Fostering diagnostic competence in prospective mathematics elementary teachers through epistemic activities.

Research on fostering teachers' diagnostic competence and thinking has become increasingly important. To this end, research has already identified several aspects of effective fostering of teachers' diagnostic competence. One of the aspects is assignment of the role as a teacher in interventions but, so far, assignment of the role of student has hardly been considered.

Measuring people's covariational reasoning in Bayesian situations.

Previous research on Bayesian reasoning has typically investigated people's ability to assess a posterior probability (i.e., a positive predictive value) based on prior knowledge (i.

Different Visualizations Cause Different Strategies When Dealing With Bayesian Situations.

People often struggle with Bayesian reasoning. However, previous research showed that people's performance (and rationality) can be supported by the way the statistical information is represented. First, research showed that using natural frequencies instead of probabilities as the format of statistical information significantly increases people's performance in Bayesian situations.

How to Improve Performance in Bayesian Inference Tasks: A Comparison of Five Visualizations.

Bayes' formula is a fundamental statistical method for inference judgments in uncertain situations used by both laymen and professionals. However, since people often fail in situations where Bayes' formula can be applied, how to improve their performance in Bayesian situations is a crucial question. We based our research on a widely accepted beneficial strategy in Bayesian situations, representing the statistical information in the form of natural frequencies.

Utility indifference pricing of insurance catastrophe derivatives.

We propose a model for an insurance loss index and the claims process of a single insurance company holding a fraction of the total number of contracts that captures both ordinary losses and losses due to catastrophes. In this model we price a catastrophe derivative by the method of utility indifference pricing. The associated stochastic optimization problem is treated by techniques for piecewise deterministic Markov processes.

The Impact of Visualizing Nested Sets. An Empirical Study on Tree Diagrams and Unit Squares.

It is an ongoing debate, what properties of visualizations increase people's performance when solving Bayesian reasoning tasks. In the discussion of the properties of two visualizations, i.e.

Integrated learning: ways of fostering the applicability of teachers' pedagogical and psychological knowledge.

In teacher education, general pedagogical and psychological knowledge (PPK) is often taught separately from the teaching subject itself, potentially leading to inert knowledge. In an experimental study with 69 mathematics student teachers, we tested the benefits of fostering the integration of pedagogical content knowledge (PCK) and general PPK with respect to knowledge application. Integration was fostered either by integrating the contents or by prompting the learners to integrate separately taught knowledge.

Integrating pedagogical content knowledge and pedagogical/psychological knowledge in mathematics.

In teacher education at universities, general pedagogical and psychological principles are often treated separately from subject matter knowledge and therefore run the risk of not being applied in the teaching subject. In an experimental study (N = 60 mathematics student teachers) we investigated the effects of providing aspects of general pedagogical/psychological knowledge (PPK) and pedagogical content knowledge (PCK) in an integrated or separated way. In both conditions ("integrated" vs.

Real-time observation of molecular motion on a surface.

The laser-induced movement of CO molecules over a platinum surface was followed in real time by means of ultrafast vibrational spectroscopy. Because the CO molecules bound on different surface sites exhibit different C-O stretch vibrational frequencies, the site-to-site hopping, triggered by excitation with a laser pulse, can be determined from subpicosecond changes in the vibrational spectra. The unexpectedly fast motion--characterized by a 500-femtosecond time constant--reveals that a rotational motion of the CO molecules, rather than pure translation, is required for this diffusion process.

Adsorption and dissociation of NO on stepped Pt (533).

We present an experimental and theoretical investigation of the adsorption, desorption, and dissociation of NO on the stepped Pt (533) surface. By combining temperature programmed desorption and reflection absorption infrared spectroscopy, information about the adsorption sites at different temperatures is obtained. Surprisingly, metastable adsorption structures of NO can be produced through variation of the dosing temperature.