Mathematics is viewed as a school subject that can develop creativity in students (Liljedahl and Sriraman in Learn Math 26:17–19, 2006 Sheffield in Creativity in mathematics and the education of gifted students. The authors found pragmatic cause for action learning within mathematics education at virtually any point in student academic lives. This argument is supported by various examples that could be helpful in practice of school teachers and university instructors. The authors argue that the entire K-20 mathematics curriculum under a single umbrella is practicable when techniques of concept motivation and action learning are in place throughout that broad spectrum. Also, stimulating questions, computer analysis (internet search included), and classical famous problems are important motivating tools in mathematics, which are particularly beneficial in the framework of action learning. The paper shows that this approach in mathematics education based on action learning in conjunction with the natural motivation stemming from common sense is effective. It details the approach used by the authors to devise insights for practitioners of mathematics teaching. This is a practice-led, conceptual paper describing selected means for action learning and concept motivation at all levels of mathematics education. Throughout the chapter, a selection of annotated vignettes on the work of GPDM teachers and their students illustrate the manner in which the legacy of Hans Freudenthal materialised and continues to materialise in Argentinean classrooms. We close with a reflection on what we have learned throughout this creative appropriation process. Next, we describe how the GPDM was formed, how participants learned about and implemented RME in their classrooms, and how the group’s sphere of influence in Grades K–12 and in pre-service and in-service mathematics teacher education expanded from the local to the regional, the national, and the international level. First, we outline the state of mathematics education reform in Argentina in the 1990s. This chapter focuses on the Grupo Patagónico de Didáctica de la Matemática (GPDM), a collective of about twenty teachers and teacher educators in Southern Argentina who, united by a shared interest in making mathematics meaningful, relevant, and accessible to all students, have been learning about, adapting, implementing, and contributing to Realistic Mathematics Education (RME). The ideas of the paper stem from the authors’ work with schoolchildren and with teacher candidates both in the classroom and in the field. The paper discusses different scenarios conducive for the emergence of collateral creativity through the study of mathematics with physical and digital tools. The main argument of the paper that tokens of collateral creativity can be observed in all students resides at the confluence of various theories which, in the context of mathematics, converge to describe creativity as a slumberous skill with potential to be awakened through the age-appropriate pedagogical mediation supported by the teachers’ awareness of often hidden complexity of seemingly mundane problems. The use of technology is described in terms of Vygotsky’s concept of the instrumental act. Creative thinking by the learners of mathematics may emerge accidentally, in a collateral way, within a classroom culture encouraging reflection on a teacher-assisted technological representation of mathematical concepts. The notion is motivated by Dewey’s conceptual framework of collateral learning which enables one gaining knowledge beyond the intent of the traditional curriculum. The paper introduces the notion of collateral creativity as an unintended outcome of the appropriate use of technology, both physical and digital, in the teaching of mathematics.
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