This paper provides an instrumental account of precalculus students' graphical process for solving polynomial inequalities. It is carried out in terms of the students' instrumental schemes as mediated by handheld graphing calculators and in cooperation with their classmates in a classroom setting. The ethnographic narrative relays an instrumental…

Students incorporate and use the implicit and explicit parameter time to support their mathematical reasoning and deepen their understandings as they participate in a differential equations class during instruction on solutions to systems of differential equations. Therefore, dynamic reasoning is defined as developing and using conceptualizations…

When the character Yoda first appeared on the silver screen, his movements were due to the efforts of famed muppeteer Frank Oz. In "Star Wars Episode II: Attack of the Clones," Yoda returned to the movies but this time the character was not a puppet but a digital image within a computer. This paper discusses the role, or, more aptly, the force, of…

Over one-third of all college mathematics enrollments are in courses considered to be developmental. While such courses have been the subject of a large body of research, one question that seems not to have been studied empirically is the alignment of the content of developmental and college level mathematics courses. This paper gives the results…

According to the Merriam-Webster dictionary, a planimeter is "an instrument for measuring the area of a plane figure by tracing its boundary line". Even without knowing how a planimeter works, it is clear from the definition that the idea behind it is that one can compute the area of a figure just by "walking" on the boundary. For someone who has…

There is growing concern in Europe that some students are not well-equipped to start a Bachelor's or Master's programme, especially when the programme has a strong mathematical focus. In particular, attention is drawn to problems with mathematics in the transition from secondary to higher education. Higher education expects a certain level of…

This project was designed to address gender issues in mathematics education. The author's findings led her to conclude that students construct their own understanding and knowledge as a result of activities in the classroom. Constructivism, a theory of knowledge based on the idea that people construct their own realities by interacting with the…

How instructional television can supplement the high school math curriculum. (Author)

Reported are the results of an experiment designed to test the effectiveness of computer use by junior college students in a calculus class. The primary objective involved the replacing of pencil and paper computations by a computer program output. The topical areas of investigation were limits, extrema, functional evaluation, and integration.…

A computer-based instructional system for teaching the notion of mathematical proof is described. The system is capable of handling formalizations of the full predicate calculus with identity and, with minor work, definite description. Designed as an instructional device, the program is also the basis for a number of research projects involving…

This brief article summarizes the major contributions of several British mathematicians to the development of the calculus. (SD)

Arithmetic combinations of functions and their arguments are discussed, and resulting properties are related to first-year calculus topics. (MP)

Described is a sequence of calculus courses utilizing the computer to enhance concepts and ideas in calculus. (JLH)

A quasi-experimental, factorial design was employed to determine the interactive effect of motivation, math preparation, and instructional method on achievement in a calculus course taught by two methods; personalized system of instruction (PSI) and the conventional method. (Author/STS)

Directions are given for using a gravity protractor in constructing an instrument for finding derivatives. (DT)