Examined the performance of a recently available full information maximum likelihood (FIML) estimator in a multiple regression model with missing data using Monte Carlo simulation and considering the effects of four independent variables. Results indicate that FIML estimation was superior to that of three ad hoc techniques, with less bias and less…

Molecular modeling by computer is used to display stereochemistry, molecular orbitals, structure of transition states, and progress of reactions. Describes new ideas for teaching 1H NMR spectroscopy using computer modeling. (Contains 12 references.) (ASK)

Examines the likely effect of grade retention on high-school dropout rate and post-high-school labor-market earnings. Uses High School and Beyond data set. Reports different estimated coefficients using ordinary least-squares versus using instrumental variables that account for endogeneity. (Contains 36 references.) (PKP)

Develops a simple model of student choice to explain why some teaching innovations have only a negligible effect on mean student performance. If students set grade targets, some students choose to learn less (despite innovations), and the change in mean student achievement will tend to be small. (Contains 20 references.) (MLH)

A method for teaching problem-solving skills to mathematics students is presented. By subtly incorporating engineering applications, the students are simultaneously exposed to an effective outreach programme. The process includes offering a complex problem that challenges students' abilities. Before allowing the students to become frustrated, the…

A simple model for how traffic moves around a closed loop of road is introduced. The consequent analysis of the model can be used as an application of techniques taught at first year undergraduate level, and as a motivator to encourage students to think critically about model formulation and interpretation.

In this paper we present three cases of instructional design that illustrates both horizontal didactising, the activity of using already established principles to design instruction, and vertical didactising the activity of developing new tools and principles for instructional design. The first case illustrates horizontal didactising by…

In this paper, we examine the use of an ordinary differential equation in modelling the SARS outbreak in Singapore. The model provides an excellent example of using mathematics in a real life situation. The mathematical concepts involved are accessible to students with A level Mathematics backgrounds. Data for the SARS epidemic in Singapore are…

Nowadays, mathematics has come to be increasingly put into practical use in various fields in society. However, Japanese students dislike mathematics. The purpose of this study is to consider the significance of teaching modelling. In this paper, I take up "Fuzzy modelling" as teaching material for senior high school students. As a…

The purpose of this article is to describe findings from a study of teachers' social interaction during discussions about students' thinking. The goal of the discussions was for the teachers to interpret their students' thinking as revealed from work on non-routine, thought-revealing mathematical tasks, known as "model-eliciting…

This paper deals with a teaching approach aimed to help students become aware of targeted techniques of significance in problem solving. The teaching approach is to present a series of tasks that all can be solved by applying the same technique. Two levels of prompting are used; first for the students to realize solutions without necessarily being…

In this article we examine students' perspectives on the customary, public work of proving in American high school geometry classes. We analyze transcripts from 29 interviews in which 16 students commented on various problems and the likelihood that their teachers would use those problems to engage students in proving. We use their responses to…

This article describes a classroom activity in which a solar eclipse is simulated and a mathematical model is developed to explain the data. Students use manipulative devices and graphing calculators to carry out the experiment and then compare their results to those collected in Koolymilka, Australia, during the 2002 eclipse.

Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical…

A new general procedure for deriving the Gibbs energy of mixing is developed through general thermodynamic considerations, and the ideal-solution model is obtained as a special particular case of the general one. The deduction of the Gibbs energy of mixing for the ideal-solution model is a rational one and viewed suitable for advanced students who…