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…

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…

Metacognition supports students in successfully working through struggle by equipping them with the tools to maintain an awareness of what they are doing and to change directions when needed to overcome obstacles. Thus, it is of little surprise that effective problem solvers spend a significant amount of time analyzing tasks relative to the amount…

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…

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…

As problems become increasingly complex, science educators need to better understand how new knowledge is constructed and applied in heterogeneous team collaborations, and how to teach students to productively engage in these processes. We discuss the emergence of insights in collaborative sensemaking and suggest a model that articulates the…

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…

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…

Mathematics is not seen as an absolute corpus of well-founded knowledge anymore, but as a human activity, a social phenomenon, part of human culture that evolves historically and intelligibly in a social context. By harnessing the indigenous cultures and their knowledge systems in-depth, this article aims to evaluate how the sustainable…

Many innovations in organizations result when people discover insightful solutions to problems. Insightful problem-solving was considered by Gestalt psychologists to be associated with productive, as opposed to re-productive, thinking. Productive thinking is characterized by shifts in perspective which allow the problem solver to consider new,…

Earthquakes, lightning, and history-changing ideas are classic examples of powerful, unpredictable forces of nature. These sorts of phenomena have been difficult to explain and predict, an often frustrating fact as humans try to understand and control the significant influences in our lives. Historically, such phenomena have been attributed to…