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Computational Creativity
 World Congres on Computational Intelligence
, 2006
"... Abstract — Creative thinking is one of the hallmarks of humanlevel competence. Although it is still a poorly understood subject speculative ideas about brain processes involved in creative thinking may be implemented in computational models. A review of different approaches to creativity, insight a ..."
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Abstract — Creative thinking is one of the hallmarks of humanlevel competence. Although it is still a poorly understood subject speculative ideas about brain processes involved in creative thinking may be implemented in computational models. A review of different approaches to creativity, insight and intuition is presented. Two factors are essential for creativity: imagination and selection or filtering. Imagination should be constrained by experience, while filtering in the case of creative use of words may be based on semantic and phonological associations. Analysis of brain processes involved in invention of new words leads to practical algorithms that create many interesting and novel names associated with a set of keywords. I.
The promise of interconnecting problems for enriching students ’ experiences in
"... enriching students ’ experiences in mathematics ..."
Article history
, 2013
"... This research is intended to study the characteristics of creativity in two practicalbased physics learning activities which are physics practical work (PPW) and physics innovative project (PIP) among preservice physics teacher at Universiti Teknologi Malaysia (UTM). The study was conducted in one ..."
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This research is intended to study the characteristics of creativity in two practicalbased physics learning activities which are physics practical work (PPW) and physics innovative project (PIP) among preservice physics teacher at Universiti Teknologi Malaysia (UTM). The study was conducted in one semester among 12 physics education undergraduates from the Faculty of Education, UTM. Two sets of survey questionnaires were used to collect data on characteristics of creativity in PPW and PIP respectively and the data was analyzed using descriptive analysis. The result of the study shows that six characteristics of creativity are highlighted more when the preservice physics teachers performed PIP except openness which are the same in both activities. Based on the findings, it is found that activities like inquiry based learning such as PIP can encourage more characteristics of creativity compared to PPW that is guided by manual books. Therefore, it is suggested that activities like PIP should be delivered to the preservice teachers as
Buad Khales
"... Abstract This study aimed at investigating the impact of a teacher training program on mathematics teaching methodologies using studentcentered learning. This study identified the teaching methods that math teachers used to implement learnercentered approach. To answer the research questions, the ..."
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Abstract This study aimed at investigating the impact of a teacher training program on mathematics teaching methodologies using studentcentered learning. This study identified the teaching methods that math teachers used to implement learnercentered approach. To answer the research questions, the researcher chose a sample of ten teachers. The researcher employed several tools in order to triangulate the data to bring it to a degree of credibility. Classroom observation, videotaping, interviews and teachers' and students' reflection analysis were all used to gather the research data. The results of the study revealed that some teaching methods were used more than others and teachers attributed this to the LTD program. The program helped them choose suitable methods that could match their students' different learning styles and different learning interests. The study results also showed the satisfaction of most of the students on the teaching methods used by teachers.
Teachers' views on creativity in mathematics education: an international survey
"... Abstract The survey described in this paper was developed in order to gain an understanding of culturallybased aspects of creativity associated with secondary school mathematics across six participating countries. All participating countries acknowledge the importance of creativity in mathematics, ..."
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Abstract The survey described in this paper was developed in order to gain an understanding of culturallybased aspects of creativity associated with secondary school mathematics across six participating countries. All participating countries acknowledge the importance of creativity in mathematics, yet the data show that they take very different approaches to teaching creatively and enhancing students' creativity. Approximately 1,100 teachers from six countries (Cyprus, India, Israel, Latvia, Mexico, and Romania) participated in a 100item questionnaire addressing teachers' conceptions about: (1) Who is a creative student in mathematics, (2) Who is a creative mathematics teacher, (3) In what way is creativity in mathematics related to culture, and (4) Who is a creative person. We present responses to each conception focusing on differences between teachers from different countries. We also analyze relationships among teachers' conceptions of creativity and their experience, and educational level. Based on factor analysis of the collected data we discuss relevant relationships among different components of teachers' conceptions of creativity as they emerge in countries with different cultures.
1 Preface
"... There are several people I would like to thank for support and help during these last four years I’ve been working on this dissertation. My main supervisors Anne Fyhn and Bharath Sriraman have been instrumental from beginning to end; offering advice, help and guidance whenever I needed it. Liv Sisse ..."
