounded in the NCTM Standards, the text develops a constructivist/developmental approach to learning mathematics that focuses on the nature of mathematical concepts and the manner in which children construct mathematical ideas. It aims to help teachers reconceptualize mathematics as a problem-solving endeavor not as a mastery of rules and procedures. An accessible synthesis of viewpoints and current research, this highly praised text includes topics ranging from the development of basic fact mastery to the important development of "number sense"--All the while encouraging teachers to consider the construction of mathematics from the child's perspective. In-depth treatment of curriculum content teaching, combined with hundreds of teaching activities aimed at conceptual development, makes Elementary School Mathematics a practical teacher's resource as well as a college text. Elementary School Mathematics: Teaching Developmentally, Second Edition, features: greater emphasis on the NCTM Curriculum Standards and the Professional Teaching Standards as the leading forces in mathematics education; a new chapter on mathematics as a "science of pattern and order"; a completely rewritten chapter on alternative assessment; expanded and improved problem-solving examples; enhanced coverage of grades 7 and 8; even more black-line masters with directions for making other useful materials; and an Instructor's Manual with instructional suggestions, activities for group homework, practicum ideas, and essay questions.

Author : National Science Foundation (U.S.). Directorate for Science and Engineering Education
Publisher : Unknown
Page : 534 pages
File Size : 52,8 Mb
Release : 1987
Category : Engineering
ISBN : MINN:30000011055807

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Directory of Awards by National Science Foundation (U.S.). Directorate for Science and Engineering Education Pdf

Author : Alistair McIntosh,Shelley Louise Dole
Publisher : Unknown
Page : 44 pages
File Size : 45,6 Mb
Release : 2004
Category : Arithmetic
ISBN : 192086525X

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Mental Computation by Alistair McIntosh,Shelley Louise Dole Pdf

Author : Alan Bishop,M.A. (Ken) Clements,Christine Keitel-Kreidt,Jeremy Kilpatrick,Colette Laborde
Publisher : Springer Science & Business Media
Page : 1336 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Education
ISBN : 9789400914650

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International Handbook of Mathematics Education by Alan Bishop,M.A. (Ken) Clements,Christine Keitel-Kreidt,Jeremy Kilpatrick,Colette Laborde Pdf

ALAN J. BISHOP Monash University, Clayton, Victoria, Australia RATIONALE Mathematics Education is becoming a well-documented field with many books, journals and international conferences focusing on a variety of aspects relating to theory, research and practice. That documentation also reflects the fact that the field has expanded enormously in the last twenty years. At the 8th International Congress on Mathematics Education (ICME) in Seville, Spain, for example, there were 26 specialist Working Groups and 26 special ist Topic Groups, as well as a host of other group activities. In 1950 the 'Commission Internationale pour I 'Etude et l' Amelioration de l'Enseignement des Mathematiques' (CIEAEM) was formed and twenty years ago another active group, the 'International Group for the Psychology of Mathematics Education' (PME), began at the third ICME at Karlsruhe in 1976. Since then several other specialist groups have been formed, and are also active through regular conferences and publications, as documented in Edward Jacobsen's Chapter 34 in this volume.

Author : National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Mathematics Learning Study Committee
Publisher : National Academies Press
Page : 52 pages
File Size : 44,8 Mb
Release : 2002-07-31
Category : Education
ISBN : 9780309131988

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Helping Children Learn Mathematics by National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Mathematics Learning Study Committee Pdf

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.

Author : James Hiebert,Merlyn J. Behr
Publisher : Routledge
Page : 0 pages
File Size : 43,5 Mb
Release : 1988
Category : Education
ISBN : 080580353X

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Number Concepts and Operations in the Middle Grades by James Hiebert,Merlyn J. Behr Pdf

For many students, learning mathematics in the middle grades represents a watershed activity. If they fall behind or fail at this point, they are unlikely to recover and to pursue a career in the sciences or other mathematics-dependent occupations. The authors reveal at least two of the reasons for this watershed experience. First, the content itself is much more complex than that at the primary grades, a complexity that is only now being fully appreciated. Second, conventional instruction often is based on faulty assumptions about the way in which the content is learned. The chapters present the latest understanding of the nature of the mathematics content in the middle grades and the processes by which it is learned.

