Presents examples of students' work when they are engaged in problem solving and reasoning tasks as they determine how to fill bottles with water to create musical notes by blowing across the tops of the bottles, and as they create mathematical models that represent these notes. (ASK)

Illustrates how a simple discontinuity in an individual's demand curve, or inverse-demand curve, affects the shape of market aggregate curves. Shows, for private goods, that an infinitesimal change in quantity can lead to large changes in consumption patterns; for collective goods, the analysis suggests a theory of coalition building. (DSK)

Introduces a model of differential equations for students--a very real overpopulation problem is occurring in the Ndumu Game Reserve in KwaZulu-Natal, South Africa, where one species of antelope, the Nyala, is crowding out another species, the Bushbuck. Constructs a competing species model to mathematically describe what is occurring in Ndumu.…

Adds a cropping or harvesting term to the animal overpopulation model developed in Part I of this article. Investigates various harvesting strategies that might suggest a solution to the overpopulation problem without actually culling any animals. (ASK)

Describes a rich, investigative approach to multivariable calculus. Introduces a project in which students construct physical models of surfaces that represent real-life applications of their choice. The models, along with student-selected datasets, serve as vehicles to study most of the concepts of the course from both continuous and discrete…

Presents three mathematical models for the evolution over time of the proportion of minorities in an academic department or similarly selected group of constant size. Analyzes both the steady-state and time-dependent behavior of the proportion of minorities and suggests a method of evaluating the fairness of a department's hiring history.…

A logit models analysis shows that access to university education in Spain is significantly affected by family income. Lower family income is associated with shorter degree programs; higher family income is associated with longer degree programs and higher degrees. A more determining factor is family cultural and educational level. Scholarships…

Social network analysis (SNA) uses indices of relatedness among individuals to produce representations of social structures and positions inherent in dyads or groups. SNA methods provide quantitative representations of ongoing transactional patterns in a given social environment. Methodological issues, applications and resources are discussed…

Describes how a mathematical model can be constructed and used to better understand human impact on natural resources. Uses the source of many current discussions in northern Idaho to present algebraic concepts and show an application of exponential functions. Contains 13 references. (ASK)

Describes a hands-on, guided-learning activity that forges vertical connections among grade levels and relies on physical models in the investigation of algebraic concepts. This lesson helps students discover that a given value can have multiple representations. Includes a sample student activity log. (AIM)

Using national longitudinal survey data, employs current duration-analysis techniques to examine the first teaching spell for a sample of teachers. Estimates of a proportional hazard model indicate that the length of a teacher's first spell is more responsive to wages than improved teaching conditions. Marriage and fertility variables are also…

Applies multilevel models of cost-effectiveness to numerous types of (British) institutions providing courses of instruction in the General Certificate of Education at Advanced Level. Different impressions may be gained about an institution's relative effectiveness when cost considerations are combined with outcome measures. Data evaluation needs…

This study examined effects of individual differences in speak-span scores and variations in memory demands on class-inclusion performance of 10-, 13-, and 15-year-olds. Results from regression analyses and the mathematical model indicated that differences in age, speak span, and memory load affected performance. Effects of speak span and memory…

Two experiments tested a neo-Piagetian model of verbal short-term memory, comparing it with the articulatory loop model. Findings indicated that the proposed model accounted for effects of M capacity, word length, and presentation modality on short-term memory. The model's fit to the data was acceptable, and parameter estimates were consistent…

Discusses the history of the development of Newton's Law of Cooling. Describes an experiment conducted in the kitchen that is designed to test the rate of cooling of a hot block of iron. Finds that Newton's law does not represent very well the mechanism of heat loss. (Contains over 10 references.) (WRM)