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…

This project seeks to understand the emergence of mathematical meanings mediated by learners' interactions with multiple artifacts. Extending our prior work which took an enactivist approach and revealed the dynamics of embodied interactions fundamental to understanding fraction division, we now employ a semiotic lens to illuminate how learners…

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…

In his "Proofs and Refutations," Lakatos identifies the "Primitive Conjecture" as the first stage in the pattern of mathematical discovery. In this article, I am interested in ways of reaching the "Primitive Conjecture" stage in an undergraduate classroom. I adapted Realistic Mathematics Education methods in an…

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…

Technology and engineering (TE) educators have long championed the infusion of mathematics into technology curriculum, especially to enhance TE learning goals and demonstrate "connections between technology and other fields of study." There is a need for curriculum development and professional development initiatives to purposefully…

This report uses NAEP background data to track time and learning since the mid-1990s in three areas: student absenteeism; classroom instructional time in mathematics, reading, music and the visual arts; and homework time expected by teachers. Key report findings are: (1) Students with higher rates of "monthly absenteeism" score…

Meanings of "surprise" are wide and include uplifting and engaging facets like wonder and amazement on the one hand as well as ones that may be of the opposite nature like interruption and disrupt on the other. Pedagogically, educators who use surprise in class activities are focusing on students being "taken aback" by a situation, hopefully…

The relationship between the research into creativity and the changes in school mathematics is investigated. Problems arising from this relationship and the research which attempts to solve them are considered. (Editor)

Describes role-play centers in which children can do math problems, invent, experiment, write with a purpose, and act out adult career roles. Examples of centers include a doctor's office, a supermarket, a fix-it or inventor's workshop, a post office, a pet store, a zoo, a veterinary clinic, a museum, and a restaurant. (DKM)

For the mathematics experience to be liberating, the curriculum must share how and why mathematical knowledge is developed, with special emphasis on its grounding in belief, intuition and subjectivity, and facilitate our understanding of the world in which we live and create and the beliefs we act upon. (Author)

This article outlines a series of investigations in graph theory which simultaneously gives exercises in visualization. It is argued that one of the advantages of classroom investigations is that students can be lead to an intuitive grasp of advanced mathematics. (PK)

Five exploratory activities arising from work by sixth-grade students are described. They concern geometric ideas and number concepts, including fractions. Illustrations are included. (MNS)

A one-to-one teaching session with a student is described and analyzed in an attempt to communicate how student attempts at discovery in mathematics can be thwarted by teachers who do not allow room for creativity. (MP)