The purpose of this study was to determine how the study of number theory might affect high school students' metacognitive functioning, mathematical curiosity, and/or attitudes towards mathematics. The study utilized questionnaire and/or interview responses of seven high school students from New York City and 33 high school students from Dalian,…

Twenty-four mathematics teachers were asked to think aloud when posing a word problem whose solution could be found by computing 4/5 divided by 2/3. The data consisted of verbal protocols along with the written notes made by the subjects. The qualitative analysis of the data was focused on identifying the structures of the problems produced and…

Classification problems ("find the odd-one-out") are frequently used as tests of inductive reasoning to evaluate human or animal intelligence. This paper introduces a systematic method for building the set of all possible classification problems, followed by a simple algorithm for solving the problems of the R-ASCM, a psychometric test derived…

Nonroutine function tasks are more challenging than most typical high school mathematics tasks. Nonroutine tasks encourage students to expand their thinking about functions and their approaches to problem solving. As a result, they gain greater appreciation for the power of multiple representations and a richer understanding of functions. This…

Two approaches are discussed for calculating the work necessary to pump water from a conical or parabolic container. The direct method derived from the definition of work is easy to misuse, as illustrated by a student's incorrect solution. (JP)

Demonstrated is how the concept of equivalence classes modulo n can provide a basis for solving a wide range of problems. Five problems are presented and described to illustrate the power and usefulness of modular arithmetic in problem solving. (MNS)

Study results indicate that teachers should be less concerned with teaching relationships between problem elements and more concerned with helping students to identify logical assumptions made in problem statement. (Author)

Six mathematics problems are posed; details are given of the solutions for six other problems. (DT)

Provides a discussion and an example of a problem which occurs in mathematical contests or entrance examinations and deals with the question of the magnitude of exponentials. Includes additional illustrative examples. (RT)

Discusses making tessellations by using a polyomino. Illustrates the various ways for various shapes of polyomino. Provides several diagrams and instructional guides. (YP)

Field tested with students in grades 10-12, this manual is designed to teach students in marketing courses basic mathematical concepts. The instructional booklet contains seven student assignments covering the following topics: why basic mathematics is so important, whole numbers, fractions, decimals, percentages, weights and measures, and dollars…