Presented is a example that shows why a certain technical lemma is necessary for a valid proof of Galois Theory. The usual proof of Galois' Theory is included as well as one using the lemma. (KR)

Presented is an alternate way to derive R from Taylor's Theorem without involving the (n + 1)st derivative of f. Included is the procedure for estimating the bounds of R. (KR)

Developed is a condition, expressed in terms of an index, that ensures that a quasinormal subgroup is normal. The arguments suggest a variety of exercises for a course in group theory or Galois theory. Included are the definitions, lemmas, and proofs. (KR)

Presented are activities that help students understand the idea of a vector field. Included are definitions, flow lines, tangential and normal components along curves, flux and work, field conservation, and differential equations. (KR)

Determines which chessboards contain a chromatic rectangle having all four corners the same color for any black-white coloring. Expands the problem to a three color problem. (YP)

Describes learning difficulties students may have with the basic notions of linear algebra and three phases of abstraction. Discusses results of a program based on the abstraction process. (YP)

Compares two methods of approaching problem solving in quantitative disciplines. The danger of looking at answers too quickly is discussed. (YP)

Presented are 44 examples in which students are invited to guess what pattern of numbers is emerging and to decide whether the pattern will persist. Topics of examples include Pascal's triangle, integers, vertices, Fibonacci numbers, power series, partition functions, and Euler's theorem. The answers to all problems are included. (KR)

MathsAid was established in 2001 as a university-wide resource for students enrolled on programmes at Kingston University that contain a mathematics or statistics component. Its broad aims are to provide a set of non-threatening remedial and motivational opportunities in maths and statistics through one-to-one tutorial support, peer-assisted…

This paper describes the implications of constructivism both for what to teach and for how to teach. The first part discusses three approaches on what to teach: (1) relating mathematical knowledge to other knowledge; (2) checking for self-consistency; and (3) putting thinking before facts. The second part is on how to teach based on…

This study is a presentation of findings which indicate the relationship between performance scores on the Remedial Developmental Studies (RDS) mathematics curriculum and grades in a specific college level course in College Algebra for students enrolled at Tennessee Technological University. Results indicated that students who had completed the…

Through individual interviews with remedial and precalculus university students, five characteristics of the student were identified that influence whether a diagram is used in solving a problem and whether its use is successful. The interviews also suggested a set of subskills that contribute to the overall ability to draw effective diagrams.…

Results of the most recent administration of the National Assessment of Educational Progress (NAEP) suggest that the majority of secondary students believe in the independence of random events. In the study reported here, a high percentage of high school and college students answered similar problems correctly. However, about half of the students…

In this paper we describe a number of types of errors and underlying misconceptions that arise in mathematical reasoning. Other types of mathematical reasoning errors, not associated with specific misconceptions, are also discussed. We hope the characterization and cataloging of common reasoning errors will be useful in studying the teaching of…

Discussed are student mathematical background, computing skills, and case studies/field studies as they relate to business studies. A list of basic skills for tertiary business studies is provided including sigma notation, basic algebra, change, and solving equations. (CW)