Describes how modifying familiar classroom formats in a college geometry class helped encourage student problem solving. Demonstrates these modified formats in the context of problems students explored, which resemble the problem-solving settings of mathematicians. (KHR)

Explores the problem posing abilities and attitudes towards mathematics of students in a university pre-calculus class and a university mathematical proof class. Reports a significant difference in numeric posing versus non-numeric posing ability in both classes. (Author/MM)

Underprepared college freshmen (212 in control group; 178 in experimental group) were monitored through 1 year of college mathematics in a study that showed cooperative learning and problem solving had a significant effect on mathematical success. An appendix contains sample problems. (MKR)

Describes and discusses a combinatorics exploration occurring in a recent course to help characterize the kind of learning communities to establish with students. (Author/MKR)

Shares a series of problems designed to provide students with opportunities to develop an understanding of applications of the definite integral. Discourages Template solutions, solutions in which students mimic a rehearsed strategy without understanding as the variety of problems helps prevent the construction of a template. (Author/ASK)

Investigates issues of mathematics instruction of problems in blocks. Discusses the best way to construct mathematical problems with connections to one another as parts of a coherent whole and how to reflect on the types of connections that can arise between them. (Author/KHR)

Proposes a calculus curriculum combining formative knowledge, mathematical foundations, and instrumental knowledge in mathematics. Discusses each of these components, the organization of a core calculus course, and the use of problem solving in calculus instruction. (10 references) (MKR)

Describes a course in problem solving for undergraduates not majoring in mathematics or science. The course was unusually successful in bringing average students to mathematical thinking. (Author/MKR)

Studied the differences between metacognitive behaviors exhibited by (n=6) graduate students in mathematics and (n=9) freshman college students. Experts possessed and used schemas to solve problems, but schema use did not fully or adequately characterize expertise. Beliefs about cognition played a more important role than control of cognition. (23…

It has become increasingly possible for mathematics students to include a limited number of approved optional, non-traditional modules in their programs. Surveys coursework in four non-specialist modules over a seven-year period, and examines work in the area of mathematical cognition. (Contains 16 references.) (Author/ASK)

Addresses the difficulties students have in acquiring graphical problem-solving skills. Presents some techniques and concepts intended to help students overcome them. Contains 15 references. (Author/ASK)

Presents a murder mystery in the form of six Calculus II review problems. Students must solve the six problems to determine the murderer, murder weapon, and time and location of the murder. (AIM)

Demonstrates examples, one of which is an extension of "guess and check," to include variables rather than numbers. The quadratic equation az2+bz+c=0, is solved by assuming a complex solution of the form z=x+iy. Explores the use of deMoivre's theorem in deriving trigonometric identities with other examples. (Author/ASK)

Examines infinite sets and cardinality classifications of empty, finite but not empty, and infinite through discussions of numbers that fall into particular categories. Categories discussed include perfect numbers, Mersenne primes, pseudoprimes, and transcendental numbers. Discusses the Null Or Infinite Set Effect (NOISE) and infinitude resulting…

Describes a course designed by Moravian College, Pennsylvania, to integrate precalculus topics as needed into a first calculus course. The textbook developed for the course covers the concepts of functions, Cartesian coordinates, limits, continuity, infinity, and the derivative. Examples are discussed. (MDH)