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There are several people I would like to thank for support and help during these last four years I’ve been working on this dissertation. My main supervisors Anne Fyhn and Bharath Sriraman have been instrumental from beginning to end; offering advice, help and guidance whenever I needed it. Liv Sissel Grønmo and Ragnar Soleng were also helpful along the way. I also want to thank my colleagues at the department of teacher education and fellow mathematics educators here at the University in Tromsø. In particular, I would like to mention my fellow doctoral student Gunnar Kristiansen who I shared an office with for four years. Gunnar and I have had many interesting and fruitful discussions over the years that have provided me with added insight and motivation in my own research project. In 20112012 I spent 7 months as a visiting scholar at the University of California, Berkeley. I want to thank the faculty of science and technology at the University of Tromsø for providing me with the opportunity to visit UC Berkeley. Finally, I want to thank my family who have always been supportive and believed in me. Thanks! This dissertation consists of an introduction and four articles. The articles are: 2
Mathematical Creativity: The Unexpected Links
"... Creativity in mathematics is identified in many forms or we can say is made up of many components. One of these components is The Unexpected Links where one tries to solve a mathematical problem in a nontraditional manner that requires the formation of hidden bridges between distinct mathematical do ..."
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Creativity in mathematics is identified in many forms or we can say is made up of many components. One of these components is The Unexpected Links where one tries to solve a mathematical problem in a nontraditional manner that requires the formation of hidden bridges between distinct mathematical domains or even between seemingly far ideas within the same domain. In this article, we design problems that express unexpected links in mathematics and suit students of intermediate and secondary levels. We prove their feasibility through teachers’ testimonies and through introducing them in classrooms and collecting students’ attitudes with respect to understanding and interest. Results confirm that students can sense such component and that designed problems had caught teachers ’ and students ’ interest.
Course Title: Mathematical Creativity: Theory and Research
"... Course Goals: In this course, the student will be exposed to contemporary research literature that involves problem sequencing in studies that attempt to study facets of creativity such as (1) reasoning by analogy, (2) Abstraction and (3) Generalization. Another aspect of the course is to situate th ..."
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Course Goals: In this course, the student will be exposed to contemporary research literature that involves problem sequencing in studies that attempt to study facets of creativity such as (1) reasoning by analogy, (2) Abstraction and (3) Generalization. Another aspect of the course is to situate the existing state of the art literature on the relationships between mathematical creativity and giftedness from mathematics education to the more general literature from psychology.
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"... This conversation began when I introduced the two authors in a hotel lobby in Cap Roig (Spain) after the close of CERME4 [1]. The conversation continued by email well after the evening had ended. (ed.) Bharath: I think that the notion of mathematical creativity among mathematicians is distinctly d ..."
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This conversation began when I introduced the two authors in a hotel lobby in Cap Roig (Spain) after the close of CERME4 [1]. The conversation continued by email well after the evening had ended. (ed.) Bharath: I think that the notion of mathematical creativity among mathematicians is distinctly different from the notion of creativity found in the mathematics education literature. What do you think? Do we even have an agreed upon definition of what mathematical creativity is? Is this important at all? Peter: I too wish to discuss the defining of creativity. This certainly is important. The writings in my dissertation express a slightly different parsing of creativity than the one you propose (i.e., among mathematicians, psychologists, teachers, mathematics educators). Bharath: I would like to give some background to the AHA! moment that you talked about (Liljedahl, 2004). The literature seems to attribute this construct to Wallas (1926) and his famous book The art of thought. Some authors erroneously attribute it to Hadamard and Poincaré due to the popularization of their writings. However, this construct was developed within Gestalt psychology in Germany in the very early part of the 20th century by Wertheimer, Koehler, and Koffka. Some historians push it back to the late 19th century to the writings of Mach (a physicist turned philosopher interested in the physiology of sensory perception). There is evidence of written communication between Poincaré, Hadamard and the Gestaltists, which could lead one to infer that Hadamard was influenced by the developments and the terminology within Gestalt psychology. Hence the use of the 3 or 4stage model from then on. I really liked your critique of the reductionist attempt of viewing creativity as a confluence of person, process and product, as well as your critique of the misconceptions that occur when using creative or creativity. Should we focus our conversation on the definition of creativity by considering each aspect (person, process and product) separately and then analyze whether this is consistent (or inconsistent) with various confluence models that combine the three along with societal variables proposed by researchers in psychology? Our attempt could perhaps be to construct a definition of creativity for the particular domain of mathematics and then seeing whether general definitions hold up?