The relationship of the harmonic mean of two positive real numbers to the geometric mean and to the arithmetic mean is discussed; two geometric constructions for the harmonic mean are given. (DT)

Investigates the differences between students' and instructors' perceptions of similarities among basic computation-related rational number skills. Results indicate that college students in developmental mathematics do see some relationships among rational number computation skills, although not necessarily the ones seen by instructors. (AIM)

In a course on proofs, a number of problems deal with identities for Fibonacci numbers. Some general strategies with examples are used to help discover, prove, and generalize these identities.

This report describes reflections from two cycles of developmental research that involved creating and refining a series of computer-based applets for reasoning about the relative magnitude of fractional quantities. The applet sequence stemmed from a cognitively demanding task used in face-to-face teacher education settings that involved placing…

Taking advantage of student's passion in using technology in the form of digital media sets the trend of this study. If this passion can be harnessed, digital media may have an important and powerful role to play in education. A methodology of teaching using digital media in the form of VCD is experimented and tested for possible effect on…

Calls for reform in mathematics education around the world state that proofs should be part of school mathematics at all levels. Turning these calls into a reality falls on teachers' shoulders. This paper focuses on one secondary school teacher's reactions to students' suggested proofs and justifications in elementary number theory. To determine…

The author investigated the effects of the concrete-representational-abstract (CRA) instructional sequence on the computation performance of students with specific learning disabilities and students identified as at risk for failure in mathematics. Researchers have showed the CRA sequence to be effective for teaching basic mathematics facts,…

Previous research has reported that children's numerical equivalence judgments are affected by surface similarity and counting ability (e.g. Mix, Huttenlocher, & Levine, 1996; Siegel, 1973), a pattern that suggests categorization processes play a role in numerical development. However, because these studies involved memory for sets, large set…

This study investigated "individual differences" in different aspects of early number concepts in preschoolers. Eighty 4-year-olds from Oxford nursery classes took part. They were tested on accuracy of counting sets of objects; the cardinal word principle; the order irrelevance principle; and predicting the results of repeated addition…

Hannula and Lehtinen (2001, 2005) defined spontaneous focusing on numerosity (SFON) as the tendency to notice the relatively abstract attribute of number despite the presence of other attributes. According to nativists, an innate concept of one to three directs young children's attention to these "intuitive numbers" in everyday situations--even…

Studies have reported high correlations in accuracy across estimation contexts, robust transfer of estimation training to novel numerical contexts, and adults drawing mistaken analogies between numerical and fractional values. We hypothesized that these disparate findings may reflect the benefits and costs of learning linear representations of…