Interdisciplinarity, Creativity, and Learning: Mathematics with Literature, Paradoxes, History, Technology, and Modeling

(Montana mathematics enthusiast,  7)

Bharath Sriraman, Viktor Freiman e Nicole Lirette-Pitre 

Information Age Publishing | 2009 | 261 páginas | rar - pdf | 2,7 Mb

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A Volume in The Montana Mathematics Enthusiast: Monograph Series in Mathematics Education Series Editor Bharath Sriraman, The University of Montana Interdisciplinarity is increasingly viewed as a necessary ingredient in the training of future oriented 21st century disciplines that rely on both analytic and synthetic abilities across disciplines. Nearly every curricular document or vision statement of schools and universities include a call for promoting creativity in students. Yet the construct of creativity and giftedness across disciplines remains elusive in the sense that the prototypical examples of such work come from eminent scientists, artists and mathematicians, and little if any work has been conducted with non-eminent individuals. This monograph is an attempt to fill this gap by putting forth the view that interdisciplinarity and creativity are related constructs, and that the cultivation of domain general creativity is possible. Mathematics has historically been anchored to numerous disciplines like theology, natural philosophy, culture and art, allowing for a flexibility of thought that is difficult to cultivate in other disciplines. In this monograph, the numerous chapters from Australia, U.S.A., Canada, Cyprus, Denmark and Japan provide a compelling illustration of the intricate connection of mathematics with literature, paradoxes, history, technology and modeling, thus serving as a conduit for interdisciplinarity, creativity and learning to occur.

ContentsSection I Interdisciplinarity in Mathematics and Literature
1 The Interdisciplinary Nature of Inductive Processes in Forming Generalizations.... 3
Bharath Sriraman and Harry Adrian
2 The Existential Void in Learning: Juxtaposing Mathematics and Literature.... 13
Bharath Sriraman and Harry Adrian
3 Mathematics and Literature: Synonyms, Antonyms or the Perfect Amalgam?...... 31
Bharath Sriraman
4 Mathematics and Literature (The Sequel): Imagination as a Pathway to Advanced Mathematical Ideas and Philosophy..... 41
Bharath Sriraman
Section II Mathematics and Paradoxes 
5 1 or 0?: Cantorian Conundrums in the Contemporary Classroom.... 55
Bharath Sriraman and Libby Knott
6 Understanding Mathematics through Resolution of Paradoxes...... 61
Margo Kondratieva
7 Mathematical Paradoxes as Pathways into Beliefs and Polymathy.... 75
Bharath Sriraman
Section II I Geometry and History
8 Voronoi Diagrams.... 97
Michael Mumm
9 An In-Depth Investigation of the Divine Ratio.... 109
Birch Fett
10 Cyclide Manipulation........ 133
Akihiro Matsuura
Section IV Interdisciplinarity and Modeling
11 Modeling Interdisciplinary Activities Involving Mathematics and Philosophy... 147
Steffen M. Iversen
12 Integrating Engineering Education within the Elementary and Middle School Mathematics Curriculum.... 165
Lyn D. English and Nicholas G. Mousoulides
13 Mathematical Modelling in the Early School Years........... 177
Lyn D. English and James J. Watters
Section V Technology and the NET Generation
14 Connected Giftedness: Mathematical Problem Solving by Means of a Web Technology: Case of the CASMI Project...... 205
Viktor Freiman and Nicole Lirette-Pitre
15 Teaching and Learning for the Net Generation: A Robotic-Based Learning Approach....217
Samuel Blanchard
16 Does Technology Help Building More Creative Mathematical Environments?... 233
Dominic Manuel

Using the Common Core State Standards in Mathematics with Gifted and Advanced Learners

Susan Johnsen e Linda Sheffield

Prufrock Press | 2012 | 136 páginas | rar - epub |1,3  Mb


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Using the Common Core State Standards in Mathematics With Gifted and Advanced Learners provides teachers and administrators examples and strategies to implement the new Common Core State Standards (CCSS) with advanced learners at all stages of development in K–12 schools. The book describes—and demonstrates with specific examples from the CCSS—what effective differentiated activities in mathematics look like for top learners. It shares how educators can provide rigor within the new standards to allow students to demonstrate higher level thinking, reasoning, problem solving, passion, and inventiveness in mathematics. By doing so, students will develop the skills, habits of mind, and attitudes toward learning needed to reach high levels of competency and creative production in mathematics fields.

