The education of mathematically gifted students: Some complexities and questions

In this paper I analyze some complexities in the education of mathematically gifted students. The list of issues presented in this paper is not inclusive; however, all of them seem to be typical on the international scope. Among these issues are: (1) the gap between research in mathematics education and the research in gifted education; (2) the role of creativity in the education of the gifted and the theoretical perspective on the relationship between creativity and giftedness, and (3) teaching the gifted and the teachers of gifted, including relationships between the equity principle in mathematics education and views on the education of gifted. In the paper I outline some actual research questions in the field of education of mathematically gifted

Looking back at the beginning: Critical thinking in solving unrealistic problems

We believe that problem-solving skills engage critical thinking at every phase of problem solution. In this research a special attention is given to the fist phase - understanding the problem . We consider this phase as a continuation of all the previous mathematical experience, in which understanding of new problems requires looking back at those solved in the past. Evaluation of the givens in the problem sometimes allows immediate solution whereas in other cases it shows that solution does not exist. We found that it is not easy for mathematics teachers to discover that a problem includes contradictory (i.e. unrealistic) conditions. We suggest that such problems should be included into teachers\u27 professional development programs to develop teachers\u27 awareness of the importance of mathematical accuracy and connectedness

Prospective teachers’ conceptions about teaching mathematically talented students: Comparative examples from Canada and Israel

In this paper we analyze prospective mathematics teachers\u27 conceptions about teaching mathematically talented students. Forty-two Israeli participants learning at mathematics education courses for getting their teaching certificates, and fifty-four Canadian pre-service (K-8) teachers participating in mathematics didactics course were asked to solve a challenging mathematical task. We performed comparative analysis of problem-solving strategies, solution results and participants\u27 success. Based on the discussion with 25 Israeli participants we composed an attitude questionnaire, in which prospective teachers were asked to express their degree of agreement with statements expressing different beliefs about education of mathematically talented students. The questionnaire was presented to 56 Canadian and 28 Israeli prospective elementary and middle school teachers. We describe similarities and differences between the attitudes of the two populations and suggest their possible explanations. Based on the results of this study we make several suggestions for teacher education programs

Learning through teaching mathematics : development of teachers knowlegde and expertise in practice

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Creativity and expertise: The chicken or the egg? Discovering properties of geometry figures in DGE

International audienceThe relationship between mathematical creativity, knowledge and expertise is a phenomenon which can be seen as a " creativity-knowledge dilemma " : Having knowledge is a necessary condition for a person to be creative; on the other hand, creativity is an important condition for knowledge construction. In this paper, we analyze mathematical activity that is directed at both the development of problem solving expertise and creativity in geometry. Creativity in this study is connected to the discovery of new properties of the given geometrical objects through investigation in DGE. We introduce a framework for the analysis of the complexity of a discovered property. Based on the analysis performed, we hypothesize that (1) discovery skills can be developed in people with different levels of problem solving expertise while the range of this development depends on the expertise; (2) the discovery process is rooted in the problem solving expertise of a person

Introduction to the papers of TWG07: Mathematical potential, creativity and talent

International audienceThis was the third CERME at which Thematic Working Group (TWG) “Mathematical potential, creativity and talent” took place. One of the central goals of this TWG was to raise attention of the mathematics education community to the field of mathematical potential, creativity and talent, and to promote empirical and theoretical research that will contribute to the development of our understanding in the field. In 2011, 25 participants from 14 countries discussed 15 contributions. This time (2015), 35 participants took part in the TWG discussions about 24 contributions by researchers and practitioners from 15 countries from different parts of the world. The TWG facilitated communication between educational researchers, mathematics educators and research mathematicians focusing on the nature and nurture of mathematical creativity in all students and high mathematical ability in particular individuals. Following the debates at TWG07 at CERME7 and CERME8, we continued an international exchange of ideas related to the research into the identification of mathematical talent, the didactics of teaching highly able students as well as the promotion of creativity in all students