This paper aims to reveal the potential of inferentialism, an emerging philosophy in mathematics education, to extend contemporary constructivist research regarding conceptual development. Going against the traditional view of a notion as the name of a corresponding concept and a constructivist way of naming second-order models, we provide a new…

The goal of this article is to review work on mind wandering, metacognition and creativity in order to consider their relationship with cognitive flexibility. I introduce a model of the role that mind wandering and metacognition have in the generation and exploration of novel ideas and products in the creative process. I argue that managing the…

How does creativity develop from a nearly ubiquitous and domain-general capacity associated with playfulness and openness to experience to a highly rarified and domain-specific ability associated with invention and innovation? In this short report, I describe creativity along two dimensions: self- and socially referenced creativity. In…

In today's dynamic and high-tech learning environment, offering flexible and innovative assignment options is crucial for engaging students across varied learning preferences and backgrounds. Alternative formats, such as gamification and storyboards, can boost engagement, spark creativity, and enhance learning outcomes in college classrooms. By…

This paper describes a model of mathematics bianshi teaching using one problem with several solutions, changes, and applications in an inquiry-based classroom. Based on the model of mathematics bianshi teaching, the author discusses a class-room experience where one Chinese mathematics teacher takes a simple plane geometry problem to guide…

In this article we focus on the co-creation of ideas. Through the use of concepts from collaborative learning and communication theory we suggest a model that will enable the cooperative nature of creative design tasks to emerge. Four objectives of the model are stated and elaborated on in the paper: that the model should be anchored in previous…

This article presents how Problem- and Project-Based Learning (PBL) in engineering education can exploit the theoretical framework of the Space-Time (ST)-Continuum, according to which educational contexts can be classified in terms of the tightness vs. looseness of the relevant conceptual space S and available time T. By crossing these two…

In this article, we seek to unpack and enrich the notion of the design concept. We do this through the use of Gilles Deleuze and Felix Guattari's 'concept' in its philosophical specificity to critique less-effective uses of the design concept. In particular, we investigate the idea that a concept is actually an aggregation of many concepts that…

This paper explores the paradigm shift in using ICT tools while teaching mathematics remotely within the TPACK framework. Remote teaching is not only one of the primary modes of teaching and learning in the present context throughout the world but the transition from paper to the digital world, where mathematics teachers struggle to visualize the…

This informal essay is based on a presentation James Tanton gave at the Australian Association of Mathematics Teachers (AAMT) 'Why Maths?' Conference in 2019. It begins by offering two first steps to problem-solving that Tanton believes are key for finding success--and joy--in doing mathematics: (1) Be human! Have an emotional reaction to the…

This paper describes the development and implementation of course modules intended to encourage creative thinking in an undergraduate general education mathematics course. The modules were designed to address the characteristics of creativity outlined in the literature through explorations of mathematics relevant to non-mathematics majors. A…

Mathematical modeling is an important and accessible process for elementary school students because it allows them to use mathematics to engage with the world and consider if and when to use it to help them reason about a situation. It fosters productive struggle and twenty-first-century skills that will aid them throughout their lifetime.

This article describes the author's experience using SCAMPER, a creativity-building technique, in a creative problem-solving session that was conducted in an environmental conflict course to generate ideas for managing postconflict stability. SCAMPER relies on cues to help students connect ideas from different domains of knowledge, explore random…

That creativity can play a role in learning seems clear. Indeed, creativity researchers and educational scholars have long asserted that theories of learning need to be broadened to include creative cognition. What is less clear, however, is the specific nature of that role. The purpose of this article is to introduce a new model of creative…

The Baltimore Mural Project (BMP) seeks to connect religious studies education to the growing literature on threshold concepts in order to address bottleneck areas in student learning. The project is designed for undergraduate service courses comprised of mostly non-majors: for example, world religions. Students in these courses often struggle to…