Addressing students' difficulties with Faraday's law: A guided problem solving approach

In traditional teaching, the fundamental concepts of electromagnetic induction are usually quickly analyzed, spending most of the time solving problems in a more or less rote manner. However, physics education research has shown that the fundamental concepts of the electromagnetic induction theory are barely understood by students. This article proposes an interactive teaching sequence introducing the topic of electromagnetic induction. The sequence has been designed based on contributions from physics education research. Particular attention is paid to the relationship between experimental findings (macroscopic level) and theoretical interpretation (microscopic level). An example of the activities that have been designed will also be presented, describing the implementation context and the corresponding findings. Since implementing the sequence, a considerable number of students have a more satisfactory grasp of the electromagnetic induction explicative model. However, difficulties are manifested in aspects that require a multilevel explanation, referring to deep structures where the system description is better defined.

Natural Language Input for a Computer Problem Solving System

The STUDENT problem solving system, programmed in LISP, accepts as input a comfortable but restricted subset of English which can express a wide variety of algebra story problems. STUDENT finds the solution to a large class of these problems. STUDENT can utilize a store of global information not specific to any one problem, and may make assumptions about the interpretation of ambiguities in the wording of the problem being solved. If it uses such information or makes any assumptions, STUDENT communicates this fact to the user. The thesis includes a summary of other English language questions-answering systems. All these systems, and STUDENT, are evaluated according to four standard criteria. The linguistic analysis in STUDENT is a first approximation to the analytic portion of a semantic theory of discourse outlined in the thesis. STUDENT finds the set of kernel sentences which are the base of the input discourse, and transforms this sequence of kernel sentences into a set of simultaneous equations which form the semantic base of the STUDENT system. STUDENT then tries to solve this set of equations for the values of requested unknowns. If it is successful it gives the answers in English. If not, STUDENT asks the user for more information, and indicates the nature of the desired information. The STUDENT system is a first step toward natural language communication with computers. Further work on the semantic theory proposed should result in much more sophisticated systems.

Truth Maintenance Systems for Problem Solving

The thesis developed here is that reasoning programs which take care to record the logical justifications for program beliefs can apply several powerful, but simple, domain-independent algorithms to (1) maintain the consistency of program beliefs, (2) realize substantial search efficiencies, and (3) automatically summarize explanations of program beliefs. These algorithms are the recorded justifications to maintain the consistency and well founded basis of the set of beliefs. The set of beliefs can be efficiently updated in an incremental manner when hypotheses are retracted and when new information is discovered. The recorded justifications also enable the pinpointing of exactly whose assumptions which support any particular belief. The ability to pinpoint the underlying assumptions is the basis for an extremely powerful domain-independent backtracking method. This method, called Dependency-Directed Backtracking, offers vastly improved performance over traditional backtracking algorithms.

Using the interact system model to analyze computer mediated communication during a small group problem-solving task

The Interact System Model (ISM) developed by Fisher and Hawes (1971) for the analysis of face-to-face communication during small-group problem solving activities was used to study online communication. This tool proved to be of value in the analysis, but the conversation patterns reported by Fisher (1980) did not fully appear in the online environment. Participants displayed a habit of "being too polite" and not fully voicing their disagreements with ideas posed by others. Thus progress towards task completion was slow and incomplete.

Math-Towers: Online Interactive Collaborative Mathematics Explorations & Problem-Solving for Students Ages 11 to 15 years (Grades 6 to 10)

Math-Towers (www.math-towers.ca) is an online resource for students in grades 6 to 10 that supports collaborative problem-solving and investigations. This paper presents the philosophical position motivating the development of Math-Towers and describes how the site presents and motivates the mathematical challenges and supports participants' exploration and collaboration.