This paper is a case study of the teaching of an undergraduate abstract algebra course, in particular the way the instructor presented proofs. It describes a framework for proof writing based on Selden and Selden (2009) and the work of Alcock (2010) on modes of thought that support proof writing. The paper offers a case study of the teaching of a…

Florida Atlantic University implemented a number of changes in the College Algebra course in an attempt to improve student success. We summarize these changes, and how they have affected the course. We also discuss possibilities for future improvements. (Contains 3 figures and 1 footnote.)

One prohibitory component to graduation rates in college is the lack of student success in college algebra. The current national passing rate of college students enrolled in college algebra is approximately 40 percent. Lack of success in college algebra creating higher enrollments in remediation courses for students has also been linked to…

Presented in this translation are three chapters. Chapter I discusses the composition of forces and several theorems of geometry are proved using the fundamental concepts and certain laws of statics. Chapter II discusses the perpetual motion postulate; several geometric theorems are proved using the postulate that perpetual motion is impossible.…

Students in three mathematics classes were assessed on two aptitudes, field independence and general reasoning, and randomly assigned for a discovery treatment. There was a significant interaction with general reasoning on the retention test. There were no interactions with field independence. (Author/MK)

The aims of lectures for large groups of mathematics students are examined. Various matters pertaining to effective lecturing (selection of content and student feedback, for example) are explored, and the future of large group lectures is discussed. (SD)

A lecture method was compared with a method based on questioning sequences that guided students to discover mathematical principles. Students with high levels of mathematics anxiety had significantly lower achievement. Students with high anxiety benefited more from the expository approach; those with low anxiety benefited more from the discovery…

A Mathematics Colloquium program for broadening the mathematics education of graduate students is described. In the program, pre-colloquium lectures are given to provide enough background material to make the general ideas of the colloquium lecture understandable to the interested graduate student. (MN)

As hypothesized, less advanced students benefited most from a high instructional support treatment (personalized system of instruction) used in an introductory calculus course. Furthermore, as level of prior mathematics preparation increased, the achievement differences between the high and low instructional support (lecture) decreased. (Author/CP)

This article describes a study of learning when students used interactive spreadsheet-based computer tutorials in a mathematical literacy course. It foregrounds theories relating to the role of computer technology (and specifically spreadsheets) as a mediator for learning of mathematics. It outlines the application of quantitative methods…

Presented is an elaboration of a course given at Moscow University for pupils in ninth and tenth grades. The development through abstraction of the general definition of distance is discussed and a class of spaces in which the notion of distance is defined, the so-called metric spaces, is introduced. The general concept of distance is related to a…

An experiment in teaching mathematics to non-science, non-mathematics majors by two different methods, lecture and "open classroom," is reported. The primary findings of the study indicate that students learn equally well in either setting and that student personality characteristics may have a slight effect on individual gains. (JMD)

Presented is an abstract of a study done to try to determine a set of variables which are capable of accounting for a significant amount of variation in algebra achievement in each of two instructional formats. Tables representing final grade distributions, initial comparison of groups, and comparability of volunteer subgroup variables are…

Describes a remedial college course in intermediate algebra designed to improve student success rate. Suggests that the course was easy and inexpensive to implement and required a minimum of reorganization. (PK)

This study investigated the effects of two modes of instruction; the experiencing mathematics instructional method, and the direct instruction expository method, and two levels of mathematics anxiety, high and low, on mathematics achievement. The final sample consisted of 160 students enrolled in a remedial arithmetic course in a four-year college…