Developing Reasoning Through Algebra And Geometry

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Developing Thinking in Geometry

Author : Sue Johnston-Wilder
Publisher : Paul Chapman Educational Publishing
ISBN 13 : 9781412911696
Total Pages : 300 pages
Book Rating : 4.9/5 (116 download)

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Book Synopsis Developing Thinking in Geometry by : Sue Johnston-Wilder

Download or read book Developing Thinking in Geometry written by Sue Johnston-Wilder and published by Paul Chapman Educational Publishing. This book was released on 2005-09-14 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: "All readers can use this book to reignite their fascination with mathematics. Fosters not only a curiosity about geometry itself but crucially focuses on how learners can actively engage in thinking about geometry and its central key ideas."-Sylvia Johnson, Professor, Sheffield Hallam University"Exudes activity and interactivity. A book for learning geometry, learning to think more deeply about geometry, and also about its teaching and learning."-David Pimm, Professor, University of AlbertaDeveloping Thinking in Geometry enables teachers and their support staff to experience and teach geometric thinking. Discussing key teaching principles, the book and its accompanying interactive CD-ROM include many activities encouraging readers to extend their own learning, and teaching practices.Drawing on innovative approaches for teaching and learning geometry developed by the Open University's Centre for Mathematics Education, this resource is constructed around the following key themes:InvarianceLanguage and points of viewReasoning using invarianceVisualizing and representing

Teaching Mathematics in Grades 6 - 12

Author : Randall E. Groth
Publisher : SAGE Publications
ISBN 13 : 1452256020
Total Pages : 513 pages
Book Rating : 4.4/5 (522 download)

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Book Synopsis Teaching Mathematics in Grades 6 - 12 by : Randall E. Groth

Download or read book Teaching Mathematics in Grades 6 - 12 written by Randall E. Groth and published by SAGE Publications. This book was released on 2012-08-10 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teaching Mathematics in Grades 6 - 12 by Randall E. Groth explores how research in mathematics education can inform teaching practice in grades 6-12. The author shows preservice mathematics teachers the value of being a "researcher—constantly experimenting with methods for developing students' mathematical thinking—and connecting this research to practices that enhance students' understanding of the material. Ultimately, preservice teachers will gain a deeper understanding of the types of mathematical knowledge students bring to school, and how students' thinking may develop in response to different teaching strategies.

Number Talks

Author : Sherry Parrish
Publisher : Math Solutions
ISBN 13 : 1935099116
Total Pages : 434 pages
Book Rating : 4.9/5 (35 download)

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Book Synopsis Number Talks by : Sherry Parrish

Download or read book Number Talks written by Sherry Parrish and published by Math Solutions. This book was released on 2010 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A multimedia professional learning resource"--Cover.

Introduction to Mathematical Thinking

Author : Keith J. Devlin
Publisher :
ISBN 13 : 9780615653631
Total Pages : 0 pages
Book Rating : 4.6/5 (536 download)

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Book Synopsis Introduction to Mathematical Thinking by : Keith J. Devlin

Download or read book Introduction to Mathematical Thinking written by Keith J. Devlin and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Mathematical thinking is not the same as 'doing math'--unless you are a professional mathematician. For most people, 'doing math' means the application of procedures and symbolic manipulations. Mathematical thinking, in contrast, is what the name reflects, a way of thinking about things in the world that humans have developed over three thousand years. It does not have to be about mathematics at all, which means that many people can benefit from learning this powerful way of thinking, not just mathematicians and scientists."--Back cover.

The Proceedings of the 12th International Congress on Mathematical Education

Author : Sung Je Cho
Publisher : Springer
ISBN 13 : 3319126881
Total Pages : 617 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis The Proceedings of the 12th International Congress on Mathematical Education by : Sung Je Cho

