College students, in three experiments, learned to recite a counting pattern in the base three number system. Although all subjects learned to a criterion of two errorless trials, learning with different rule systems resulted in different levels of understanding and performance on transfer tasks. (GDC)

Argues that the effective use of calculators is important for employees in many areas. Suggests ways that schools might incorporate calculators into mathematics instruction. (PK)

Students are given a computational rule to follow for the first set of problems and must then discover the rule for the second set. Four worksheets for grades 1-8 are included. (MNS)

Defines arithmetic, harmonic, and weighted harmonic means, and discusses their properties. Describes the application of these properties in problems involving fuel economy estimates and average rates of motion. Gives example problems and solutions. (CW)

The study examined basic counting competencies, difficulties, skill progressions, and variation among 36 moderately retarded and 64 mildly retarded students (ages 5-14). Quantitative and qualitative analyses indicated deficiencies in basic counting competencies and systematic oral- and object-counting errors. Striking individual differences in…

This article describes the instructional efforts and success of two first grade teachers who cooperated in a year-long subtraction study with a university research team. Performance profiles of students in the experimental and control groups are presented, and implications for teaching are discussed. (PK)

Summarizes a simple design algorithm which identifies nested loops of equations which must be solved by trial-and-error methods. The algorithm is designed to minimize such loops, provides guidance to the selection of variables, and delineates the order in which systems of equations are to be solved. Examples are included. (TW)

Ten activities that give learners in grades 5-8 a chance to explore mathematics with calculators are provided. The activity cards involve such topics as odd addends, magic squares, strange projects, and conjecturing rules. (MNS)

Offers a way of teaching quantitative thinking through a software program called, "Hot Dog Stand." This simulation provides students with practice in planning expenses, in computing problems, and in dealing with a situation in which outcomes depend on random events. Also includes suggestions for computer use during non-scheduled time. (ML)

Discusses several recommendations for the mathematics curriculum, focusing on problem solving, understanding, several content topics, and topic integration and placement. Groups that influence the curriculum, and ways they can do so, are also discussed. (RH)

The federal government assists students and their parents in meeting the costs of postsecondary education through two student loan programs, the Federal Family Education Loan Program and the William D. Ford Direct Loan Program. Although the two programs provide similar benefits to borrowers, their structures and operations differ greatly. As a…

This study investigated the fluency with which first-graders with strong, moderate, or weak mathematical abilities apply the decomposition-to-10 and tie strategy on almost-tie sums with bridge over 10. It also assessed children's memorized knowledge of additions up to 20. Children's strategies were analysed in terms of Lemaire and Siegler's model…

In this report we present preliminary results of a study on the relationship between informal out-of-school and formal in-school mathematics and the ways each can inform the other in the development of new mathematical knowledge, in this case concerning computation in base 12, 24 or 60. This study is based on a teaching experiment involving a…

A Case Study is presented in this article, where there is a contradiction between pre-algebraic language semantic and syntax used to solve word problems through a negative integers subtraction. Appendix includes answer key. (Contains 1 figure.) [For complete proceedings, see ED500859.]

This paper shows how the concept of general objectivity can be used to improve behavioral science measurement, particularly as it applies to the Lexile Framework, a tool for objectively measuring reading comprehension. It begins with a dialogue between a physicist and a psychometrician that details some of the differences between physical science…