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…

In an elementary undergraduate abstract algebra or group theory course, a student is introduced to a variety of methods for constructing and deconstructing groups. What seems to be missing from contemporary texts and syllabi is a theorem, first proved by Edouard Jean-Baptiste Goursat (1858-1936) in 1889, which completely describes the subgroups of…

The "Cognitive Tutor[R] Algebra I" curriculum, published by Carnegie Learning, is an approach that combines algebra textbooks with interactive software. The software is developed around an artificial intelligence model that identifies strengths and weaknesses in each individual student's mastery of mathematical concepts. It then…

This paper describes an intervention at the 8th grade level where university mathematics researchers presented a series of lessons on introductory concepts in probability and statistics. Pre- and post-tests, and interviews were conducted to examine whether or not students at this grade level can understand these concepts. Students showed a…

In early 2008 researchers from the University of Melbourne's "New Technologies for Teaching Mathematics" project created a lesson for the Year 10 students at their Victorian research schools. Two important goals of secondary school mathematics education are to build students' conceptual knowledge and to teach students to think…

This article describes a problem-centered curriculum for grades 9-12, using problem sets developed by a mathematics department and designed to take the place of textbooks. The students discover mathematical concepts in the context of the problems and activities in the materials.

This article is in two parts: discussion of mathematical concepts involved in converting the reading from the tape-recorder counter which counts the turns of the run-off spool to that from the counter which counts turns of the take-up spool; calculating the length of tape run off when given the reading from the tape-recorder counter of the run-off…

Age-related changes in children's performance on simple division problems (e.g., 6 divided by 2, 72 divided by 9) were investigated by asking children in Grades 4 through 7 to solve 32 simple division problems. Differences in performance were found across grade, with younger children performing more slowly and less accurately than older children.…

This booklet contains some 80 problems in mathematics suitable for computer solution. The problems range from very simple to complex. Problems have been included from most mathematic disciplines, including number theory, analytical geometry, probability and statistics, trigonometry, equations, and sequence and limits. For the most part these…

Aspects of the source of power of mathematics and the ways in which mathematics works are discussed. The author discusses various philosophies about mathematics, presents several unusual "real world" problems, and reviews the social consequences of the "imposition of mathematics" on humanity. (MP)

Describes a model for geometrical probability. Presents two examples of basic theories of probability using geometrical probability. Provides three problems using the described theorem. (YP)

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)

This paper describes a proportional reasoning problem set within a real-life context and a complete analysis of one small group discussion of this problem over the course of a 90-minute block. The seventh-grade students' discourse is described to provide insights into typical mathematical interpretations of this problem, as well as some…

This resource package deals with elementary level mathematics in daily living, substituting newspapers as a refreshing change from mathematics texts. A total of 40 exercises are intended to provide review and reinforcement for skills previously taught in formal lessons. Skill or concept areas included are: reading large numbers; basic operations;…