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This paper investigates creativity in students' constructions of everyday examples about basis in Linear Algebra. We analyze semi-structured interview data with 18 students from the United States and Germany with diverse academic and social backgrounds. Our analysis of creativity in students' everyday examples is orga- nized into two parts. First, we analyze the range of students' creative products by investigating the mathematical variability in the more commonly mentioned examples. Second, we unpack some of the collective processes in the construc- tion of students' examples. We examine how creativity was distributed through the interactions among the student, the interviewers, and other artifacts and ideas. Thus, in addition to contributing to the process vs. product discussion of creativity, our work also adds to the few existing studies that focus on collec- tive mathematical creativity. The paper closes with connections to anti-deficit perspectives in mathematics education and some recommendations for individual and collective creativity in the classroom. [ABSTRACT FROM AUTHOR]

Creativity is a broad phenomenon that scholars have interpreted in a multitude of ways. We notice that a majority of the views describe creativity as something innate. This paper aims to verge from this perspective and explore creativity in terms of the constant mutual interaction of a person and their environment. Using the theoretical framework, enactivism, and the notion of emergence, we investigate the creative processes involved in musical improvisations of south In- dian classical or Carnatic music and mathematical proof generation. Interview excerpts from professional Carnatic musicians and research mathematicians on their respective creative processes during musical improvisation and proof gen- eration are analyzed. This study gives a perspective to think about creativity, with an emphasis on emergence. This paper has been partly informed by self- reections on musical improvisations and mathematical proof generation by the first author, who is a performing Carnatic vocalist and a mathematician. [ABSTRACT FROM AUTHOR]

As mathematics teachers, we hope our students will approach problems with a spirit of creativity. One way to both model and encourage this spirit | and, at the same time, to keep ourselves from getting bored | is through creative ap- proaches to problem design. In this paper, we discuss TACTivities, mathematical activities with a tactile component, as a creative outlet for those of us who teach mathematics, and as a resource for stimulating creative thinking in our students. We use examples, such as our derivative fridge magnets TACTivity, to illustrate the main ideas. We emphasize that TACTivities can be engaging, to teachers and learners alike, at any level of mathematics, by including examples from dif- ferent mathematics courses (calculus and mathematics for elementary teachers). As an example, our derivative fridge magnets have moving pieces of words that look like small refrigerator magnets. These small pieces can be combined to make true mathematical statements, of the form d=dx (some function) = some other function. There was creativity involved in the creation of these magnets, as the mathematics had to be challenging enough not to bore students yet have an easy entry for students to be successful. The students working with the magnets can use their creativity along with their mathematical knowledge while learning and/or reviewing a mathematical concept|in this case derivatives. We will ex- pand on the creative side of the creation and implementation of TACTivities in this paper. Note that our definition of tactile only means moving pieces (usually pieces of paper), as this is different than work from others that involves tactile props such as pipe cleaners, yarn, Spirographs, building blocks, and so on. This other work is invaluable, and we use props like these ourselves at times, but we believe that our TACTivities add a different dimension to tactile learning. [ABSTRACT FROM AUTHOR]

Although much creativity research has suggested that creativity is inuenced by cultural and social factors, these have been minimally explored in the context of mathematics and mathematics learning. This problematically limits who is seen as mathematically creative and who can enter the discipline of mathematics. This paper proposes a framework of creativity that is based in what it means to know or do mathematics and accepts that creativity is something that can be nurtured in all students. Prominent mathematical epistemologies held since the beginning of the twentieth century in the Western mathematics tradition have different implications for promoting creativity in the mathematics classroom, with fallibilist and social constructivist perspectives arguably being most conducive for conceiving of creativity as a type of action for all students. Thus, this paper proposes a framework of creative mathematical action that is based in these epistemologies and explains key aspects of the framework by drawing connections between it and research in the field of creativity. [ABSTRACT FROM AUTHOR]

The goal of the Creativity in Mathematics and Science project, funded by the National Science Foundation's [NSF's] Improving Undergraduate STEM Educa- tion program, is to reconsider how we teach mathematics at the collegiate level. Over the last three years, we have developed interdisciplinary modules that seek to encourage students, including non-STEM majors, to see mathematics in un- expected places, make connections to their own interests and disciplines, and explore creativity in mathematics. Relying on traits of creativity such as the abil- ity to connect ideas, be inquisitive, question norms, and have exibility [1], we encouraged students to participate and understand mathematics in unconven- tional ways. The scheduling of a professional juggling company's performance at our on-campus theater inspired us to create a module connecting mathematics and juggling for both a general education mathematics course and a mechanics course. We drew from research on the mathematics of juggling [2, 3] to de- velop a module that encouraged students to explore the patterns, notations, and mathematical elements of juggling in a variety of ways. Their final projects, rep- resenting further explorations, were displayed in our theater's lobby and featured interactive displays and demonstrations. In this paper we describe our experi- ences developing and implementing this juggling module, students' experiences with the modules, and their development of final projects. [ABSTRACT FROM AUTHOR]

Teaching to develop creativity often requires a shift in instructional tasks. In this paper, we first summarize the body of research related to instructors facilitat- ing and recognizing mathematical creativity. We then provide details as to how one graduate course, designed to help mathematics educators develop a sense of school mathematics from an advanced standpoint, provided opportunities for students to: recognize the difference between problems and exercises, pose prob- lems, reect on the quality of the tasks they created and review tasks created by others. This series of activities were designed to help the graduate students rec- ognize and appreciate mathematical creativity. We then review the instructional activities in light of the five overarching principles to maximize creativity in K-12 mathematics classrooms suggested by Sriraman [36] and discuss how these might relate to the post-secondary and graduate education of mathematics educators. [ABSTRACT FROM AUTHOR]

Modelling could be characterised as one of the core activities in mathematics education. However, when learning and teaching mathematics, mathematical modelling is mostly used to apply and deepen mathematical knowledge and competencies. Our educational study aims to explore how mathematical modelling, using real objects and high-quality mathematical technologies, could be utilised to acquire mathematical knowledge and competencies, and how learners could creatively use their existing knowledge. To discover the potential of mathematical modelling using real objects and high-quality mathematical technologies to acquire mathematical knowledge and competencies, and to stimulate learners' creativity, first, we combined cognitive and creative spirals and mathematical modelling cycles. Then, in a case study, we tested this combination of cognitive and creative spirals and mathematical modelling cycles in a secondary school and teacher education. Applying the combination of cognitive and creative spirals and mathematical modelling cycles, we discovered that it could be collaboration among learners and technological knowledge and skills of learners that determine whether knowledge can be acquired in mathematical modelling. [ABSTRACT FROM AUTHOR]

Too often mathematics is viewed by students and the general public alike as a set of formulas and techniques. However, mathematicians know that it involves so much more than banal procedures and requires deep thought and creativity. In this work we introduce an activity designed to make creative mathematical exploration accessible to young students and still interesting for those with many years of mathematical training. Popular culture often references the nautilus shell as an example of a golden spiral in nature. While many mathematicians assert this claim is false based on the formal definition, others have provided potential avenues for a relationship between the spiral created in the nautilus shell and the golden ratio. We spell out this debate and ask students to explore this question and see what patterns they can find in the nautilus shell. Might an alternative frame give the nautilus shell a golden hue or is it really just fool's gold?. [ABSTRACT FROM AUTHOR]

Eccentricity, though not inevitable, happens. Lightheartedly classifying examples, the author traces it back to factors, like creativity and absorption, essential to mathematical success, and recommends an attitude of amused tolerance towards others as well as to ourselves. [ABSTRACT FROM AUTHOR]