Download or read book The Proceedings of the 12th International Congress on Mathematical Education written by Sung Je Cho and published by Springer. This book was released on 2015-02-10 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises the Proceedings of the 12th International Congress on Mathematical Education (ICME-12), which was held at COEX in Seoul, Korea, from July 8th to 15th, 2012. ICME-12 brought together 3500 experts from 92 countries, working to understand all of the intellectual and attitudinal challenges in the subject of mathematics education as a multidisciplinary research and practice. This work aims to serve as a platform for deeper, more sensitive and more collaborative involvement of all major contributors towards educational improvement and in research on the nature of teaching and learning in mathematics education. It introduces the major activities of ICME-12 which have successfully contributed to the sustainable development of mathematics education across the world. The program provides food for thought and inspiration for practice for everyone with an interest in mathematics education and makes an essential reference for teacher educators, curriculum developers and researchers in mathematics education. The work includes the texts of the four plenary lectures and three plenary panels and reports of three survey groups, five National presentations, the abstracts of fifty one Regular lectures, reports of thirty seven Topic Study Groups and seventeen Discussion Groups.

Approaches to Algebra

Author : N. Bednarz
Publisher : Springer Science & Business Media
ISBN 13 : 9400917325
Total Pages : 342 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Approaches to Algebra by : N. Bednarz

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.

Taking Shape

Author : Joan Moss
Publisher :
ISBN 13 : 9780134153490
Total Pages : 272 pages
Book Rating : 4.1/5 (534 download)

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Book Synopsis Taking Shape by : Joan Moss

Download or read book Taking Shape written by Joan Moss and published by . This book was released on 2016-04-29 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Enrich Your Geometry Curriculum and Extend Your Students' Spatial Reasoning Research shows that children with good spatial skills perform better in mathematics overall. This research-based resource is a unique blend of professional learning and classroom activities. It includes: 32 field-tested and research-based activities designed to appeal to young children Guided lesson plans, including 15 videos, that serve as models for best practice in instruction Tips on observing, questioning, and assessing young children's geometric and spatial thinking Free access to website with videos, curriculum correlations, line masters, and observation guides

Thnking Mathematically

Author : J Mason
Publisher : Pearson Higher Ed
ISBN 13 : 027372892X
Total Pages : 266 pages
Book Rating : 4.2/5 (737 download)

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Book Synopsis Thnking Mathematically by : J Mason

Download or read book Thnking Mathematically written by J Mason and published by Pearson Higher Ed. This book was released on 2011-01-10 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thinking Mathematically is perfect for anyone who wants to develop their powers to think mathematically, whether at school, at university or just out of interest. This book is invaluable for anyone who wishes to promote mathematical thinking in others or for anyone who has always wondered what lies at the core of mathematics. Thinking Mathematically reveals the processes at the heart of mathematics and demonstrates how to encourage and develop them. Extremely practical, it involves the reader in questions so that subsequent discussions speak to immediate experience.

Bulletin

Author : Kansas Association of Teachers of Mathematics
Publisher :
ISBN 13 :
Total Pages : 1060 pages
Book Rating : 4.0/5 ( download)

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Book Synopsis Bulletin by : Kansas Association of Teachers of Mathematics

Download or read book Bulletin written by Kansas Association of Teachers of Mathematics and published by . This book was released on 1927 with total page 1060 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Developing Mathematical Thinking

Author : Jonathan D. Katz
Publisher : Rowman & Littlefield
ISBN 13 : 147581058X
Total Pages : 145 pages
Book Rating : 4.4/5 (758 download)

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Book Synopsis Developing Mathematical Thinking by : Jonathan D. Katz

Download or read book Developing Mathematical Thinking written by Jonathan D. Katz and published by Rowman & Littlefield. This book was released on 2014-07-07 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this country we have done a poor job of helping students come to see the wonder, beauty and power of mathematics. Standards can be brought into the picture, but unless we think about what it means to truly engage students in mathematics we will continue to be unsuccessful. The goal of this book is to begin to change the way students experience mathematics in the middle and high school classrooms. In this book you will find a theoretical basis for this approach to teaching mathematics, multiple guides and questions for teachers to think about in relation to their everyday teaching, and over 30 examples of problems, lessons, tasks, and projects that been used effectively with urban students.

