The undergraduate curriculum in differential equations has undergone important changes in favor of the visual and numerical aspects of the course primarily because of recent technological advances. Yet, research findings that have analyzed students' thinking and understanding in a reformed setting are still lacking. This paper discusses an ongoing…

In an attempt to promote the development of understanding over rote memorization, writing in mathematics has received increased attention in recent years. In Calculus, the Rule of Three (based on communicating ideas thorough algebraic, graphical and numerical means) has been replaced by the Rule of Four in which writing plays a central role.…

This study investigated six students' understandings of and difficulties with qualitative and numerical methods for analyzing differential equations. From an individual cognitive perspective, the obstacles found to influence the development of students' understandings included the function dilemma, the tendency to overgeneralize, interference from…

As part of an effort to reform calculus instruction practices, Chattanooga State Technical Community College (CSTCC), in Tennessee, participates in two consortia. One consortium, the Chattanooga Calculus Consortium (CCC), is headed by the University of Tennessee at Chattanooga and involves one other four-year institution and three Chattanooga-area…

In this paper are described some features of the intensive use of math software, primarily DERIVE, in the context of modeling in an introductory university course in differential equations. Different aspects are detailed: changes in the curriculum that included not only course contents, but also the sequence of introduction to various topics and…

In an effort to increase faculty use and knowledge of computers, Oakland Community College (OCC), in Michigan, developed a Summer Technology Institute (STI), and a Computer Technology Grants (CTG) project beginning in 1989. The STI involved 3-day forums during summers 1989, 1990, and 1991 to expose faculty to hardware and software applications.…

This paper studies the modes of thought that occur during the act of solving problems in mathematics. It examines the two main instantiations of mathematical knowledge, the conceptual and the structural, and their role in the act. It claims that awareness of mathematical structure is the lever that educes mathematical knowledge existing in the…