Argumentation and participation in the primary mathematics classroom: Two episodes and related theoretical abductions

The main assumption of this article is that learning mathematics depends on the student's participation in processes of collective argumentation. On the empirical level, such processes will be analyzed with Toulmin's theory of argumentation and Goffman's idea of decomposition of the speaker's role. On the theoretical level, different statuses of participation in processes of argumentation will be considered. By means of the method of comparative analysis, different grades of autonomy according to the interactional contribution of a student can be reconstructed. The paper finishes with remarks about consequences for improving mathematics teaching in schools and mathematics teacher education at university level.     

The wholes that are greater than the sum of their parts: employing cooperative learning in mathematics teachers’ education

This paper presents a study on employing different types of cooperative learning (CL) settings in mathematics teacher education based on multiple research data. The study analyzes mechanisms in which CL contributes to the development of teacher knowledge of three kinds: subject matter knowledge, pedagogical content knowledge, and curricular content knowledge. Additionally, it reflects on interactions between different kinds of teachers’ knowledge in the process of development. Two wholes, which are greater than the sum of their parts, are analyzed in this paper. The first is a course whose design combines different CL settings, hence enhances different mechanisms for teachers’ professional development. The second whole, teachers’ “collaborative mind,” is presented as an outcome of the first. To exemplify possible contributions of employing CL in teacher education, this paper first zooms in on the structure of one particular course for mathematics teachers and then focuses on one particular mathematical activity.     

Risk management in power markets: The Hedging value of production flexibility

Since the 1990s power markets are being restructured worldwide and nowadays electrical power is traded as a commodity. The liberalization and with it the uncertainty in gas, fuel and electrical power prices requires an effective management of production facilities and financial contracts. Thereby derivatives build essential instruments to exchange volume as well as price risks. The challenge for participants in the newly competitive market environment is how to design, price and hedge derivative contracts in particular combination with the flexibility embedded in dispatch strategies of production assets. Accordingly, an adequate basis for management and investment decisions is needed which responds to the highly complex market situation.     

Developing a measure of risk adjusted revenue (RAR) in credit cards market: Implications for customer relationship management

Current models of customer lifetime value (CLV) consider the discounted value of profits that a customer generates over an expected lifetime of relationship with the firm. This practice can be misleading in the financial services markets because it ignores the risk posed by the customer (such as delinquency and default). Specifically, in the credit card market, the correlation between revenue and risk is positive. Therefore, firms need to adjust a customer’s profits for the associated risk before developing a measure of customer lifetime value. We propose a new measure, risk adjusted revenue (RAR), that can incorporate multiple sources of risk and demonstrate the usefulness of the proposed measure in correctly assessing the value of a customer in the credit card market. The model can be extended to compute risk adjusted lifetime value (RALTV). We use the RAR metric to understand the effectiveness of different modes of acquisition, and of retention strategies such as affinity cards and reward cards. We find that both reward- and affinity-cardholders generate higher RAR than non-reward and non-affinity cardholders respectively. The ordering of different modes of acquisition with respect to RAR (in decreasing order) is as follows: Internet, direct mail, telesales, and direct selling.