Contribution: This article compares student success via different pathways in which students take mathematics courses required for engineering degrees. Background: Mathematics courses are an integral part of engineering curriculum. Many institutions require or recommend the order in which students take Calculus II, Multivariable Calculus,…

This study examines students' visual behaviors when they tackle two types of synthesis problems, sequential and simultaneous problems. Sequential synthesis tasks can be solved by applying pertinent concepts consecutively, whereas simultaneous synthesis tasks require concurrent application of multiple concepts. Twenty-two students from an…

Effectiveness of mathematical education as non-linear, composite and open system, formation and development of cognitive abilities of the trainee are wholly defined in the solution of complex tasks by means of modern achievements in science to high school practice adaptation. The possibility of complex tasks solution arises at identification of…

Learning progressions (LPs) describe the development of domain-specific knowledge, skills, and understanding. Each level of an LP characterizes a phase of student thinking en route to a target performance. The rationale behind LP development is to provide road maps that can be used to guide student thinking from one level to the next. The validity…

Resequencing Calculus is a project that has reordered the typical delivery of Calculus material to better serve the needs of STEM majors. Funded twice by the National Science Foundation, this project has produced a three-semester textbook that has been piloted at numerous institutions, large and small, public and private. This paper describes the…

Most beginning calculus courses spend little or no time on a technical definition of the limit concept. In most of the remaining courses, the definition presented is the traditional epsilon-delta definition. An alternative approach that bases the definition on infinite sequences has occasionally appeared in commercial textbooks but has not yet…

A sequence of number pairs can be used to generate many interesting examples in teaching mathematics subjects at various levels. It is often used in elementary or middle school mathematics classes to illustrate the concept of "patterns." In this paper the authors present a few interesting ways of using this sequence to form examples for high…