Journal articles on the topic 'Mathematics and visual arts'

Mathematics and visual arts have long shared aspects of both form and function. One such ancient connection is found in the golden ratio. This article introduces the reader to this unique mathematical phenomenon in three separate contexts: (1) historical, (2) mathematical, and (3) pedagogical. A brief history of this fascinating number, various teaching strategies, and a project for middle school mathematics students will be explored. A list of resources is given for further study.

AbstractThis study evaluates the effects of the Mathematics, Arts, and Creativity in Education (MACE) program on students’ ability in geometry and visual arts in the upper grades of elementary school. The program consisted of a lesson series for fourth, fifth, and sixth grade students in which geometry and visual arts were integrated, alongside with a professional development program for teachers. A quasi-experimental study was conducted in which three groups of teachers and their classes were investigated. One group of teachers taught the lesson series and followed a professional development program (n = 36), one group of teachers only taught the lesson series (n = 36), and a comparison group taught a series of traditional geometry lessons from mathematical textbooks (n = 43). A geometrical ability, creativity, and vocabulary test and a visual arts assignment were used in a pre- and post-measurements to test the effects of the MACE program. Results showed that students who received the MACE lesson series improved more than students who received regular geometry lessons only in geometrical aspects perceived in a visual artwork. Regarding students’ understanding and explanation of geometrical phenomena and geometrical creative thinking, all students improved, but no differences between the groups were found, which implies that on these aspects the MACE program was as effective as the comparison group that received a more traditional form of geometry education.

The Mathematics of beauty and beauty in mathematics are important ingredients in learning in the liberal arts. The Fibonacci numbers play an important and useful role in this. This paper seeks to present and illustrate a grounding of visual aesthetics in natural mathematical principles, centered upon the Fibonacci numbers. The specific natural mathematical principles investigated are the Fibonacci numbers, the Fibonacci Spiral, and the Cosmic Bud.

This article addresses the need for research in the areas of Grade R curriculum and pedagogy, Grade R teacher professional development, and early years mathematics teaching. More specifically, it responds to the need for teacher professional development in Grade R mathematics teaching of the geometric concepts of space and shape. The article describes a study about teachers’ understanding of how visual arts can be used as pedagogical modality. The study was prompted by the findings of a ‘Maths and Science through Arts and Culture Curriculum’ intervention undertaken with Grade R teachers enrolled for a Bachelor of Education (Foundation Phase) degree at a South African university. Post-intervention, teachers’ classroom practices did not change, and they were not using visual arts to teach mathematical concepts. The lessons learned from the research intervention may contribute to the wider debate about Grade R teaching and children’s learning.

When designing a mathematics capstone course for preservice teachers entitled 'Mathematical Patterns and Structures through Inquiry,” I wanted to include contexts in which mathematics provides the underlying structure for various visual and performing arts. The book Mathematical Quilts: No Sewing Required (Venters and Ellison 1999, p. 78) looks at a number of ways that mathematical concepts—such as the golden ratio, logarithmic spirals, Pythagorean triples, and Penrose tiles—are useful to know when designing various quilt patterns.

The author experiments with a product-delay algorithm as a means of creating graphic de-signs on a computer. With the product-delay algorithm and a little imagination, it is possible to create a wide variety of artistic patterns, several examples of which are presented here.

Abstract I have investigated interfaces about the arts and digital media in mathematics education, conceptualizing the notion of digital mathematical performance (DMP). In this article, I discuss connections between: (a) the mathematical strands and processes of the K-8 Ontario Mathematics Curriculum in Canada, and; (b) DMP produced by students. Based on the analysis of twenty-two DMP, I argue that DMP may offer ways to: (1) explore most of the mathematical processes of the Ontario Curriculum, and; (2) open windows into the exploration of math contents. I highlight the educational significance in practicing DMP as an innovative process that integrates multimodality, playfulness, and creativity. In contrast, I have found that the production of DMP does not guarantee the in-depth connection between the math strands and processes of the Curriculum. Generally, students explored contents about Geometry, which is not surprising, regarding the visual nature of both: geometrical and digital media representations.

In its document, the Curriculum and Evaluation Standards for School Matheniatics (1989), the National Council of Teachers of Mathematics recommended instruction connecting mathematics to other content areas. The “IDEAS” section for this month presents activities that offer connections between mathematics and the visual arts.

There is a growing interest in the use of visual thinking techniques for promoting conceptual thinking in problem solving tasks as well as for reducing the complexity of ideas expressed in scientific and technical formats. The products of visual thinking, such as sketchnotes, graphics and diagrams, consist of ‘multimodal complexes’ that combine language, images, mathematical symbolism and various other semiotic resources. This article adopts a social semiotic perspective, more specifically a Systemic Functional Multimodal Discourse Analysis approach, to study the underlying semiotic mechanisms through which visual thinking makes complex scientific content accessible. To illustrate the approach, the authors analyse the roles of language, images, and mathematical graphs and symbolism in four sketchnotes based on scientific literature in physics. The analysis reveals that through the process of resemiotization, where meanings are transformed from one semiotic system to another, the abstractness of specialized discourses such as physics and mathematics is reduced by multimodal strategies which include reformulating the content in terms of entities which participate in observable (i.e. tangible) processes and enhancing the reader/viewer’s engagement with the text. Moreover, the compositional arrangement creates clear stages in the development of the ideas and arguments that are presented. In this regard, visual thinking is a form of cultural communication through which abstract ideas are translated and explained using a multimodal outline or summary of essential parts by adapting resources (e.g. linguistic resources and mathematical graphs), using new resources (e.g. stick figures and other simple schematic drawings) and maintaining others from the original text (e.g. mathematical symbolic notation), resulting in a congruent (or concrete) depiction of abstract concepts and ideas for a non-specialist audience.

