The present analysis describes an analytically simple and systematic approximation procedure for modelling the free diffusive spreading of initially super-Gaussian profiles. The approach is based on a self-similar ansatz for the evolution of the diffusion profile, and the parameter functions involved in the modelling are determined by suitable…

Recently, there have been many efforts to use the research techniques developed in the field of physics education research to improve the teaching and learning of quantum mechanics. In particular, part of this research is focusing on misconceptions held by students. For instance, a set of misconceptions is associated with the concept of stationary…

The Magic Mathworks Travelling Circus is a touring maths lab--in and of itself, a good thing. When children enter it, they find particular pieces of apparatus captioned with particular challenges--which is perhaps not such a good thing. Students are faced with an apparatus that can do only one thing, and so are not encouraged to look again at…

The Flynn Effect [Flynn, J. R. (1984). The mean IQ of Americans: Massive gains 1932 to 1978. Psychological Bulletin 95, 29-51.] is an increase in IQ of around 0.33 points per year, observed in developed (and some developing) countries during the past century. It emerges from problem solving and other non-verbal components of IQ. The cause has been…

The construct validity of algebra word problems for measuring quantitative reasoning was examined, focusing on an analysis of problem attributes and on the analysis of constructed-response solutions. Constructed-response solutions to 20 problems from the Graduate Record Examinations (GRE) General Test were collected from 51 undergraduates.…

This paper discusses a study that explored the mental models of fifth (n=35) and sixth (n=49) graders attending two urban public elementary schools in South Korea in word problem solving. Two levels of mental models (problem model and mathematical model) constructed in the process of word problem solving were investigated. Coding categories for…

It is argued that mastery learning is one explanation for the documented differences in mathematics achievement between Japanese and American students. Given its emphasis on mastery at one stage before moving on to the next stage, and the potential accumulated benefits of this approach over time, mastery learning appears to be very similar to what…

The standards developed for reform in mathematics education by the National Council of Teachers of Mathematics (NCTM) de-emphasize the algorithmic manipulation of mathematical symbols. The NCTM takes the position that the rapidly changing workplace is an environment that requires problem-solving skills with computers being used to perform routine…

The validation of key contextual features of algebra word problems was studied in two phases. In the first phase, five experts were asked to assess the appropriateness of the concepts in the problems and the adequacy of the assignment of the contextual features to the problems. In the second phase, construct validity was established by having 6…

The Mathematics, Science, and Technology Educators and Researchers of The Ohio State University (MSaTERS-OSU) is a newly formed student organization. Papers from the conference include: (1) "Was the Geometry Course, The Nature of Proof, Taught by Harold Pascoe Fawcett the Best Course Ever Taught in Secondary School?" (Frederick Flener); (2) "A…

Students' performances on mathematical problems varying in symbolic form and the kinds of symbolic representations and translation used in instruction were explored. The sample consisted of 29 students enrolled in Algebra II in a summer program for minority students. All students were Black or Hispanic American and most were about to enter grade…

This study examines the construct of problem representation and the processes used by learners to construct or modify problem representations in problem-solving situations. Students (n=14) from freshman calculus courses at the University of California at San Diego participated in videotaped interviews in which they were asked to think aloud as…

This teacher's guide is the ninth in a set of 20 activity booklets for teaching mathematics to children in grades 1-8. The 20-level curriculum embodies carefully delineated areas of learning arranged in progressive stages, eliminating grade restrictions and permitting continuous growth according to the individual's ability and rate of learning.…

The objective of this presentation is to focus on the use of a hand-held graphics calculator. The specific machine referred to in this monograph is the Casio fx-7000G, chosen because of its low cost, its large viewing screen, its versatility, and its simple operation. Sections include: (1) "Basic Operations with the Casio fx-7000G"; (2) "Graphical…

The purpose of this notebook is to assist educators who are designing and implementing inservice education programs to facilitate the effective use of computer integrated instruction (CII) in schools. The book is divided into the following five sections: (1) Effective Inservice (a brief summary of inservice literature focused on inservice…