Author : Patrick M. Jenlink
Publisher : IAP
Page : 265 pages
File Size : 50,9 Mb
Release : 2022-02-01
Category : Education
ISBN : 9781648027468

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Mathematics as the Science of Patterns by Patrick M. Jenlink Pdf

Mathematics as the Science of Patterns: Making the Invisible Visible to Students through Teaching introduces the reader to a collection of thoughtful, research-based works by authors that represent current thinking about mathematics, mathematics education, and the preparation of mathematics teachers. Each chapter focuses on mathematics teaching and the preparation of teachers who will enter classrooms to instruct the next generation of students in mathematics. The value of patterns to the teaching and learning of mathematics is well understood, both in terms of research and application. When we involve or appeal to pattern in teaching mathematics, it is usually because we are trying to help students to extract greater meaning, or enjoyment, or both, from the experience of learning environments within which they are occupied, and perhaps also to facilitate remembering. As a general skill it is thought that the ability to discern a pattern is a precursor to the ability to generalize and abstract, a skill essential in the early years of learning and beyond. Research indicates that the larger problem in teaching mathematics does not lie primarily with students; rather it is with the teachers themselves. In order to make changes for students there first needs to be a process of change for teachers. Understanding the place of patterns in learning mathematics is a predicate to understanding how to teach mathematics and how to use pedagogical reasoning necessary in teaching mathematics. Importantly, the lack of distinction created by the pedagogical use of patterns is not immediately problematic to the student or the teacher. The deep-seated cognitive patterns that both teachers and students bring to the classroom require change. Chapter 1 opens the book with a focus on mathematics as the science of patterns and the importance of patterns in mathematical problem solving, providing the reader with an introduction. The authors of Chapter 2 revisit the work of Po lya and the development and implementation of problem solving in mathematics. In Chapter 3, the authors present an argument for core pedagogical content knowledge in mathematics teacher preparation. The authors of Chapter 4 focus on preservice teachers’ patterns of conception as related to understanding number and operation. In Chapter 5 the authors examine the role of visual representation in exploring proportional reasoning, denoting the importance of helping learners make their thinking visible. The authors of Chapter 6 examine patterns and relationships, and the importance of each in assisting students’ learning and development in mathematical understanding. The authors of Chapter 7 examine the use of worked examples as a scalable practice, with emphasis on the importance of worked examples in teaching fraction magnitude and computation is discussed. In Chapter 8, the authors expand on the zone of proximal development to investigate the potential of Zankov’s Lesson in terms of students analyzing numerical equalities. The authors of Chapter 9 focus on high leverage mathematical practices in elementary pre-service teacher preparation, drawing into specific relief the APEX cycle to develop deep thinking. In Chapter 10, the author focuses on number talks and the engagement of students in mathematical reasoning, which provides opportunities for students to be sensemakers of mathematics. Chapter 11 presents an epilogue, focusing on the importance of recognizing the special nature of mathematics knowledge for teaching.

Author : John A. Van de Walle
Publisher : Addison Wesley Publishing Company
Page : 630 pages
File Size : 40,7 Mb
Release : 1998
Category : Education
ISBN : UOM:39015039926871

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Elementary and Middle School Mathematics by John A. Van de Walle Pdf

John A. Van de Walle has written a book that helps readers make sense of mathematics and become confident in their ability to teach mathematics to children K to 8. Elementatry and Middle School Mathematics consists of 16 chapters reflecting the view that all mathematics can be taught through a problem-solving approach that motivates children and builds their confidence as they learn. This book thoroughly discusses the new standards and clearly develops four key aspects of teaching mathematics: the nature of mathematics as a science of pattern and order; an understanding of how children learn mathematics; a problem solving view of teaching mathematics; and specific methods for integrating assessment with instruction. Simple yet effective classroom activities are woven throughout the chapters as well as suggestions for technology and literature.