Mathematical Creativity and Mathematical Giftedness

This is another one of several ICME-13 monographs published after the 13th quadrennial International Congress on Mathematical Education held in Hamburg, Germany in July 2016. The contents include multiple perspectives on mathematical creativity and giftedness; learning environments for supporting mathematical creativity; strategies in problem-solving and problem posing; and technological tools to enhance learning with understanding. Contributions come from researchers in 12 countries: Romania, Cyprus, Germany, Spain, Israel and Palestine, Czech Republic, Italy, Greece, Latvia, Canada, Chile, and the USA. The volume begins with a chapter by the editor and ends with a commentary, while the bulk of the volume is divided into four parts organized around the following themes: frameworks for studying mathematical creativity and giftedness; characteristics of students with exceptional promise; teaching activities to foster creative learning; and tasks and techniques to enhance creative capacities. The book synthesizes papers presented at ICME-13 Topic Study Group 4 on Activities for, and Research on, Mathematically Gifted Students and ICME-13 Topic Study Group 29 on Mathematics and Creativity.

 

At least eight of the 14 chapters contain problems used in the authors’, or other researchers’, work on mathematical creativity. These are worthy of consideration by readers for use in their own courses. Problems are at all levels, even primary grades. For example:

 

 

Many problems are geometrical in nature and are hard to include in this review. 

 

Chapter 1 was written by the editor, Florence Mihaela Singer, of the University of Ploiesti in Romania, who provides helpful background, including evidence that creativity is domain specific so that it makes sense to speak of mathematical creativity, as opposed to general creativity. Also, cultivating mathematical creativity should include a variety of activities oriented toward abstraction and generalization.

 

Interestingly, Chapter 8 is devoted to twice-exceptional children—those with both high mathematical potential and educational special needs, such as difficulties with reading, spelling, or writing, attention deficit disorders, or autism. One difficulty with researching twice-exceptional children is the “masking effect”—such children are particularly at risk for having neither their mathematical potential nor their disabilities recognized. 

 

The volume has much to recommend it, especially to someone like me, who has not previously specifically considered research on mathematical giftedness. Still, one drawback is the subject index, which is remarkably skimpy at just 57 entries, each often having just one page number cited. For example, the term “cognitive demand” does not even occur, although Chapter 7 is titled. “The Cognitive Demand of a Gifted Student’s Answers to Geometric Pattern Problems: Analysis of Key Moments in a Pre-algebra Teaching Sequence.”

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Annie Selden is Adjunct Professor of Mathematics at New Mexico State University and Professor Emerita of Mathematics from Tennessee Technological University. She regularly teaches graduate courses in mathematics and mathematics education. In 2002, she was recipient of the Association for Women in Mathematics 12th Annual Louise Hay Award for Contributions to Mathematics Education. In 2003, she was elected a Fellow of the American Association for the Advancement of Science. She remains active in mathematics education research and curriculum development.