Aesthetics as a liberating force in mathematics education?

Abstract

This article investigates different meanings associated with contemporary scholarship on the aesthetic dimension of inquiry and experience, and uses them to suggest possibilities for challenging widely held beliefs about the elitist and/or frivolous nature of aesthetic concerns in mathematics education. By relating aesthetics to emerging areas of interest in mathematics education such as affect, embodiment and enculturation, as well as to issues of power and discourse, this article argues for aesthetic awareness as a liberating, and also connective force in mathematics education.

The Role of Sequence in the Experience of Mathematical Beauty

“…Instead, the question under consideration is why this sequence was aesthetically compelling to these students in this context. Certainly, aesthetic experiences vary by individual [18] and the meaning generated during a story is a mixture of a reader's goals, experience, and purpose, and thus is individual in nature [15]. Since the audience of the enacted mathematical story described earlier was arguably the students, I maintain that the students' evaluation of the experience is the appropriate measure of its aesthetic value.…”

“…After this, I discuss the role of sequence with regard to how the students came to this aesthetic moment and also explore what might have changed if the sequence were altered. Finally, I end with a discussion of mathematical beauty, drawing connections and distinctions with other theories, stories, and analyses (e.g., [4,11,12,14,18,19]). …”

Surprise and the Aesthetic Experience of University Students: A Design Experiment

“…From a theoretical standpoint, the case of interest is situated at the crossroad of two general perspectives for conceptualizing mathematical beauty, objectivism and subjectivism, the latter also referred to as projectivism [6,36]. From the perspective of objectivism, mathematical beauty is an intrinsic property of a problem, theorem, or proof, and is consequently independent of the observer and the socio-historical context surrounding it [6].…”

“…Clarifying this approach is McAllister [24], who regards beauty as "a value that is projected into or attributed to objects by observers, not a property that intrinsically resides in objects" (page 15). Under this approach, what is considered to be mathematically beautiful is influenced by personal taste, previous personal knowledge and experience, age of the observer, and socio-historical cultural context (compiled from [3,9,31,34,36,38]). From an educational point of view, empirical research has shown evidence that students do in fact hold aesthetic sensibilities for mathematics, though their aesthetic views and judgments often differ from those of mathematicians, possibly as a result of different personal and psychological needs [3,4,19,35].…”

“…However, it should be noted that in both these cases, the type of surprise discussed is only addressed on an intellectual level, and with no reference to any affective or bodily aspects relating to the mere act of being surprised. Keeping in mind that affect plays a major role in mathematics education (e.g., [14,25]), and that cognition, affect, and aesthetics are strongly intertwined during mathematical activities [33,36], we recognize that further investigation is needed as to the role and impact of surprise at an emotional level.…”