A worked-out or an open inventing problem with contrasting cases can prepare learners for learning from subsequent instruction differently regarding motivation and cognition. In addition, such activities potentially initiate different learning processes during the subsequent ("future") learning phase. In this experiment (N = 45…

DBL is a novel pedagogical approach intended to improve students' conditional knowledge and problem-solving skills by exposing them to a sequence of branching learning decisions. The DBL software provided students with ample opportunities to engage in the expert decision-making processes involved in complex problem-solving and to receive…

Student problem solving in the context of a dynamic mathematics environment (DME) has previously been investigated primarily through the lens of whether or not the student could complete a problem-solving task. Herein, we investigate what trajectories students employ in the realms of mathematics, technology, and problem solving as they attempt to…

These proceedings contain the papers of the 12th International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA 2015), October 24-26, 2015, which has been organized by the International Association for Development of the Information Society (IADIS), co-organized by Maynooth University, Ireland, and endorsed by the…

When groups engage in math problem solving in an online environment like the VMT (Virtual Math Teams) service, they can face significant challenges from troubles of individual and group understanding that emerge in their problem-solving process. We are interested in how shared understanding is interactionally constructed and accomplished in a…

Representational fluency (RF) includes an ability to interpret, create, move within and among, and connect tool-based representations of mathematical objects. Taken as an indicator of conceptual understanding, there is a need to better support school algebra students' RF in learning environments that utilize both computer algebra systems…

Interactive learning is beneficial to students in that it allows the continual development and testing of many skills. An interactive approach enables students to improve their technical capabilities, as well as developing both verbal and written communicative ability. Problem solving and communication skills are vital for engineering students; in…

This paper addresses the use of scaffolding in learning contexts that incorporate technologically based novel problems. We suggest that in computer contexts extended conceptualisations of scaffolding are needed in order to gain greater insights into teaching and learning processes. Our work has revealed that traditional forms of scaffolding, based…

"Mathematics is more than skills... it is also the excitement of discovery." This is how Derek Holton, one of the contributing authors to this book, defines mathematics. His enthusiasm and energy are echoed throughout by many of the other writers. This is a book to delight mathematics teachers at all stages: experienced and inexperienced;…

In this study, the authors compared four multimedia learning arrangements differing in instructional approach on effectiveness and efficiency for learning: (a) hypermedia learning, (b) observational learning, (c) self-explanation-based learning, and (d) inquiry learning. The approaches all advocate learners' active attitude toward the learning…

Despite the challenges inherent in adopting problem-based learning (PBL) in the middle school classroom, successful PBL teachers are able to find suitable solutions. In this exploratory study we examined the perceptions and practices of five successful middle school PBL teachers regarding the specific difficulties encountered with PBL and the…

This document explains the importance of problem solving in the high school physics curriculum and points out the lack of opportunities in textbooks for students to practice their problem solving skills. The necessity of having introductory-level work texts cannot be ignored and having a work-text book would be beneficial from the teachers' point…

This paper describes the global feedback in ActiveMath, a Web-based adaptive learning environment for mathematics and beyond. It addresses some of the cognitive foundations and the architecture of the suggestion mechanism with its components. This architecture separates components for diagnosis from components for suggestions and different types…

Today's "digital child" has never known a time bereft of computers, change, or easy communication systems. Computers and other technologies have irreversibly transformed kids' learning environment, temperament, and conceptions of work and playtime, relationships, location, technological advancement, relevant knowledge, and flexibility. (MLH)

The Internet, an exciting and radically different medium infiltrating pop culture, business, and education, is also a powerful educational tool with teaching and learning potential for mathematics. Web-based instructional tools allow students and teachers to actively and interactively participate in the learning process (Lynch, Moyer, Frye & Suh,…