The effectiveness of the erratum in avoiding error propagation in physics

The propagation of errors in physics research is studied, with particular attention being paid to the effectiveness of the erratum in avoiding error propagation. We study the citation history of 17 physics papers which have significant errata associated with them. It would appear that the existence of an erratum does not significantly decrease the frequency with which a paper is cited and in most cases the erratum isnot cited along with the original paper. The authors comment on implications for the responsibilities of authors.     

The Rumsfeld effect: the unknown unknown

A set of studies tested whether people can use awareness of ignorance to provide enhanced test consistency over time if they are allowed to place uncertain items into a "don't know" category. For factual knowledge this did occur, but for a range of other forms of knowledge relating to conceptual knowledge and personal identity, no such effect was seen. Known unknowns would appear to be largely restricted to factual kinds of knowledge.     

Inconsistency in mathematics and the mathematics of inconsistency

No one will dispute, looking at the history of mathematics, that there are plenty of moments where mathematics is “in trouble”, when paradoxes and inconsistencies crop up and anomalies multiply. This need not lead, however, to the view that mathematics is intrinsically inconsistent, as it is compatible with the view that these are just transient moments. Once the problems are resolved, consistency (in some sense or other) is restored. Even when one accepts this view, what remains is the question what mathematicians do during such a transient moment? This requires some method or other to reason with inconsistencies. But there is more: what if one accepts the view that mathematics is always in a phase of transience? In short, that mathematics is basically inconsistent? Do we then not need a mathematics of inconsistency? This paper wants to explore these issues, using classic examples such as infinitesimals, complex numbers, and infinity.     

The unknown Fechner

Summary Despite Fechner's universal fame as the founder of psychophysics, his work is not very well known among contemporary psycholgists. To correct this situation, the present issue of Psychological Research contains some excerpts from previously untranslated works of Fechner. By way of introduction to the translations, some popular misconceptions about Fechner's outer psychophysics are corrected, and a brief introduction to his inner psychophysics is given.     

The mathematics of geographic profiling

We begin by describing some of the mathematical foundations of the geographic profiling problem. We then present a new mathematical framework for the geographic profiling problem based on Bayesian statistical methods that makes explicit connections between assumptions on offender behaviour and the components of the mathematical model. It also can take into account local geographic features that either influence the selection of a crime site or influence the selection of an offender's anchor point. Copyright © 2009 John Wiley & Sons, Ltd.     

The methodology of testing naive beliefs in the physics classroom

Many undergraduates harbor a variety of misbeliefs about physical objects in motion--for instance, that a bomb will fall straight down when dropped from a moving airplane. The evidence that these misbeliefs are resistant to correction by college-level physics courses, however, has often been based on methodologies that lack adequate internal validity. We used a quasi-experimental "before and after" design to assess the impact of two college physics courses, and we examined selection-bias, test-retest, and task-format factors directly. Initial accuracy and significant improvements due to instruction varied considerably by problem category and subject group; thus, in several ways, the results refute the general conclusion that conventional physics instruction does little to correct students' misbeliefs. We conclude by advocating the quasi-experimental approach for studies of naive beliefs in physics as well as for other situations in which the impact of classroom instruction is of interest.     

The paradox of phase transitions in the light of constructive mathematics

Synthese - The paradox of phase transitions raises the problem of how to reconcile the fact that we see phase transitions happen in concrete, finite systems around us, with the fact that our best...     

The relation of the structure of language to performance in mathematics

The relationship of performance in mathematics to syntactical language factors obtained from speech samples was investigated with 95 senior high school geometry students. Statistical procedures included correlation analysis and stepwise regression. The findings indicated that certain syntactical measures indicating logical thought processes correlated significantly with measures of mathematical performance. In addition, these syntactical measures added a statistically significant amount to intelligence in predicting performance in mathematics.     

The teaching of mathematics in Chinese elementary schools

China is a country with a long history and glorious civilization. Its tradition of putting emphasis on early education, especially children's learning of mathematics, is well known throughout the world. The superior achievements of elementary school students in mathematical learning have been attributed to the unique characteristics of the Chinese language, the simplicity of the Chinese number naming system, and the specific social environmental influence in Chinese society. Aside from the logical reasoning characteristics of the Chinese language, people usually count things in numerical order, e.g., Weekday 1, Weekday 2; Month 1, Month 2, etc., so that Chinese children become familiar with numbers at an early age, and are skillful in mental arithmetic operations. Training in good computational skills is crucial in the early period of mathematics learning. By use of the multiplication table, a cultural heritage of more than 2000 years that consists of a set of rhythmic formulae of multiplications, children can easily recall the product of two single‐digit numbers quickly and accurately, and find the quotient of a division directly. Mathematics teaching in elementary schools plays an essential role in the development of children's mathematical thinking ability, always a core task of teaching in China. Elementary school teachers have initiated various teaching methods to promote children's thinking to follow the course from the concrete to the abstract. Some of these effective methods are introduced in this paper. In the educational reform of China, the Ministry of Education proclaimed a new standard for the teaching of mathematics courses in elementary schools. Due to the availability of computers, some changes have been made in the requirements for written calculations. Intuitive thinking as well as creative abilities are to be cultivated. In order to meet the new standards, the role of the teacher is emphasized. The teaching/learning plan will be an interactive programme between teacher and students.