Table of Contents
Foreword
Preface
Acknowledgments
Introduction
The Common Core State Standards
Rationale for the Work
Alignment to 21st Century Skills
Research Support for the Effort
Differentiating the Common Core State Standards for Gifted and Advanced Students
Linking Mathematics and English Language Arts Standards
Differentiating Assessments to Encourage Higher Level Reasoning and Creativity
Talent Trajectory: Creating Pathways to Excellence in Mathematics
Implementing the Common Core State Standards With Various Program Models in Gifted Education
Alignment of the Common Core State Standards With the Gifted Education Programming Standards
Implications for Professional Learning When Implementing the Common Core State Standards
Collaboration With General and Special Education
A Possible Timeline for Implementing the Common Core State Standards Locally
Resources to Assist With the Implementation Process
References
Appendix A: Definitions of Key Terms
Appendix B: Evidence-Based Practices in Gifted Education
Appendix C: Annotated References on Mathematical Creativity and Giftedness
Appendix D: Additional Mathematics Resources
About the Editors
About the Contributors
About the Copublisher

Creativity, Giftedness, and Talent Development in Mathematics

Bharath Sriraman, The University of Montana 

The Montana Mathematics Enthusiast, Monograph 4 | 2008 | RAR - PDF | 2,59 Mb

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Our innovative spirit and creativity lies beneath the comforts and security of today's technologically evolved society. Scientists, inventors, investors, artists and leaders play a vital role in the advancement and transmission of knowledge. Mathematics, in particular, plays a central role in numerous professions and has historically served as the gatekeeper to numerous other areas of study, particularly the hard sciences, engineering and business. Mathematics is also a major component in standardized tests in the U.S., and in university entrance exams in numerous parts of world. 
Creativity and imagination is often evident when young children begin to develop numeric and spatial concepts, and explore mathematical tasks that capture their interest. Creativity is also an essential ingredient in the work of professional mathematicians. Yet, the bulk of mathematical thinking encouraged in the institutionalized setting of schools is focused on rote learning, memorization, and the mastery of numerous skills to solve specific problems prescribed by the curricula or aimed at standardized testing. Given the lack of research based perspectives on talent development in mathematics education, this monograph is specifically focused on contributions towards the constructs of creativity and giftedness in mathematics. This monograph presents new perspectives for talent development in the mathematics classroom and gives insights into the psychology of creativity and giftedness. The book is aimed at classroom teachers, coordinators of gifted programs, math contest coaches, graduate students and researchers interested in creativity, giftedness, and talent development in mathematics.

CONTENTS
Table of Contents. 
Preface Bharath Sriraman 
1. The characteristics of mathematical creativity Bharath Sriraman
2. Mathematical giftedness, problem-solving and the ability to formulate generalizations. Bharath Sriraman 
3. Gifted ninth graders' notions of proof: Investigating parallels in approaches of mathematically gifted students and professional mathematicians Bharath Sriraman 
4. Are mathematical giftedness and mathematical creativity synonyms? A theoretical analysis of constructs. Bharath Sriraman 
5. Does mathematics gifted education need a working philosophy of creativity? Viktor Freiman & Bharath Sriraman 
6. Designing opportunities for all students to demonstrate mathematical prowess Sylvia Bulgar 
7. Problems to discover and to boost mathematical talent in early grades: A challenging situations approach Viktor Freiman 
8. Mathematical problem solving processes of Thai gifted students Supattra Pattivisan & Margaret L. Niess 
9. Knowledge as a manifestation of talent: Creating opportunities for the gifted. Alexander Karp 
10. An ode to Imre Lakatos: Bridging the ideal and actual mathematics classrooms Bharath Sriraman 
11. Mathematically gifted Korean elementary students' revisiting of Euler's polyhedron theorem Jaehoon Yim, Sanghun Song & Jiwon Kim 
12. Mathematically promising students from the space age to the information age Linda Sheffield 
13. Revisiting the needs of the gifted mathematics students: Are students surviving or thriving? Alan Zollman 
14. Playing with Powers Bharath Sriraman & Pawel Strzelecki

Developing Math Talent

Susan Assouline, Ann Lupkowski-Shoplik

Prufrock Press | 2010 | 420 páginas | PDF | 2,6 Mb

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Build student success in math with the only comprehensive guide for developing math talent among advanced learners. The authors, nationally recognized math education experts, offer a focused look at educating gifted and talented students for success in math. More than just a guidebook for educators, this book offers a comprehensive approach to mathematics education for gifted students of elementary or middle school age.

