We introduce learning modules in cryptography that can be crafted to motivate many abstract mathematical ideas, and we illustrate with a sample module. These modules can be used in a variety of ways, such as the core for a cryptography course or as motivating topics in other courses such as abstract and linear algebra or number theory.

This qualitative descriptive case study explores how genealogists describe the mechanism of epistemic change in their research, highlighting the roles of epistemological doubt, epistemological volition, and resolution strategies. It explores the integration of digital technologies in genealogical practices in the United States and their…

Spatial thinking is ubiquitous in design. Design education across all age groups encompasses a range of spatially challenging activities, such as forming and modifying mental representations of ideas, and visualizing the scenarios of design prototypes being used. While extensive research has examined the cognitive processes of spatial thinking and…

In this contribution, we address the gap that has appeared in mathematics education research and practice with the emergence of dynamic geometry environments and build on the opportunities these environments offer to school geometry. In our qualitative empirical study, we investigate how to elaborate on the general model of conceptual knowledge to…

Background: The study of emotions in engineering education (EEE) has increased in recent years, but this emerging, multidisciplinary body of research is dispersed and not well consolidated. This paper reports on the first systematic review of EEE research and scholarship. Purpose: The review aimed to critically assess how researchers and scholars…

Contribution: Using threshold concepts as the framework for curriculum design, a project on neural network methods for solving differential equations is presented, with a rich set of transformative concepts from mathematics and computer science. Projects of this kind complement a typical curriculum with expertise that is crucial for critique and…

Ideation methods and outcomes have been evaluated in a variety of ways. Our study extends existing work through a qualitative analysis of idea characteristics based on the ideation method used. Beginning engineering students completed two short ideation sessions with a single design problem while following Individual Brainstorming and then Design…

Teachers working to transform classrooms towards equity and justice must resist the continual press of dominant culture, which seeks to reproduce longstanding arrangements of inequity and injustice. Little is known about the learning that supports teachers in this resistance. This article offers the Teacher Learning for Transformation (TLT)…

Social design produces strategic, systematic solutions or new cultures as a response to the complexity of social changes and, in consequence, designers who are used to the traditional way of ideation may not be well prepared for the requirements of social design. This paper identified the characteristics of the concept generation of industrial…

Both professional and classroom-based scientific communities develop and test explanatory models of the natural world. For students to take up models as tools for sensemaking, practice must be agentive (where students use and revise models "for" specific purposes) and conceptually productive (where students make progress on their ideas).…

This article discusses two mechanisms through which understanding static mathematical concepts (basic and more advanced mathematical concepts) in terms of fictive motions or motion events enhance our understanding of these concepts. It is suggested that at least two mechanisms are involved in this enhancing process. The first mechanism enables us…

A variety of studies have attempted to explain the dispositions of imagination; notably, imagination engages and develops an individual's creativity. In the present study, we propose that three types of imagination dispositions (i.e., epistemic, sensory, and future imagination) serve as cognitive mechanisms for the ability to efficiently generate…

The learners' conceptual understanding has become one of the leading research areas conducted by educational researchers. Both students and current educators should actively work to improve their understanding of alternative conceptions and deepen their conceptual knowledge. One of the essential concepts in chemistry learning is colligative…

In acquiring new conceptual knowledge, learners often engage in the generation of examples that illustrate the to-be-learned principles and concepts. Learners are, however, bad at judging the quality of self-generated examples, which can result in suboptimal regulation decisions. A promising means to foster judgment accuracy in this context is…

An exciting recent development in chemistry has been the ability to control nanoparticle crystal morphology or shape. Nanoparticles of different shapes present different crystal surfaces (or facets) with respect to the surrounding environment. Synthetic control over nanoparticle morphology has enabled the study of the influence of surface facets…