math makes sense a constructivist approach to the teaching and learning of mathematics

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Math Makes Sense

Author : Ana Helvia Quintero
ISBN : 9781783268665
Genre : Mathematics
File Size : 66. 56 MB
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The methods for teaching mathematics usually follow the structure of mathematics. The problem with this is that the structure of mathematics took centuries of elaboration to develop and is not the same as how one originally experiences mathematics. Based on research of how mathematics is actually learned, this book presents an innovative approach for teaching mathematics that will engage pupils and can have lifelong benefits for how they take on board more advanced mathematical topics. Math Makes Sense! makes use of the realistic mathematics education (RME) philosophy, which bridges the gap between informal mathematics learning (such as in day-to-day life) and more formal teaching in school. Many real-life situations as examples for learning are included, as well as different mathematical and logic puzzles that will stimulate learning and foster understanding. The ideas presented are not confined to one national curriculum and so can be helpful worldwide to teachers/ instructors (both in practice and those still in training), private tutors, homeschooling parents, and educational researchers. Contents:PrefaceAcknowledgmentsAbout the AuthorsFostering the Learning of MathematicsConstruction of Concepts and Mathematical InterpretationsNumberingAddition and SubtractionMultiplication and DivisionFractions, Decimals, and PercentagesMeasurementExploring SpaceProbability and StatisticsPatterns, Relations, and FunctionsThe Joy of PuzzlesTechnology: A Tool for Analysis and InterpretationAssessmentConcluding Remarks Readership: Teachers, trainee teachers, researchers interested in mathematics education, homeschool parents, and parents with children in primary/ elementary school. Key Features:This book is grounded on solid mathematics learning research, as well as on the authors' own observations in the classroom, and so combines theoretical knowledge with practiceWritten in an accessible mannerGives educators ideas which they can easily implement in the classroom

Winning The Math Wars

Author : Martin Abbott
ISBN : 9780295989679
Genre : Education
File Size : 85. 64 MB
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n this volume, four scholars at the Washington School Research Center (WSRC) at Seattle Pacific University present original research drawn from statistical studies of state educational data and from thousands of classroom observations carried out by The BERC Group. They assess the current state of math education and-- review its history and development. The authors also provide a dispassionate review of the extensive international, national, and state literature. The in-depth observational research in Winning the Math Wars confirms that the real issue is neither the approach to teaching--traditional or reform--nor the type of curriculum. If America's goal of educational equity and excellence is to be achieved, then math teachers everywhere must be fully supported in developing the specific skills that are ideal for educating all students. The authors discussion focus on four principles for improving math teaching and learning: fidelity to reform efforts by all involved; an emphasis on instruction and instructional tools; the critical nature of mathematical knowledge; and the need for transformational change. --Winning the Math Wars is an important book for policy makers, school leaders, practitioners of mathematics education, parents, and anyone who wants to make sense of the "math wars."--Martin Abbott, Ph.D., is director of the WSRC and professor of sociology at Seattle Pacific University. He specializes in evaluation research and statistical analysis of large data sets. Duane Baker, Ed.D., is president of The BERC Group and an expert in assessment, classroom observation, and teaching reforms. Karen Smith, Ed.D., is winner of a presidential award in mathematics education and an experienced elementary math teacher, school administrator, and consultant to public schools. Thomas Trzyna, Ph.D., is a specialist in international education and a co-author of Toward a Global Ph.D.-

Constructing Mathematical Knowledge

Author : Paul Ernest
ISBN : 9780750703543
Genre : Education
File Size : 26. 95 MB
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First published in 1994. Routledge is an imprint of Taylor & Francis, an informa company.

Constructing Mathematical Know

Author :
ISBN : 9781136364792
Genre : Education
File Size : 34. 87 MB
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First published in 1994. Routledge is an imprint of Taylor & Francis, an informa company.

