The negotiation of meaning presupposes a taken-to-be-shared understanding of a situation. Uses an example to illustrate how negotiation of meaning and task may be linked in ways inappropriate to the learning of modeling and critical reflections. Contains 16 references. (Author/ASK)

Analyzes the results of a Mexican/British project that used the sociocultural approach to investigate ways in which mathematics is used in the practice of school science and the role of spreadsheets as a mathematical modeling tool. Suggests the possibility of enhancing students' capability to shift between a wider range of representations using…

Investigates 6th-grade students' use of equations to describe and represent problem situations prior to formal instruction in algebra. Describes students' preinstructional uses of equations to generalize problem situations and raise questions about the most appropriate curriculum for building on students' intuitive knowledge of algebra. (Contains…

Observes the application of probability theory to a game between two players. Shows how basic techniques such as tree diagrams can be used to demonstrate optimum strategies, how the art of bluffing can be quantified, and how this might be applied to a game of poker. (Author/ASK)

Learning styles encapsulate the preferences of the students, regarding how they learn. By including information about the student learning style, computer-based educational systems are able to adapt a course according to the individual characteristics of the students. In accomplishing this goal, educational systems have been mostly based on the…

In tasks as diverse as stock market predictions and jury deliberations, a person's feelings of confidence in the appropriateness of different choices often impact that person's final choice. The current study examines the mathematical modeling of confidence calibration in a simple dual-choice task. Experiments are motivated by an accumulator…

The insightful discussions by Raudenbush, Rubin, Stuart and Zanutto (RSZ) and Reckase identify important challenges for interpreting the output of VAM and for its use with test-based accountability. As these authors note, VAM are statistical models for the correlations among scores from students who share common teachers or schools during the…

The dataset presented here illustrates to students the utility of logistic regression. Its analysis results in a fit that explains much of how senators vote on a particular bill, and allows for quantification of the effects of ideology and money on the vote. A number of interesting quantitative interpretations follow from a good fit. A successful…

One of the objectives of the process technology curriculum at Wageningen University is that students learn how to design mathematical models in the context of process engineering, using a systematic problem analysis approach. Students find it difficult to learn to design a model and little material exists to meet this learning objective. For these…

This paper discusses a result of Li and Shen which proves the existence of a unique periodic solution for the differential equation x[dots above] + kx[dot above] + g(x,t) = [epsilon](t) where k is a constant; g is continuous, continuously differentiable with respect to x , and is periodic of period P in the variable t; [epsilon](t) is continuous…

This paper shows how inequalities can be utilized in reducing dimensionality of problems associated with the partition of unit fractions into the sums of two, three, and four like fractions. The need for such a reduction in this context stems from using a spreadsheet as a modelling tool. Activities described in this paper are grounded in standards…

The students of a Mathematical Modeling and Problem Solving class investigate and explore the mathematics involved in fitting a box spring mattress up a stairwell by solving various optimization problems and by using The Geometer's Sketchpad. The results show that a very small fraction of the class was actually able to solve the problem without…

The behavioral economic concept of unit price predicts that consumption and response output (labor supply) are determined by the unit price at which a good is available regardless of the value of the cost and benefit components of the unit price ratio. Experiment 1 assessed 4 pigeons' consumption and response output at a range of unit prices. In…

We report a study of repairs in communication between workers and visiting outsiders (students, researchers or teachers). We show how cultural models such as metaphors and mathematical models facilitated explanations and repair work in inquiry and pedagogical dialogues. We extend previous theorisations of metaphor by Black; Lakoff and Johnson;…

Autonomously developing organisms face several challenges when learning reaching movements. First, motor control is learned unsupervised or self-supervised. Second, knowledge of sensorimotor contingencies is acquired in contexts in which action consequences unfold in time. Third, motor redundancies must be resolved. To solve all 3 of these…