• Prof. Hristo Beloev, Rector of the University of Rousse, Bulgaria.

• Prof. Mārcis Auziņš, Rector of the University of Latvia.

• Prof. Margarita Teodosieva, Dean of the Faculty of Natural Sciences and Education of the University of Rousse, Bulgaria.

The goal of Discussing Group 9 is to support productive discussions about important current problems, issues and challenges relevant to promoting creativity for all students in mathematics education.
This discussion group will have four main aims:

• to examine the concept of mathematical creativity;

• to analyze whether all students can and should be mathematically creative;

• to explore environmental effects on the mathematical creativity of students;

• to consider how mathematical creativity might be assessed and how assessment might affect the development of mathematical creativity.

The group will address these focus questions and/or others that may be suggested by interested participants. Research in support of responses to these questions is strongly encouraged.

1. WHAT IS MATHEMATICAL CREATIVITY AND WHICH MATHEMATICS STUDENTS CAN AND SHOULD BE CREATIVE?

• Is mathematical creativity a property of a person, a problem, a solution, a process or a teaching technique?

• Is mathematical creativity domain specific?

• How does mathematical creativity relate to general concepts of mathematics, mathematical problem solving, problem posing, research, and creativity? Can ‘concepts’ be creative, rather than simply ‘problems’ or ‘solutions? What would this mean?

• Should mathematical creativity be something new to the world or can it be just new to the creator?

• Is it enough to have ideas that are novel and innovative or must creative mathematics be applied to mathematical problem solving?

• Can all mathematics students be creative? Is mathematical creativity dependent on mathematical talent or is it a distinct trait?

• Can creativity be developed? Is it innate? Can it be taught?

• Is an in-depth knowledge of mathematics a prerequisite for becoming mathematically creative?

2. WHAT IS THE ROLE OF THE TEACHER AND OTHERS IN RECOGNIZING AND PROMOTING MATHEMATICAL CREATIVITY? WHAT IS THE GOAL IN DOING THIS?

• How should we prepare teachers to foster mathematical creativity in all students?

• Is there a difference between the ‘creative teacher’ and the ‘productive teacher’? between the ‘creative teacher’ and the teacher of mathematical creativity?

• Must the teacher be mathematically creative to foster student creativity?

• Should a teacher to demonstrate his or her mathematical creativity? If so, how and when should this be done?

• What might teachers, students, parents, or others do to foster (or inhibit) creativity?

• Should mathematical creativity be made an explicit goal/critical area in mathematic education? If so, how?

• Will a focus on mathematical creativity distract from other critical areas of mathematics education?

• Should mathematical concepts and skills be learned creatively or should they be memorized before students are encouraged to be creative?

• What methods of instruction might stimulate students to create new problems, solve problems uniquely, conduct research work in mathematics, etc.?

• What is the role of motivation in creativity?

• When do we look for creativity? How? Where?

• Is it ever too late to search for creativity?

• What might the benefits be of teaching creativity in mathematics, for students who will not become mathematicians? Are we developing creative students simply for the benefit of society (or of the economy)? Or is there an intrinsic value to the individual of developing the faculty of creativity?

3. HOW MIGHT MATHEMATICAL PROBLEMS BE USED TO DEVELOP MATHEMATICAL CREATIVITY? HOW MIGHT MATHEMATICAL CREATIVITY BE ASSESSED? HOW DO WE EVALUATE OUR SUCCESS IN DEVELOPING MATHEMATICAL CREATIVITY IN ALL STUDENTS?

• What are examples of good investigations and problems that can be useful for promoting mathematical creativity?

• How might problems best be used to develop mathematical creativity?

• Can all mathematical problems be used to evoke a creative response? Should they be used in this way?

• How might assessment be used to promote rather than inhibit mathematical creativity so that all students might be creators and not simply consumers of knowledge?

• What are the effects of standardized or standards-based assessment on mathematical creativity?

• How do we know when creativity has ‘happened”? How do we put this phenomenon to use?

• What criteria might be used to recognize, encourage, and assess creativity? How do we recognize a creative act? Can we teach our students to recognize one? Is it the surprising solution? The brief solution? The solution that uses advanced notions? Or the simplest notions?

• How do we evaluate whether we have been successful at developing mathematical creativity?

4. HOW DO TECHNOLOGY, OTHER RESOURCES, AND THE ENVIRONMENT AFFECT THE MATHEMATICAL CREATIVITY OF THE STUDENT?

• Does the use of technology promote or inhibit students’ mathematical creativity?

• How might technology and other resources, including those outside the school setting, best be used?

• What environment best nurtures creativity? How does this environment differ from student to student, from grade to grade, from level to level, from subject area to subject area?

• How do these environments (or even the goals of these environments) vary in different cultures? Does ‘creativity’ mean the same thing in different social contexts? How is the creative individual viewed in different cultures?

• How do political contexts affect our work? How can we adapt to the constraints set up by our political situation? How can we influence the making of political decisions that affect us?

5. WHAT HAVE WE LEARNED AND WHERE DO WE GO FROM HERE?

• Can we summarize our findings?

• Are there major suggestions for future research?

• Should we explore a permanent professional society? Should it include both mathematical creativity and mathematical giftedness, talent, or promise? What about mathematical challenge?

<a style=“color:RED”href=“/document/get/447”>THE PAPERS OF 62 PARTICIPANTS FROM 25 COUNTRIES ARE INCLUDED IN THE PROCEEDINGS OF THE DG 9

The proceedings of the DG 9 ware published through the generous support of:

• the University of Rousse, Bulgaria, www.ru.acad.bg

• the University of Latvia, Riga, Latvia, www.lu.lv

• the Faculty of Natural Sciences and Education of the University of Rousse, Bulgaria.www.ru.acad.bg

Editors: Emiliya Velikova and Agnis Andžāns

• Linda Sheffield, USA