The authors provide concrete suggestions for identifying mathematically talented students, tools for instructional planning, and specific programming approaches. Developing Math Talent features topics such as: strategies for identifying mathematically gifted learners, strategies for advocating for gifted children with math talent, how to design a systematic math education program for gifted students, specific curricula and materials that support success, and teaching strategies and approaches that encourage and challenge gifted learners.

The Elements of Creativity and Giftedness in Mathematics

Bharath Sriraman, Kyeong Hwa Lee

Sense Publishers | 2010 | 240 páginas | PDF | 9 MB

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The Elements of Creativity and Giftedness in Mathematics edited by Bharath Sriraman and KyeongHwa Lee covers recent advances in mathematics education pertaining to the development of creativity and giftedness. The book is international in scope in the "sense" that it includes numerous studies on mathematical creativity and giftedness conducted in the U.S.A, China, Korea, Turkey, Israel, Sweden, and Norway in addition to cross-national perspectives from Canada and Russia. The topics include problem -posing, problem-solving and mathematical creativity; the development of mathematical creativity with students, pre and in-service teachers; cross-cultural views of creativity and giftedness; the unpacking of notions and labels such as high achieving, inclusion, and potential; as well as the theoretical state of the art on the constructs of mathematical creativity and giftedness. The book also includes some contributions from the first joint meeting of the American Mathematical Society and the Korean Mathematical Society in Seoul, 2009. Topics covered in the book are essential reading for graduate students and researchers interested in researching issues and topics within the domain of mathematical creativity and mathematical giftedness. It is also accessible to pre-service and practicing teachers interested in developing creativity in their classrooms, in addition to professional development specialists, mathematics educators, gifted educators, and psychologists.

