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.

Non-University Higher Education and the Relationship of Its Graduates and the World of Work: Colombia

The non-university sector has been part of the Colombian higher education system for more than 50-years. Despite its long years of existence, it has never occupied such an important role within the education system as the one it is having today. Therefore, the aim of this work is to analyze the development of the non-university sector in the framework of the country’s social, educational and economic demands. Likewise, its actual situation and certain aspects of the relationship between its graduates and the world of work, i.e., graduates’ employment characteristics, the relationship of higher education studies and their work, as well as their early career success, are examined. In order to generate the required information, a graduate survey was carried out in Atlántico (Colombia). The target population was graduates from higher education institutions registered in Atlántico who were awarded a technical, technological or professional degree in 2008 from any of the following knowledge areas: Fine Arts, Health Science, Economy-Administration-Accountancy and similar, and Engineering-Architecture-Urban planning and similar. Besides, interviews with academic and administrative staff from non-university institutions were carried out, and higher education related documents were analyzed. As a whole, the findings suggest that the non-university sector is expanding and may help to achieve some of the goals, for which it is widely promoted i.e., access expansion for under-represented groups, enhancement of the higher education system, and the provision of programs pertinent to the needs of the market. Nevertheless, some aspects require further consideration, e.g., the sector’s consolidation within the system and its quality. As for the relationship between non-university higher education and the world of work, it was found to be close; particularly in those aspects related to the use of knowledge and skills in the work, and the relationship between graduates’ studies and their work. Additionally, the analysis of the graduates’ in their early career stages exposes the significant role that the socioeconomic stratum plays in their working life, particularly in their wages. This indicates that apart from education, other factors like the graduates’ economic or social capital may have an impact on their future work perspectives