Teaching Mathematics In Secondary Schools

Author : Linda Haggarty
ISBN : 9781136414930
Genre : Education
File Size : 85. 32 MB
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A companion to Aspects of Teaching Secondary Mathematics, this book introduces and explores the contemporary issues and key ideas entailed in the teaching and learning of this subject. This book is concerned with exploring the bigger picture of mathematics education, and is aimed particularly at those learning to teach mathematics; teachers in the classroom who want to continue thinking and developing as mathematics teachers; and those concerned with education who would like to be better informed about mathematics education. Divided into seven sections to help structure reading, this book offers a completely up-to-date, comprehensive overview, written by the most-known, well-respected experts in the field.

How Children Learn

Author : John Holt
ISBN : 9780786746903
Genre : Education
File Size : 35. 64 MB
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This enduring classic of educational thought offers teachers and parents deep, original insight into the nature of early learning. John Holt was the first to make clear that, for small children, “learning is as natural as breathing.” In this delightful yet profound book, he looks at how we learn to talk, to read, to count, and to reason, and how we can nurture and encourage these natural abilities in our children.”

Helping Children Learn Mathematics 11th Edition

Author : Robert E. Reys
ISBN : 9781119034063
Genre : Education
File Size : 26. 10 MB
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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).

Teaching Mathematics

Author : Peter Sullivan
ISBN : 174286046X
Genre : Effective teaching
File Size : 76. 38 MB
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Teaching Number

Author : Robert J Wright
ISBN : 9781446204245
Genre : Education
File Size : 37. 34 MB
Format : PDF, Kindle
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The book lets teachers identify where their students are in terms of number skills, and sets out a strategy for developing their knowledge. The authors show how to advance children's learning across five stages of early arithmetical learning - emergent, perceptual, figurative, initial number, and facile number. This provides for increasingly sophisticated number strategies across addition, subtraction, multiplication and division, as well as developing children's number word and numeral knowledge, and their ability to structure number and have grouping strategies. The approach used nine guiding principles for teaching. Each chapter has clearly defined teaching procedures which show how to take the children onto the next more sophisticated stage. The teaching procedures are organized into key teaching topics, and each includes: o a clearly defined purpose o detailed instructions, activities, learning tasks and reinforcing games o lists of responses which children may make o application in whole class, small group and individualised settings o a link to the Learning Framework in Number (see Early Numeracy- second edition, 2005) o how the guiding principles for teaching can be used to allow teachers to evaluate and reflect upon their practice Primary practitioners in Australia, the United States, the United Kingdom and Canada have tested the teaching procedures which can be used in conjunction with each country's numeracy strategy. Primary teachers, especially of the early years, mathematics co-ordinators, heads of school, mathematics advisers, special educationalists, learning support personnel, teacher assistants, lecturers in initial teacher training and educational psychologists will all find this book invaluable.

Mathematics Education As A Research Domain A Search For Identity

Author : Anna Sierpinska
ISBN : 9789401151948
Genre : Education
File Size : 45. 11 MB
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No one disputes how important it is, in today's world, to prepare students to un derstand mathematics as well as to use and communicate mathematics in their future lives. That task is very difficult, however. Refocusing curricula on funda mental concepts, producing new teaching materials, and designing teaching units based on 'mathematicians' common sense' (or on logic) have not resulted in a better understanding of mathematics by more students. The failure of such efforts has raised questions suggesting that what was missing at the outset of these proposals, designs, and productions was a more profound knowledge of the phenomena of learning and teaching mathematics in socially established and culturally, politically, and economically justified institutions - namely, schools. Such knowledge cannot be built by mere juxtaposition of theories in disci plines such as psychology, sociology, and mathematics. Psychological theories focus on the individual learner. Theories of sociology of education look at the general laws of curriculum development, the specifics of pedagogic discourse as opposed to scientific discourse in general, the different possible pedagogic rela tions between the teacher and the taught, and other general problems in the inter face between education and society. Mathematics, aside from its theoretical contents, can be looked at from historical and epistemological points of view, clarifying the genetic development of its concepts, methods, and theories. This view can shed some light on the meaning of mathematical concepts and on the difficulties students have in teaching approaches that disregard the genetic development of these concepts.

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