Applications and modelling in mathematics teaching

The aim of this paper is a comprehensive presentation of some important basic and general aspects of the topic applications and modelling, with emphasis on the secondary school level. Owing to the review character of this paper, some overlap with the survey paper Blum and Niss (1989) for ICME-6 in Budapest is inevitable. The paper will consist of three parts. In part 1, I shall try to clarify some basic concepts and remind the reader of a few application and modelling examples suitable for teaching. In part 2, I shall formulate some general aims for mathematics instruction and, on that basis, summarise the most important arguments for and against applications and modelling in mathematics teaching. Finally, in part 3, I shall discuss some relevant instructional aspects resulting from the considerations in part 2.

Mathematical modelling in mathematics education and instruction

This paper aims at giving a concise survey of the present state-of-the-art of mathematical modelling in mathematics education and instruction. It will consist of four parts. In part 1, some basic concepts relevant to the topic will be clarified and, in particular, mathematical modelling will be defined in a broad, comprehensive sense. Part 2 will review arguments for the inclusion of modelling in mathematics teaching at schools and universities, and identify certain schools of thought within mathematics education. Part 3 will describe the role of modelling in present mathematics curricula and in everyday teaching practice. Some obstacles for mathematical modelling in the classroom will be analysed, as well as the opportunities and risks of computer usage. In part 4, selected materials and resources for teaching mathematical modelling, developed in the last few years in America, Australia and Europe, will be presented. The examples will demonstrate many promising directions of development.

Analysis of applications and of conceptions for an application-oriented mathematics instruction

In connection with the (revived) demand for considering applications in the teaching of mathematics, various schemata or lists of criteria have been developed since the end of the sixties, which set up requirements about closeness to the real world or about the type of mathematics being used, and which have made it possible to analyze the available applications in their light. After having stated the problem (in section 1), we present (in section 2) a sketch of some of the best known of these and of some earlier schemata, although we are not aiming for a complete picture. Then (in section 3) we distinguish among different dimensions.in the analysis of applications. With this as a basis, we develop (in section 4) our own suggestion for categorizing types of applications and conceptions for an application-oriented mathematics instruction. Then (in section 5) we illustrate our schemata by some examples of performed evaluations. Finally (in section 6), we present some preliminary first results of the analysis of teaching conceptions.

Reforming Cooperative Credit Structure in India for Financial Inclusion

In the drive for financial inclusion in India, cooperative banks assume prime importance as they are much more accessible to the rural poor than commercial banks. While more accessible, cooperative banks' financial health is rather poor and, therefore, might not be able to serve the needy in a sustained manner. A committee led by Prof. Vaidyanathan has outlined a revival package for cooperatives. Besides suggesting an infusion of funds, it called for the adherence to certain stringent norms to ensure the financial viability. The recommendations provided in the committee’s report are under various stages of implementation in India. The book examines the progress of this reform drive in Bihar, a state in Eastern India. It discusses the background for appointing the committee and its recommendations and also presents the findings of a field study conducted in this regard. The findings inform further policy suggestions which are of general interest to the drive for financial inclusion also in other countries.

Factors affecting choice of financial services among rural consumers: Emerging experiences from Gicumbi District, northern Province in Rwanda

Enhancement of financial inclusivity of rural communities is often recognised as a key strategy for achieving economic development in third world countries. The main objective of this study was to examine the factors that influence consumers’ choice of a rural bank in Gicumbi district of Rwanda. Data was collected using structured questionnaires and analysed using a binary probit regression model and non-parametric procedures. Most consumers were aware of Popular Bank of Rwanda (BPR) and Umurenge SACCO through radio advertisements, social networks and community meetings. Accessibility, interest rates and quality of services influenced choice of a given financial intermediary. Moreover, the decision to open a rural bank account was significantly influenced by education and farm size (p<0.1). These results indicate the need for financial managers to consider these findings for successful marketing campaigns.