In this paper, we discuss the diffusion (of an innovation) and relate it to our attempt to spread our initial design of a mathematics practical paradigm in the teaching of problem solving.

This article presents a discussion of research and theoretical perspectives on creativity and instructional design, offering a conceptual model of the connection between these two constructs that was originally proposed in the dissertation work of the first author (Clinton, Creativity and design: A study of the learning experience of instructional…

This study describes the mathematical construction of a real-life model by means of parametric equations, as well as the two- and three-dimensional visualization of the model using the software GeoGebra. The model was initially considered as "determining the parametric equation of the curve formed on a plane by the point of a pen, positioned…

This article describes "modeling" as the act of creating an "idealized version of a real-life situation" that has been "translated into mathematical terms." By exploring an open-ended investigation involving proportional reasoning, sixth grade students were able to walk through both problem solving and modelling. The…

This study investigated the effects of applying mathematical modeling on revising students' preconception of the process of optimizing area enclosed by a string of a fixed length. A group of 28 high school pre-calculus students were immersed in modeling activity that included direct measurements, data collecting, and formulating algebraic…

In this action research, first-graders were challenged to cope with a sequence of modelling tasks involving an analysis of given situations and choices of mathematical tools. In the course of the sequence, they underwent a change in the nature of their problem-solving processes and developed modelling competencies. Moreover, during the task…

In two experiments, participants judged the average numerosity between two sequentially presented dot patterns to perform an approximate arithmetic task. In Experiment 1, the response was given on a 0-20 numerical scale (categorical scaling), and in Experiment 2, the response was given by the production of a dot pattern of the desired numerosity…

This study examines detailed usage of online training videos that were designed to address specific course problems that were encountered in an online computer programming course. The study presents the specifics of a programming course where training videos were used to provide students with a quick start path to learning a new programming…

Developing critical thinking since the educational revolution gave rise to flourishing movements toward embedding critical thinking (CT henceforth) stimulating classroom activities in educational settings. Nevertheless the process faced with complications such as teachability potentiality, lack of practical frameworks concerning actualization of…

Providing training for pre-service teachers at historic sites necessitates a reorientation for historic site-based teacher education programs away from strict content learning towards programs that emphasize the modeling of disciplinary problem solving and transfer learning. Outlined here is a History Lab model for teacher education that uses the…

Learning theory provides a powerful framework for analyzing instructional consultations and increasing their effectiveness. In this paper, the authors review the main tenets of learning theory, apply them to consultation scenarios, and present a complex case study to show how they can guide analysis and problem solving around challenging…

This special section contributes to an inclusive cognitive model of information problem solving (IPS) activity, touches briefly IPS learning, and brings to the notice methodological pitfalls related to uncovering IPS processes. Instead of focusing on the IPS process as a whole, the contributing articles turn their attention to what is regarded the…

Case-based instruction (CBI) offers a promising method for promoting problem-solving skills in learners. However, during CBI, the instructor shoulders major responsibility for shaping the learning that takes place. Research indicates that the facilitation techniques used during case discussions influence what gets covered, and to what extent,…

The Humanitarian Engineering and Social Entrepreneurship (HESE) Program engages students and faculty across Penn State in the rigorous research, design, field-testing, and launch of technology-based social enterprises that address global development challenges. HESE ventures are embedded in a series of five courses that integrate learning,…

Mathematical ability of students creative thinking is a component that must be mastered by the student. Mathematical creative thinking plays an important role, both in solving the problem and well, even in high school students. Therefore, efforts are needed to convey ideas in mathematics. But the reality is not yet developed the ability to…