The present paper introduces the conceptual framework for an artificial system for visual creativity addressing the idea of niche creativity that is domain specific and non-anthropocentric in its conceptual approach. We think that the visual creative output of the system reflects the artificial medium and the specific artificial processes engaged in its production and, therefore, it is an expression of the idea of embodied creativity with the proposed system offering in this sense an example of digital embodiment of creativity. Although our approach to artificial creativity is non-anthropocentric, the system design is inspired by processes in the natural world that lead to the production of new and useful structures in both living and non-living systems with human creative cognition being included among these processes. The main problem raised by this abstract approach to artificial creativity in visual arts is the compatibility of its artistic production with human aesthetics, the ultimate goal of the proposed system being to produce visual output that would aesthetically engage human visual perception.

This essay looks at the seminal work of Bauhaus practitioners Wassily Kandinksy and Oskar Schlemmer in terms of their multidisciplinary approach to the performing arts, and the dance in particular. Whilst their contribution has been widely recognized in terms of a cross-pollination of ideas from the fine arts to the performing arts, this essay also addresses the influence that compositional methods, based on techniques derived from figural drawing, as well as the study of form and geometry, might have had in their choreographic practice. I argue that despite stylistic similarities, these works present a divergent approach to the question of a geometrized motion design, which Schlemmer called ‘mathematics in motion’. I discuss the concept of ‘abstract dance’ promoted by Kandinsky, in terms of a visualistic method, where movement is rendered both as a succession of still images and as an imaginary process. Schlemmer, on the other hand, promoted a synthesis of abstract and physical, as part of a model for live performance known as ‘balletic mathematics’. I expand on this distinction in terms of a differential sense schematic approach to movement, one being visual, the other proprioceptive. Landmark works produced by these artists during the Bauhaus years (1922–1933) are called upon as case studies, including Kandinsky's Dance Curves (after Gret Palucca), and Schlemmer's renowned Stäbetanz.

“Fractions have always represented a considerable challenge for students, even into the middle grades,” noted Van de Walle (2004, p. 242), and the instructional experiences of most teachers validate this statement. Despite the fact that proportional reasoning is an important curriculum topic and a valuable life skill, students struggle to meaningfully grasp fraction concepts. To aid development of the concept of fractions, the National Council of Teachers of Mathematics (2000) recommends that students represent fractions by using physical materials and number lines. The visual and tactile input these materials afford, coupled with carefully designed reflection on the use of these tools, can bolster learning about fractions.

ObjectiveUsing a science, technology, engineering, arts, and mathematics (STEAM) curriculum, we developed, piloted, and tested the Headache and Arts Program. This program seeks to increase knowledge and awareness of migraine and concussion among high school students through a visual arts–based curriculum.MethodsWe developed a 2-week Headache and Arts Program with lesson plans and art assignments for high school visual arts classes and an age-appropriate assessment to assess students' knowledge of migraine and concussion. We assessed students' knowledge through (1) the creation of artwork that depicted the experience of a migraine or concussion, (2) the conception and implementation of methods to transfer knowledge gained through the program, and (3) preassessment and postassessment results. The assessment was distributed to all students prior to the Headache and Arts Program. In a smaller sample, we distributed the assessment 3 months after the program to assess longitudinal effects. Descriptive analyses and p values were calculated using SPSS V.24 and Microsoft Excel.ResultsForty-eight students participated in the research program. Students created artwork that integrated STEAM knowledge learned through the program and applied creative methods to teach others about migraine and concussion. At baseline, students' total scores averaged 67.6% correct. Total scores for the longitudinal preassessment, immediate postassessment, and delayed 3-month postassessment averaged 69.4%, 72.8%, and 80.0% correct, respectively.ConclusionThe use of a visual arts–based curriculum may be effective for migraine and concussion education among high school students.

Many studies have shown a link between being competent in early mathematics and achievement in school. Early math skills have the potential to be the best predictors of later performance in reading and mathematics. Movement and songs are activities that children like, making it easier for teachers to apply mathematical concepts through this method. This study aims to develop audio-visual learning media in the form of songs with a mixture of western and traditional musical idioms, accompanied by movements that represent some of the teaching of early mathematics concepts. The stages of developing the ADDIE model are the basis for launching new learning media products related to math and art, and also planting the nation's cultural arts from an early age. These instructional media products were analyzed by experts and tested for their effectiveness through experiments on five children aged 3-4 years. The qualitative data were analyzed using transcripts of field notes and observations and interpreted in a descriptive narrative. The quantitative data were analyzed using gain score statistics. The results showed that there was a significant increase in value for early mathematical understanding of the concepts of geometry, numbers and measurement through this learning medium. The results of the effectiveness test become the final basis of reference for revision and complement the shortcomings of this learning medium. Further research can be carried out to develop other mathematical concepts through motion and song learning media, and to create experiments with a wider sample. Keywords: Early Mathematical Skills, Movement and Song Idiom Traditional, Audio-visual Learning Media References An, S. A., & Tillman, D. A. (2015). Music activities as a meaningful context for teaching elementary students mathematics: a quasi-experiment time series design with random assigned control group. 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The author reflects on the process by which his background in science and engineering and interest in the arts inspired his creation of an original painting style that he calls Wave Space Art, along with the invention/discovery of a mathematical conception of geometric transformations called GridField Geometry. He reviews the development of his techniques, including his employment of mathematics, optics, color psychology, the science of sound and the structure of music.