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The paper deals with the possibility of enriching the curriculum in mathematics, informatics and art by means of visual modelling of abstract paintings. The authors share their belief that in building a computer model of a construct the students gain deeper insight into the construct and are especially motivated to elaborate their knowledge in math...
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... Integrating computational design into mathematics and art lessons seems to be a promising combination to engage students in these areas [33]. Sendova et al. [32] provide examples of computational design in the service of creative and artistic experiments, suggesting that in such an environment, it is easier to experiment with abstract concepts like colors, harmony, and tensions. ...
... These in the arts. Early constructionist scholars Bamberger and Sendova sought to use computation to elevate music and art education, respectively (Bamberger, 1996;Bamberger & Hernandez, 2000;Sendova, 2001;Sendova & Grkovska, 2005). Bamberger's work leveraged computational composition of music, allowing students to construct music from differing primitive sizes and representations (Bamberger, 1996). ...
... Bamberger's work leveraged computational composition of music, allowing students to construct music from differing primitive sizes and representations (Bamberger, 1996). Sendova's work was situated between math, computing, and art fields, and strongly featured the computational creation of abstract art (Sendova, 2001;Sendova & Grkovska, 2005). In this work, Sendova designed learning experiences in which learners could enrich the study of mathematics, informatics, and art by visually modeling abstract paintings (Sendova & Grkovska, 2005). ...
... Sendova's work was situated between math, computing, and art fields, and strongly featured the computational creation of abstract art (Sendova, 2001;Sendova & Grkovska, 2005). In this work, Sendova designed learning experiences in which learners could enrich the study of mathematics, informatics, and art by visually modeling abstract paintings (Sendova & Grkovska, 2005). Across these initiatives, they found that learners used not only used great creativity in making their artistic representations but needed to apply mathematical knowledge and practices (i.e., transformations, rabatment, rule of thirds), observed the world around them with a new perspective, and used mathematic and computational knowledge to gain deeper insight into art compositions (Sendova & Chehlarova, 2013;Sendova & Grkovska, 2005). ...
Art has been tied to scientific and technological advancements throughout history, providing methods and mediums for communication, expression, and exploration. Art is a dialogic domain that evolves with the technological advances in society–incorporating technology and computational tools to create new genres of art. We live in an increasingly computational and technological society, which is reflected in the emergence of many new tech-based and computational genres of art. Computers and computation have dramatically changed how and what artists can create and what ideas can be explored. Yet is naïve to assume that this is a one-way relationship that computing has changed the arts. In fact, since the advent computation, artists have been leveraging, critiquing, extending, and creating, computational tools as part of their artistic practice. The relationship between the artist and computer is important to people in both the arts and sciences, as well as to society as a whole.
Our increasingly computational world necessitates greater computational literacy. Not only are computers being used in everyday contexts, but the practices in myriad domains are transformed as they incorporate new computational tools and methods. As such, there has been an increased push for computing education and while these efforts have received support from funders and educators, major questions remain unanswered regarding how best to facilitate computing education for all–or for that matter, what computing education should entail. This dissertation seeks to contribute towards these efforts expanding computing for all by pushing on our understanding and exploration of the concept of computational thinking (CT). As we move toward providing all students with opportunities and experiences in computing, it is vital to reflect on how we are representing computational ways of thinking and knowing, in additional to computational practices. Are we, as a field, privileging computing education that is designed to fill future jobs, or are we representing the diverse ways that computing can be leveraged in real world contexts?
In parallel with other constructionist scholars exploring the intersection of CT and Science, Technology, Engineering and Mathematical disciplines (STEM), this work constructs a situated definition of CT in the arts in order to broaden access to computational and artistic practice as well as to increase the perspectives and epistemologies represented in computing education. We are at a beautiful time in history where computation is relatively young and evolving at a rapid pace. Artists are in the process of incorporating these computational tools, negotiating what computation should mean for society, and sparking new pathways for computational progress. In order to capture these practices, this work leverages methodological approaches of others who have constructed situated definitions of CT in STEM through interviews with practicing computational scientists and mathematicians–exploring the computational art experiences of artists in order to capture their unique perspectives.
