Fostering students' mathematical creativity is important for their understanding and success in mathematics courses as well as their persistence in STEM, but it necessitates intentional instructional actions, such as designing and implementing tasks that have the potential to foster creativity. As teaching innovation requires support for…

In my Keynote Address to PME-NA 45, I offer an embodied framework for naming what makes mathematics powerful for mathematicians and scientists, yet intractable for many learners. The essential claim is this: Students reside in the Real World, where math is grounded, embodied and meaningful, while mathematics resides in the ungrounded, disembodied…

Epistemic curiosity is a desire for knowledge accompanied by positive emotions, increased arousal, and exploratory behavior (Grossnickle, "Educational Psychology Review," 28(1), 23-60, 2016). Although curiosity has typically been characterized as a domain-general construct, domain-general conceptualizations do not acknowledge systematic…

Based on a detailed reading of Graham Wallas' "Art of Thought" (1926) it is argued that his four-stage model of the creative process (Preparation, Incubation, Illumination, Verification), in spite of holding sway as a conceptual anchor for many creativity researchers, does not reflect accurately Wallas' full account of the creative…

This article details how certain mathematical "discoveries" that Cavazos' fourth graders made were recorded throughout the year. Cavazos invited a math professor, a biologist, a literacy professor, a chemist, a statistician, and an engineering student, as well as their school principal and computer lab technician, both of whom are…

We argue that student research skills in mathematics should be honed throughout the curriculum just as such skills are built over time in the natural and physical sciences. Examples used in the mathematics program at St. Olaf College are given.

The Calculator Controlled Robots activities are designed to engage students in hands-on inquiry-based missions. These activities address National science and technology standards, as well as specifically focusing on mathematics content and process standards. There are ten missions and three exploration extensions that provide activities for up to…

In this note we develop a framework that makes explicit the inherent dynamic structure of certain mathematical definitions by means of the four facets of context-entity-process-object. These facets and their interrelations are then used to capture and interpret specific aspects of student constructions of the concept of solution to first order…

The Magic Mathworks Travelling Circus is a touring maths lab--in and of itself, a good thing. When children enter it, they find particular pieces of apparatus captioned with particular challenges--which is perhaps not such a good thing. Students are faced with an apparatus that can do only one thing, and so are not encouraged to look again at…

Learning through discovery and inquiry is one of the cornerstones of mathematics education theory. The examples provide scope for the students to rediscover mathematics in an enjoyable way.

Explores the mathematical practices of three young mathematicians in an extended interview setting. Focuses on the interaction of discovery and verification, the role of conjecture in discovery, and the place of intuition and understanding in research. Indicates an interesting mismatch between how they valued their own guesses and how they reacted…

The study was intended to determine the effect of the mode of verbalization of a discovered generalization on short-term retention of ability to use the generalization. Fifty preservice elementary teachers were assigned to one of the five verbalization methods: speaking, listening, writing, reading, or no verbalization. Each performed on six…

Describes three major difficulties plaguing most discovery-learning teaching systems and presents a theoretical operational approach for offsetting these difficulties. (SL)