Contents
AIMS AND SCOPE
1. WHAT ARE THE ELEMENTS OF GIFTEDNESS AND CREATIVITY IN MATHEMATICS?: An Overview of the KMS-AMS Symposium and the Book
INTRODUCTION
ACKNOWLEDGEMENT
2. AN EXPLORATORY STUDY OF RELATIONSHIPS BETWEEN STUDENTS’ CREATIVITY AND MATHEMATICAL PROBLEM-POSING ABILITIES: Comparing Chinese and U.S Students
INTRODUCTION
CONCEPTUAL FRAMEWORK
Guilford’s Structure of Intellect Model
Mathematical Problem-posing Framework
STUDY VARIABLES AND DEFINITION OF STUDY TERMS
Definition of Creativity
Definition of Mathematical Problem Posing
RESEARCH DESIGN
PARTICIPANTS
Participants from China
Participants from the United States
MEASURES AND INSTRUMENTATION
The Mathematics Content Test
The Torrance Tests of Creative Thinking
The Mathematical Problem-Posing Test
The Translation of the Tests from English to Chinese
DATA ANALYSIS
The Scoring of the Mathematics Content Test
The Scoring of the TTCT Tests
The Scoring of the Mathematical Problem-posing Test
RESULTS
Comparison of the Mathematics Content Test Scores
Comparison of TTCT Scores
Comparison of the Mathematical Problem-posing Test Scores
Correlations between TTCT and the Mathematical Problem-posing Test
DISCUSSION
LIMITATIONS OF THIS STUDY
The Participants
The Translation of the Instruments
The Time and Distance Restrictions
CONCLUSIONS AND IMPLICATIONS
REFERENCES
3. ARE MATHEMATICALLY TALENTED ELEMENTARY STUDENTS ALSO TALENTED IN STATISTICS?
INTRODUCTION
CONCEPTUAL ANALYSIS OF AVERAGE
METHOD
Participants
Tasks
Administration and Analysis
RESPONSES AND FINDINGS
Average as Being Representative
Mathematical Abstract Construction
Treatment of Variation
SUMMARY AND DISCUSSION
REFERENCES
4. DOES HIGH ACHIEVING IN MATHEMATICS = GIFTED AND/OR CREATIVE IN MATHEMATICS
INTRODUCTION
CREATIVITY AND MATHEMATICAL CREATIVITY
The Gestalt principle:
The Aesthetic principle:
The Scholarly principle:
The Free market principle:
The Uncertainty principle:
INTELLIGENCE AND MATHEMATICAL INTELLIGENCE
GIFTEDNESS AND MATHEMATICAL PRECOCIOUSNESS
Exceptional Abilities from a Young Age
Late Development of Mathematical Giftedness
Identifying Precociuosness
Programmes for the Highly Gifted Youth
SEVEN CASES OF VARIOUS LEVELS OF GIFTEDNESS AND ACHIEVEMENT
John, Gifted but not High Achieving in Mathematics
Lisa, High Achieving Merely through Hard Work
Steve, Late Discovery of Mathematical Precociousness
Annie, Initially a High Achiever by Strategic Social and Mathematical Behaviour
Chris, from Above Average to Low Achieving
Mary, High Achieving, Gifted and Creative
Nelly, Gifted but not Creative
DISCUSSION
The Labels High Achiever, Gifted and Creative in Mathematics
Social Impact and Changed Development
Assessment and School Practice
REFERENCES
5. DEVELOPING MATHEMATICAL POTENTIAL IN UNDERREPRESENTED POPULATIONS THROUGH PROBLEM SOLVING, MATHEMATICAL DISCOURSE AND ALGEBRA
INTRODUCTION
THEORETICAL FRAMEWORK
Participation Gap among Diverse Learners in Accessing Rigorous Mathematics
METHODOLOGY
Participants
Design Features of the Project
Focusing on the Core Traits of Mathematically Proficient Students
Procedures
RESULTS
Selecting Tasks and Sequences of Related Problems
Integrating Pedagogical Content Tools to Extend Students’ Reasoning
Orchestrating Classroom Discourse through Pedagogical Moves and Questioning
CONCLUSIONS
REFERENCES
6. ON TRACK TO GIFTED EDUCATION IN MATHEMATICS IN SWEDEN
INTRODUCTION
A HISTORICAL REVIEW – DEVELOPMENT OF THE SCHOOL SYSTEM AND THE CURRICULUM
NATIONAL POLICIES
ADVOCACY
GIFTED EDUCATION RESEARCH RELEVANT FOR MATHEMATICS EDUCATION
GIFTED EDUCATION IN THE SWEDISH TEACHER EDUCATION
IMPLEMENTATION OF GIFTED EDUCATION IN SCHOOLS
CHALLENGES FACING SWEDISH GIFTED EDUCATION IN MATHEMATICS
Legal Recognition of Gifted Students
Strengthening the Connection between Research and Implementation of Gifted Education
Identification of Gifted Students
Gifted Educa tion in the Swedish Teacher Education
Coordinating Measures for Gifted Students
Social Dimensions of Giftedness
CONCLUDING REMARK
REFERENCES
7. TEACHERS’ IMAGES OF GIFTED STUDENTS AND THE ROLES ASSIGNED TO THEM IN HETEROGENEOUS MATHEMATICS CLASSES
INTRODUCTION
THEORETICAL BACKGROUND
Mathematically able Students
Teachers of MAS
THE STUDY
Participating Teachers
Procedure
Data Analysis
FINDINGS
Teachers’ Images of Gifted Students
High abilities as a gift of god.
A gift is like a jug with a narrow opening.
A gifted student is a cyclamen with a lowered head.
Students’ Roles in the Classroom
MAS as a catalyst for class discussion.