This dissertation leverages qualitative methodology, particularly in-depth case studies, to develop an understanding of the computational practices and perspectives of artists. A new theory and associated methodology, called computational art ecologies, is explicated and applied to analyze the ten distinct cases and then used to systematically characterize artists’ practice within the rich landscape of computational and technology-based art. These cases highlight unique practices, perspectives, experiences, and relationships between computation and art. They also highlight the rigorous computational practices and epistemologies that emerge in computational art. Finally, the practices and perspectives identified through these cases are consolidated to develop an emergent Framework of Computational Engagement and Perspectives in the Arts. This framework advances scholarship around computational thinking, particularly that of constructionist scholars who have worked to develop situated definitions of computational thinking across contexts and domains. This new theory and associated methodology are introduced to allow for a systematic approach to capturing these diverse artistic experiences with computation. Additionally, we contribute to efforts in computing education to identify situated computational thinking and to expand definitions of computing education to reflect the diversity of computational practice in the world.
... This finding is compatible with the findings of Laborde, Kynigos, Hollebrands and Strasser (2006); in that learning is not quite easy in the environments where dynamic geometry construction is used as the students reconstituted their own geometry knowledge. In addition, Baltaci and Yildiz (2015) and Sendova and Grekovska (2005) pointed out that building a computer model of a construct is motivated to elaborate one's knowledge in mathematics. ...
Geometric constructions have already been of interest to mathematicians. However, studies on geometric construction are not adequate in the relevant literature. Moreover, these studies generally focus on how secondary school gifted students solve non-routine
mathematical problems. The present study aims to examine the geometric construction abilities of ninth-grade (15 years old) gifted students in solving real-world geometry problems; thus a case study was conducted. Six gifted students participated in the study. The data consisted of voice records, solutions, and models made by the students on the GeoGebra screen. Results indicate that gifted students use their previous knowledge effectively during the process of geometric construction. They modeled the situations available in the problems through using mathematical concepts and the software in coordination. Therefore, it is evident that gifted students think more creatively while solving problems using GeoGebra.
... Mathematics teachers and instructors are attempting to develop various strategies to make mathematics interesting and meaningful (Penas & Guzon, 2011). Several studies indicate that classroom work may be made more enjoyable using dynamic geometry software (Furner & Marinas, 2011;Kutluca & Zengin, 2011;Sendova & Grekovska, 2005;Wakwinji, 2011). Therefore, teachers should be attentive and use GeoGebra efficiently in their classrooms (Baltaci & Yildiz, 2015). ...
One of the definitions of mathematics is that it is "a science of patterns and themes". Within the scope of this definition, the current software technology facilitates the creation of visuals and patterns. Thus, GeoGebra software was used. The study was carried out in two stages. In the first stage, the Dynamic Geometry Software and the Discovery of Mathematical Concepts class was taught. In the last stage, the preservice primary mathematics teachers were given an assignment and asked to continue in groups. The groups were told that they were expected to produce aesthetically pleasing visuals and patterns. Therefore this research aimed at investigating how preservice teachers determine the design process and how they solve problems encountered during the process. Thus, as can be seen in the literature, the method and design as a long term study are the new contributions to the literature. Case study was carried out with 39 second-year preservice mathematics teachers. The research data were collected through preservice teachers' finalized projects which included a Microsoft-Word document that described in detail the process, screenshots, and GeoGebra applications. The data were analyzed by using the content analysis technique. As a result of this study, preservice mathematics teachers entered into research and analysis activities, investigated to create original designs, spent more time on the significance of visuals and patterns and so many groups made various creative tasks.
... By building computer models of a given painting the students can gain deeper insight in its structure and elaborate their understanding in mathematics, informatics and art. An inspirational synergy among these disciplines was achieved in the context of visual modeling [10] within the pre-service teacher education (4 th year students in mathematics and informatics) at the Faculty of mathematics and informatics (Sofia University). The first topic for the students was to create variations on models of costumes designed by the great French artist from Russian origin Sonia Delaunay for the Diaghilev's ballet (Fig. 4) With all the models we would start with a stylized version and then identify the geometric figures and transformation to be used in order to create a close enough approximation of the model. ...
The paper presents the authors’ experience in stimulating the synergy of disciplines via active learning methods; the emphasis
being on project based learning. Promoting this method is demonstrated in the context of teachers’ training courses and developing
a set of IT textbooks. Numerous examples are presented showing that the synergy of various disciplines is quite natural when
performed in the context of studying IT. The project samples developed by teachers are inspired by ideas in textbooks and
are accomplished by means of specially designed computer applications. The importance of working on projects tuned to the
learner’s interest as a decisive motivation factor is emphasized. In addition authors show that the bouquet of projects becomes more colorful with every new issue of the courses thanks to the learners’ creativity and the collaborative
knowledge building.
