The difficulty in observing, recording, and examining internal representations has been well documented (Goldin & Shteingold, 2001). However, the important role that these internal representations play in the learning and understanding of mathematical concepts has been noted (Yackel, 2000). This study sought to develop a framework for…

Authoring tools for Intelligent Tutoring System (ITS) have been shown to decrease the amount of time that it takes to develop an ITS. However, most of these tools currently do not extend to collaborative ITSs. In this paper, we illustrate an extension to the Cognitive Tutor Authoring Tools (CTAT) to allow for development of collaborative ITSs that…

Science as inquiry and mathematics as problem solving are conjoined fraternal twins attached by their similarities but with distinct differences. Inquiry and problem solving are promoted in contemporary science and mathematics education reforms as a critical attribute of the nature of disciplines, teaching methods, and learning outcomes involving…

Jeannette Wing's influential article on computational thinking 6 years ago argued for adding this new competency to every child's analytical ability as a vital ingredient of science, technology, engineering, and mathematics (STEM) learning. What is computational thinking? Why did this article resonate with so many and serve as a rallying cry for…

This article is based on a systematic review of educational research, policy and professional literature relating to creative environments for learning in schools. Despite the search yielding 210 documents, comparatively few empirical studies were published between 2005 and 2011 that addressed the review objectives. Only 18 studies included in the…

The links between the mathematical and cognitive models that interact during problem solving are explored with the purpose of developing a reference framework for designing problem-posing tasks. When the process of solving is a successful one, a solver successively changes his/her cognitive stances related to the problem via transformations that…

"Success stories," i.e., cases in which mathematical problems posed in a controlled setting are perceived by the problem posers or other individuals as interesting, cognitively demanding, or surprising, are essential for understanding the nature of problem posing. This paper analyzes two success stories that occurred with individuals of different…

In this study, we used problem posing as a measure of the effect of middle-school curriculum on students' learning in high school. Students who had used a standards-based curriculum in middle school performed equally well or better in high school than students who had used more traditional curricula. The findings from this study not only show…

Interactive digital media, or video games, are a powerful new medium. They offer immersive experiences in which players solve problems. Players learn more than just facts--ways of seeing and understanding problems so that they "become" different kinds of people. "Serious games" coming from business strategy, advergaming, and entertainment gaming…

Background: Native Americans are underrepresented in science, technology, engineering, and mathematics (STEM). We investigated whether having to violate cultural taboos might be a factor in the decisions of some Native Americans not to pursue STEM degrees. Many STEM faculty likely know very little about Native Americans' historical experiences…

Research indicates that parental involvement in children's education is positively related to academic achievement in mathematics; however, there are few studies on the role of parental involvement in the context of developing countries. The purpose of this paper is to document the iterative development using design-based research (DBR) of a…

Educator preparation in comprehension strategy instruction (CSI) is essential to meeting the needs of English learners (ELs) in contemporary schools. This article provides teacher educators and professional developers with concrete examples of practices to prepare classroom teachers in comprehensive strategy instruction, based on an experimental…

Problem-Based Learning (PBL) is well known for enhancing students' problem solving skills and teamwork, while the role of PBL tutors is to facilitate discussion rather than teach. This study used four focus groups to explore PBL tutors' motivation, challenges and support mechanisms, and the relationship between these. The study found that there…

Since the foundation of the Khan Academy (2006), a great deal of attention has been generated to the term "flipped classrooms" (also known as "reverse" or "backwards" classrooms), which is a (new) pedagogical movement that reverses the traditional paradigm of class lecture and homework. This approach subordinates…

"Thinking like a lawyer" is traditionally associated with rational-analytical problem solving and an adversarial approach to conflict. These features have been correlated with problems of psychological, or emotional, distress amongst lawyers and law students. These problems provide a strong argument for incorporating a consideration of…