In most mathematics problem solving work, students' motivation comes from trying to please their teachers or to earn a good grade. The questions students must tackle are almost never generated by their own interest. Seven open-ended college algebra-level problems are presented in which the solution of one question suggests other related questions.…

This study tested the benefits of matching field dependent (FD) learners to an algorithmic method and field independent (FI) learners to a discovery method relative to mathematics achievement. It also attempted to discover if FD learners reacted more positively to computer experience than did FI learners. A total of 126 college algebra students…

College students who were either monolingual speakers of English or bilingual Hispanics participated in two studies dealing with the comprehension of sentences containing negations. Both the influence of different sentence constructions on comprehension, as well as the heuristics and misconceptions exhibited by subjects as they attempted to…

This document, intended as a resource for calculus reform, contains 75 separate contributions, comprising a very diverse set of opinions about the shape of calculus for a new century. The authors agree on the forces that are reshaping calculus, but disagree on how to respond to these forces. They agree that the current course is not satisfactory,…

This publication focuses on the work of one bright but math avoidant student in a writing seminar in mathematics. The introductory portion of the document explains the philosophy, goals, and activities of the seminar. The course is intended to provide opportunities for students in the humanities to experience mathematics as a discipline at once…

For the remainder of the century, large numbers of students will transfer from two-year to four-year colleges. In light of this, two- and four-year mathematics faculty need to sharpen their understanding of each other and to plan improved interaction. The problem in communication between two- and four-year mathematics faculty comes from living in…

In light of substantial declines in enrollments in liberal arts mathematics courses in two-year colleges, this paper looks at some of the reasons for these declines and suggests ways of revitalizing the traditional "great ideas" mathematics course. First, a brief outline is presented of the history of liberal arts mathematics, focusing on the…

Drawing from literature on research, innovative programs, and association positions, this paper provides an overview of two-year college mathematics curricula, instruction, and faculty. Introductory material places the discussion in the context of changes that have taken place in the community college over the past 20 years, highlighting increases…

This study explored the relationship between students' high school mathematics courses and grades; the affective variables--mathematics anxiety, effectance motivation, and attitude toward success; and performance in the first quarter developmental studies algebra course. The study reports significant differences between males and females on…

This paper presents the thesis that pair problem-solving serves as an aid to students in developing their metacognitive skills. Metacognition has been defined as knowledge and cognition about cognitive objects and as any kind of monitoring. The ability to monitor one's thoughts and actions is greatly facilitated through the pair problem-solving…

This document argues that qualitative graphing is an effective introduction to mathematics as a construction for communication of ideas involving quantitative relationships. It is suggested that with little or no prior knowledge of Cartesian coordinates or analytic descriptions of graphs using equations students can successfully grasp concepts of…

The contributions of acceptance of misconceptions about mathematics, mathematical self-concept, and arithmetic skills to mathematics anxiety and to statistics course performance were studied in 92 adult students aged 18 to 57 with a median age of 27, (16 males and 76 females). Results showed that acceptance of misconceptions and mathematical…

The study was designed to investigate: (1) the relative effectiveness of three techniques for teaching verbal problem solving to general education mathematics students in a junior college; and (2) the relationships between various student variables and problem-solving ability after treatment. Three classes (N=72) at Florida College were randomly…

Presented are the mathematical explanation of the algorithm for representing rational numbers in base two, paper-and-pencil methods for producing the representation, some patterns in these representations, and pseudocode for computer programs to explore these patterns. (MNS)

During the first 12 weeks of an applied calculus course, two classes of college students studied calculus concepts using graphical and symbol-manipulation computer programs to perform routine manipulations. Three weeks were spent on skill development. Students showed better understanding of concepts and performed almost as well on routine skills.…