MAS as a scaffold for class discussion.
MAS as a springboard for class discussion.
CONCLUDING REMARKS
NOTES
REFERENCES
8. MATHEMATICAL CREATIVITY AND MATHEMATICS EDUCATION: A Derivative of Existing Research
INTRODUCTION
IDENTIFICATION AND DEVELOPMENT OF MATHEMATICAL CREATIVITY
THE PROCESS OF CREATIVE MATHEMATICAL ACTIVITY
THE WALLAS MODEL OF PROBLEM SOLVING
MORE REMARKS ON INCUBATION
FALLIBILITY AND CRATIVE MATHEMATICAL ACTIVITY
THINKING AS MATHEMATICIANS
CONCLUSION
NOTES
REFERENCES
9. GIFTED EDUCATION IN RUSSIA AND THE UNITED STATES: Personal Notes
ABOUT MY EXPERIENCE
ON TECHNOLOGY IN MATHEMATICS GIFTED EDUCATION
ON THE PLACE OF TEACHING THE MATHEMATICALLY GIFTED IN THE EDUCATION SYSTEM
SOME PRACTICAL OBSERVATIONS
Public Opinion
Opportunities for Children
On Teachers
CONCLUSION: SO WHAT SHOULD WE DO?
REFERENCES
10. SEMIOTIC MICROWORLD FOR MATHEMATICAL VISUALIZATION
INTRODUCTION
MICROWORLD TOOLS FOR MATHEMATICAL VISUALIZATION
SEMIOTIC TOOLS FOR MATHEMATICAL VISUALIZATION
MATHEMATICAL VISUALIZATION WITH TURTLE BLOCKS
CLOSING REMARKS
REFERENCES
11. MATHEMATICALLY GIFTED STUDENTS IN INCLUSIVE SETTINGS: The Example of New Brunswick, Canada
INTRODUCTION: CONTEXT AND ISSUES
GIFTED EDUCATION IN CANADA: A BRIEF PORTRAYAL
NEW TRENDS IN MATHEMATICS EDUCATION: WHAT DOES IT BRING TO GIFTED STUDENTS?
INNOVATIVE PROJECTS AND NEW OPPORTUNITIES FOR GIFTED
EXAMPLES OF EXTRACURRICULAR INITIATIVES
CONCLUSIVE REMARKS ON UNSOLVED ISSUES
REFERENCES
12. PROSPECTIVE SECONDARY MATHEMATICS TEACHERS’ MATHEMATICAL CREATIVITY IN PROBLEM SOLVING: A Turkish Study
CONCEPTUAL FRAMEWORK
THE STUDY
THE PROBLEMS
DATA SOURCES
A SAMPLE PROBLEM AND SOLUTIONS
Problem
S9’s Solution for the Problem
S5’s Solution to the Problem
S4’s Solution for the Problem
Excerpt from S4’s Journal [solution has been translated/described above]
DATA ANALYSIS AND RESULTS
FINDINGS AND DISCUSSION
Logical Thinking
DISCUSSION
Difficulties
Creative Thinking Skills
Personal Choices
Logical and Intuitive Thinking
Other Affective Factors
Differences between Uses of Strategies
CONCLUSIONS
NOTES
REFERENCES
13. WHAT CHARACTERISES HIGH ACHIEVING STUDENTS’ MATHEMATICAL REASONING?
INTRODUCTION
Research Question
Literature Review
CONCEPTUAL FRAMEWORK
CREATIVE REASONING
IMITATIVE REASONING
Memorized Reasoning
Algorithmic Reasoning
METHODS
Procedures
Participants
Tasks
ANALYSIS
METHODOLOGICAL ISSUES
Validity
Reliability
RESULTS
Attacking the Problem
– Alf Description
Interpretation
– Anna Description
Interpretation
– Hege Description
Interpretation
The Prompt and Solution
– Alf Description
Interpretation
– Anna Description
Interpretation
– Hege Description
Interpretation
DISCUSSION
REFERENCES
14. FOSTERING CREATIVITY THROUGH GEOMETRICAL AND CULTURAL INQUIRY INTO ORNAMENTS
INTRODUCTION
CREATIVITY PATHWAYS
MATHEMATICS EDUCATION IN CULTURAL CONTEXT
EDUCATIONAL FRAMEWORK
EXAMPLES OF CREATIVE ACTIVITIES
Example 1
Example 2
Example 3
Experience of Learning Mathematics with Applications
Experience of Learning Geometry in Cultural Context
Experience of Connecting Geometry with Culture and Art
Geometrical View of Visual Patterns
Curiosity and Pride in Own Cultural Heritage
Interest, Motivation and Readiness to Teach Geometry in Cultural Context
Self-directed Inquiry
The Impact of the Technion Seminar
DISCUSSION AND CONCLUSION
ACKNOWLEDGEMENT
REFERENCES

Meeting the Needs of Your Most Able Pupils: Mathematics

(The Gifted and Talented Series)
McClure, Piggott

Routledge | 2007 | 147 páginas | PDF | 1,7 MB

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Meeting the Needs of Your Most Able Pupils: Mathematics provides specific guidance on:

• recognising high ability and potential
• planning, differentiation, extension and enrichment in Mathematicss
• teacher questioning skills
• support for more able pupils with special educational needs (dyslexia, ADHD, sensory impairment)
• homework
• recording and assessment
• beyond the classroom: visits, competitions, summer schools, masterclasses, links with universities, businesses and other organisations.

The book includes comprehensive appendices with linked resources available online that feature:

• lesson plans and examples of activities
• departmental procedures and action plans
• identification strategies
• guidance on auditing provision for more able pupils.

This book is an essential resource for secondary teachers, subject heads of departments, leading teachers for G&T Education (gifted and talented co-ordinators), SENCos and LA advisers.