This article features a fifth grade mathematics exploration planned to facilitate students' productive struggle. The exploration was a catalyst for a team of educators to unpack the teacher's experience when facilitating students' productive struggle. The team called this "teacher productive struggle" and shares about the construct…

Creative fluency and originality are pivotal indicators of creative potential. Both have been embedded in hierarchical intelligence models as part of the ability to retrieve information from long-term memory; an ability that is often measured with indicators of retrieval fluency. Creative fluency and retrieval fluency, both expressed by the count…

The process of creative problem-solving (CPS) commonly demands that individuals consciously or unconsciously integrate creative ideas from a vast array of diverse information. Using a masked priming paradigm and the Chinese remote associates test (RAT), this study provides innovative behavioral evidence for the integration of multiple unconscious…

This paper seeks to initiate a theory of "imaginative dialogues" by articulating four dialogical principles that enable such a dialogue to occur. It is part of a larger project that takes the Socratic dialogue, a widely utilized conversation technique in philosophy education, as a starting point and aims to reinterpret it by shifting…

The term "creative" is commonly used in everyday language and in academic discourse to discuss the nature of artistic and innovative productions. This usage inherently implies the existence of a variable of creativity that allows different creative works to be compared. The standard definition of creativity asserts that a production must…

Since its first notable appearance in the "Second Handbook of Research on Mathematics Teaching and Learning," the phrase productive struggle has garnered support from a few, yet very influential, educational researchers. However, since the phrase was popularized by Hiroko Warshauer in 2011, examinations of the productive struggle have…

The digital age 4.0 governs the progress of society and individuals require the acquisition of skills to face this reality. Education is the only way that will allow human beings to adapt to the new global challenges. Therefore, the achievement of productive experiences must be the priority of the current educational system to train competent…

Uncertainties are inherent in education as learners encounter gaps in their awareness of topics, receive new information that potentially conflicts with prior understandings, and grapple with known unknowns in order to construct new knowledge. While researchers have shown that students productively struggling with problematized and uncertain…

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…

This study investigated what 12 prospective mathematics teachers (PTs) in a middle school mathematics method course reported during a video-stimulated recall interview about their experiences when they were engaged in a doing math task that yielded an Opportunity for Productive Struggle (OPS). We investigated their reported feelings during the…

The issue of low math performance, particularly in schools serving historically marginalized communities, requires immediate attention. Despite implementing various interventions, including leadership changes, curriculum updates, and hiring consultants, student achievement in math has remained stagnant at Ida B. Wells Academy (Wells). This case…

This study investigated whether the framework of writing for English learners should be guided by the well-established reading-writing relation or by the receptive and productive nature of literacy skills. The writings of 209 advanced English learners in Korea were analyzed in relation to receptive and productive vocabulary knowledge and reading…

There is broad agreement among executives on the importance of innovation and creativity in organizations. The paper aimed to provide information on the effectiveness of a new cognitive style inventory, the Productive-Reproductive Thinking Inventory (P-R), in identifying people with creative problem-solving potential. Participants completed the…

Past efforts to teach novices programming through pair programming and project-based learning utilizing different low floors, high ceilings and wide walls platforms have been successful. Building from related work, this study investigates the effectiveness of Productive Failure (PF) pedagogical design in supporting youth and novices when learning…

Recent education reforms highlight the importance of engineering design as a tool to improve student science learning in this new view of K-12 science education. However, little research has investigated the thought processes students use while engaging in the highly complex activity of design. Therefore, building on theories of productive…