On first looking into education statistics for the United Kingdom

The main data in Education Statistics for the United Kingdom 1986, which concerns the academic or financial year 1984‐85, are described from the point of view of a researcher who is not an expert about statistics. Where interesting trends can be discerned, these are highlighted. More often, however, the data raise questions of interpretation and some indication is given of the more detailed collections of statistical data which need to be consulted. The specific issue of the shortage of teachers of mathematics, physics and technology is used to illustrate the most important missing ingredients: the need for the data to correspond more closely to the division of educational provision into different kinds of activities and the need for the data to be placed in a context of data for other professions and other branches of government.     

Mathematical discussion and mathematical understanding

A longitudinal study is being undertaken into the question of whether or not discussion in the mathematical classroom is an aid to understanding. Preliminary analysis shows that, while the hypothesis that discussion aids understanding is very attractive, evidence to support the hypothesis has been limited. Classroom observations during the first year of the study have led to a method of classification of mathematical talk in the classroom which we expect will prove useful in investigating links between mathematical discussion and mathematical understanding.The ability to say what you mean and mean what you say should be one of the outcomes of good mathematics teaching .... Pupils need the explicit help, which can only be given by extended discussion, to establish these relationships (between different mathematical topics); even pupils whose mathematics attainment is high do not easily do this themselves. (Cockcroft, 1982, England)In all other topics, we saw teachers there (Kitamaeno School in Tokyo) using peer group dialogues ... (they) justified their use of group dialogue because of their large classes (35–43) and the unusually independent spirit of many of the 600 pupils. Mathematics achievement was very high by American standards. (Easley, 1984, on a Japanese project)We need to recognise the importance of verbalisation. Putting thoughts into words requires students to organise their thinking and to confront their incomplete understanding. Listening to others affords them the opportunities to contemplate the thinking of others and to consider the implications for their own understanding. (California State Department of Education, 1987)This article is based on the first year of a longitudinal study intended to shed light on the question of whether or not discussion in the mathematics classroom is an aid to mathematical understanding. Before looking further at the research context in which this project is set, we wish to offer our definitions of the two notions in the title.     

Cost-Sharing in Higher Education: Differences between countries and between distinct socio-economic groups

The paper studies the relation between different national cost-sharing models and how students from different socio-economic backgrounds finance their higher education in six different European countries: the Czech Republic, England, Germany, the Netherlands, Norway, and Spain. The findings reveal considerable differences both between the countries and also between different socio-economic groups of students within each country. Even though there are only small social differences in the students’ level of income, there are considerable social differences in the students’ sources of income. The findings are discussed related to the country’s specific policy and higher education funding structures.