Intellectual Development and Mathematics Learning

Author : Chongde Lin
Publisher : Springer Nature
ISBN 13 : 9811987572
Total Pages : 277 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Intellectual Development and Mathematics Learning by : Chongde Lin

Download or read book Intellectual Development and Mathematics Learning written by Chongde Lin and published by Springer Nature. This book was released on 2023-03-30 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the outcomes of author’s 40 years of research, especially the theory of “the Triangular Pyramid Structure of Thinking” that he independently proposed, and the application of his development theory in the field of mathematics education. The book firstly explains the substantial character of intelligence, the development law of intelligence, and the relationship between intelligence development and creativity cultivation. Secondly, it discusses the structure of mathematical thinking of children and adolescents from 0 to 18 years old, and the methods of developing students’ thinking ability and the quality of intelligence through arithmetic learning. In the end, this book also demonstrates the characteristics of the development of mathematical thinking ability of children at age 0-6, elementary school students, and secondary school students, and the related latest research in this field. Based on the theory of “the Triangular Pyramid Structure of Thinking”, a number of examples are given to illustrate how the theory of intelligence development can be used in mathematics teaching to promote the development of students’ thinking abilities and to improve the quality of teaching. This book covers various areas including psychology, mathematics, and education. It has a great reference value for scholars in the field of psychology to study the theory of intelligence and the structure of thinking, providing guidance for parents and mathematics teachers to promote children’s quality of intelligence and mathematical thinking abilities, and to enhance their mathematics learning effects. In addition, it provides examples for psychological research to serve specific subject teaching in elementary and secondary schools.

Researching and Using Progressions (Trajectories) in Mathematics Education

Author :
Publisher : BRILL
ISBN 13 : 9004396446
Total Pages : 255 pages
Book Rating : 4.0/5 (43 download)

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Book Synopsis Researching and Using Progressions (Trajectories) in Mathematics Education by :

Download or read book Researching and Using Progressions (Trajectories) in Mathematics Education written by and published by BRILL. This book was released on 2019-02-04 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: The relationship between research and practice has long been an area of interest for researchers, policy makers, and practitioners alike. One obvious arena where mathematics education research can contribute to practice is the design and implementation of school mathematics curricula. This observation holds whether we are talking about curriculum as a set of broad, measurable competencies (i.e., standards) or as a comprehensive set of resources for teaching and learning mathematics. Impacting practice in this way requires fine-grained research that is focused on individual student learning trajectories and intimate analyses of classroom pedagogical practices as well as large-scale research that explores how student populations typically engage with the big ideas of mathematics over time. Both types of research provide an empirical basis for identifying what aspects of mathematics are important and how they develop over time. This book has its origins in independent but parallel work in Australia and the United States over the last 10 to 15 years. It was prompted by a research seminar at the 2017 PME Conference in Singapore that brought the contributors to this volume together to consider the development and use of evidence-based learning progressions/trajectories in mathematics education, their basis in theory, their focus and scale, and the methods used to identify and validate them. In this volume they elaborate on their work to consider what is meant by learning progressions/trajectories and explore a range of issues associated with their development, implementation, evaluation, and on-going review. Implications for curriculum design and future research in this field are also considered. Contributors are: Michael Askew, Tasos Barkatsas, Michael Belcher, Rosemary Callingham, Doug Clements, Jere Confrey, Lorraine Day, Margaret Hennessey, Marj Horne, Alan Maloney, William McGowan, Greg Oates, Claudia Orellana, Julie Sarama, Rebecca Seah, Meetal Shah, Dianne Siemon, Max Stephens, Ron Tzur, and Jane Watson.

Graduate Catalog

Author : University of Michigan--Dearborn
Publisher :
ISBN 13 :
Total Pages : 212 pages
Book Rating : 4.3/5 (97 download)

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Book Synopsis Graduate Catalog by : University of Michigan--Dearborn

Download or read book Graduate Catalog written by University of Michigan--Dearborn and published by . This book was released on 2007 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometry

Author : G. D. Chakerian
Publisher :
ISBN 13 : 9780895824301
Total Pages : 0 pages
Book Rating : 4.8/5 (243 download)

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Book Synopsis Geometry by : G. D. Chakerian

Download or read book Geometry written by G. D. Chakerian and published by . This book was released on 1998 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Proof and Proving in Mathematics Education

Author : Gila Hanna
Publisher : Springer Science & Business Media
ISBN 13 : 9400721293
Total Pages : 468 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Proof and Proving in Mathematics Education by : Gila Hanna

Download or read book Proof and Proving in Mathematics Education written by Gila Hanna and published by Springer Science & Business Media. This book was released on 2012-06-14 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: *THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.

