Many students view mathematics as a collection of theorems and facts that were discovered by intelligent mathematicians and all they have left to do is to study them carefully. Some believe it is important to help students change this view (Lavy & Shriki, 2003). One possible way is to enable students to modify the attributes of a given situation,…

Some examples from different areas of mathematics are explored to give a working knowledge of the computer algebra system Maple. Perfect numbers and Mersenne primes, which have fascinated people for a very long time and continue to do so, are studied using Maple and some questions are posed that still await answers.

Current theories of learning emphasize the importance of learner-centered, active, authentic, environments for meaningful knowledge construction. From this perspective, computerized case-based learning systems afford practice fields for learners to build domain knowledge and problem-solving skills and to support contextualized transfer of…

Through numerical investigations, this paper studies examples of the forced Duffing type spring equation with [epsilon] negative. By performing trial-and-error numerical experiments, the existence is demonstrated of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions. Subharmonic boundaries are…

The Spanish educational system will require certain changes in order to achieve the Bologna objectives for the European Higher Education Area, including a more professional profile, with new activities and roles for both students and teachers, who must assume new skills that will affect concepts and attitudes related to the teaching and learning…

A new computerized environment introducing a variety of metacognitive support mechanisms (MSMs) in different phases of the problem-solving process was designed to influence students' transfer from solving structured problems (near transfer) to solving open-ended problems (far transfer). Two hundred and thirty one students (aged 13-14 years) were…

In this study, we discuss the scaffolded design of ODRES (Observe, Discuss, and Reason with Evidence in Science), a computer tool that was designed to be used with elementary school children in science, and report on the effects of learning with ODRES on students' conceptual understandings about light, color, and vision. Succinctly, dyads of…

Research on help seeking with a computer coach providing on-demand help has not produced fully adequate models of the process from a cognitive perspective. The present study postulates a model of help seeking from a cognitive perspective and tests this model in a learning situation characterized as problem-based and computer-supported. The…

This supplementary volume presents appendixes A-E associated with a 1-year study which determined what secondary school students were doing as they engaged in the Chelsea Bank computer software simulation activities. Appendixes present the SCANS Analysis Coding Sheet; coding problem analysis of 50 video segments; student and teacher interview…

In earlier times, practically everything was taught by apprenticeships. Schools are a recent invention that use many fewer teaching resources, but the computer enables us to go back to the resource-intensive mode of education, in a form called cognitive apprenticeship. This involves the use of modeling, coaching, reflecting on performance, and…

This paper is designed to provide the educator with an overview of instructional applications of the computer, along with important issues related to each application. Applications discussed include computer managed instruction, drill and practice, simulation, computer assisted testing, instructional games, tutorials, problem solving, and…

A course in computer programing is being developed as a vehicle for research in tutorial modes of computer-assisted instruction. Methods for monitoring and aiding the student as he works on interesting programing problems are employed. The problems are individually selected via an optimization scheme based on a model of the student's ability and…

Learner controlled instruction in which the student controls the computer (e.g., computer programing) instead of it controlling the student (e.g., drill-and-drill-and-practice) is described. The nature of this mode of computer use is explored, and some examples based on case studies conducted by the author are given. A rationale for learner…

Most computer assisted instruction programs cannot answer student questions for the simple reason that these programs do not "know" the subject matter they teach. But programs that can perform certain tasks could be augmented into computer tutors that can at least solve problems or answer questions in the subject matter under consideration. Based…