A Volume in The Montana Mathematics Enthusiast: Monograph Series in Mathematics Education Series Editor Bharath Sriraman, The University of Montana 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.
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. Enabling more students to achieve mathematical success: A case study of Sarah 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.