Cases on Technology Integration in Mathematics Education

Author : Polly, Drew
Publisher : IGI Global
ISBN 13 : 1466664983
Total Pages : 551 pages
Book Rating : 4.4/5 (666 download)

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Book Synopsis Cases on Technology Integration in Mathematics Education by : Polly, Drew

Download or read book Cases on Technology Integration in Mathematics Education written by Polly, Drew and published by IGI Global. This book was released on 2014-09-30 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Common Core education standards establish a clear set of specific ideas and skills that all students should be able comprehend at each grade level. In an effort to meet these standards, educators are turning to technology for improved learning outcomes. Cases on Technology and Common Core Mathematics provides a compilation of cases and vignettes about the application of technology in the classroom in order to enhance student understanding of math concepts. This book is a timely reference source for mathematics educators, educational technologists, and school district leaders employed in the mathematics education or educational technology fields.

Developing Maths Lesson Planning and Frameworks: Mastery, Logic and Reasoning in the Classroom

Author : Linda (Yuqian) Wang
Publisher : McGraw-Hill Education (UK)
ISBN 13 : 0335251811
Total Pages : 169 pages
Book Rating : 4.3/5 (352 download)

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Book Synopsis Developing Maths Lesson Planning and Frameworks: Mastery, Logic and Reasoning in the Classroom by : Linda (Yuqian) Wang

Download or read book Developing Maths Lesson Planning and Frameworks: Mastery, Logic and Reasoning in the Classroom written by Linda (Yuqian) Wang and published by McGraw-Hill Education (UK). This book was released on 2023-11-24 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: “This book highlights the essential relationship between lesson planning and key mathematical elements such as mastery and reasoning. The exemplification of ideas through useful classroom strategies gives the book a practical basis, as well as theoretical. I have no doubt that even experienced teachers will find this book enlightening and encourage them to re-evaluate elements of their practice.” Hayley Hands, Secondary PGCE Mathematics Lead, Newcastle University, UK “Developing Maths Lesson Planning and Frameworks provides much food for thought and includes many immediate ‘take aways’ to reflect on or try out. This book will help enhance any maths teacher's lesson planning, from the trainee teacher to the experienced practitioner.” Rose-Marie Rochester, Archimedes NE Maths Hub Lead/BHCET Director of Maths, UK Addressing the maths skills gap, Wang et al. propose a new method for maths lesson planning that harnesses the power of reasoning in mathematics teaching. Using a pedagogical approach called the Causal Connectivity Framework (CCF), this book helps teachers to support students in actively discovering the logical foundations upon which classroom activities are linked together. The authors have diverse expertise and experiences as maths teachers, teacher educators and researchers, and this alternative approach is the result of long-term collaboration aimed at building up successful maths lessons from the very first steps – lesson planning. Developing Maths Lesson Planning and Frameworks: •Offers practical advice within a theoretical framework •Ties in with UK National Curriculum requirements •Contains detailed practical examples and visual aids throughout Reasoning is a critical component of maths learning, making this essential reading for maths teachers and teacher trainees as they help students to achieve maths mastery. Linda Wang is Assistant Professor and PGCE secondary maths Lead at Durham University, UK. She is particularly interested in curriculum design at both secondary and lower primary level mathematics, and developing the educational impact partnership model to deliver Continuing Professional Development (CPD) to future-orientate Mathematics education. Chris Brown is Professor of Education at the University of Southampton, UK. His research interests include using Professional Learning Networks (PLNs) to promote the collaborative learning of teachers, as well as how research evidence can and should, but often doesn’t, aid the development of education policy and practice. Jeremy Dawson is Area Co-ordinator for the Advanced Maths Support Programme at Durham University, UK. He has worked in a variety of diverse school settings around North East England and has extensive experience of teaching mathematics from KS2-KS5, as well as contributing and assisting on gifted and talented programs for prospective university entrants.