Simulation as a Resource in the Calculus Solving Problem

This article is derived from the research project and developed at School of Computer Sciences of the National Polytechnic Institute of Mexico. The article reports on the problems found among engineering students with respect to their resistance to using different representation registers when solving optimization problems in the Calculus Learning Unit. Use of such registers could help the students to build mathematics knowledge and to solve calculus problems. As a didactic strategy, simulations are used in an electronic environment in order to support the students by fostering their use of tabular, graphical and algebraic representation registers. Interviews are undertaken of six of the professors who gave the calculus courses, and a diagnostic questionnaire was applied to 68 students prior to and after working with the proposal. As for the theoretical framework, the work reported by Duval and Hitt is salient in this report, particularly their emphasis of the fact that working on activities by way of one single representation system is not sufficient. From the first responses provided by the students, one can conclude that the algebraic register is preferred by the majority of students. It is however used in a mechanical fashion without affording any meaning to the content of the problem and to the process of solving it. Another conclusion reported is that implementing tasks in the classroom in which the mathematics activity requires coherent use of different representations is necessary

Preservice Mathematics Teachers' Representation Transformation Competence Levels in the Process of Solving Limit Problems

In this study, representations used by preservice mathematics teachers in the process of solving limit problems were determined, the inter-representation transformation competence levels were investigated and the relationship between them was examined. In this context, “Limit Representation Transformation Test” with a reliability of .908 was administered to 50 preservice teachers attending to a state university in the Central of Turkey. Preservice teachers had most difficulty in solving problems that had verbal representation inputs, especially they achieved low performances in transformation from verbal to numerical representation. Although, in general, they achieved the highest performance in the problem that had numerical representation input, they also achieved very high performances in the problems that had graphical and algebraic representation inputs. Specifically, they performed very well in the problems that required transformation from an algebraic representation to a verbal representation. Moreover, significant positive correlations were found among preservice teachers’ representation transformation competence levels.

Focus and contrastive topic in questions and answers, with particular reference to Turkish

Much recent research has recognized the importance of focus and contrastive topic in assertions for discourse coherence. However, with few exceptions, it has been neglected that focus and contrastive topic also occur in questions, and have a similar role in establishing coherence. We propose a framework of dynamic interpretation based on the notion of Commitment Spaces that show that a uniform interpretation of focus and contrastive topic is possible. The algebraic representation format is rich enough so that a separate introduction of discourse trees is not necessary. The paper discusses these phenomena for Turkish, a language with an explicit focus marker for polar and alternative questions, which distinguishes focus from contrastive topic.