Didactic Restrictions on the Teacher’s Practice: The Case of Limits of Functions in Spanish High Schools

The Anthropological Theory of Didactics describes mathematical activity in terms of mathematical organisations or praxeologies and considers the teacher as the director of the didactic process the students carry out, a process that is structured along six dimensions or didactic moments. This paper begins with an outline of this epistemological and didactic model, which appears as a useful tool for the analysis of mathematical and teaching practices. It is used to identify the main characteristics of the mathematical organisation around the limits of functions as it is proposed to be taught at high school level. The observation of an empirical didactic process will finally show how the internal dynamics of the didactic process is affected by certain mathematical and didactic constraints that significantly determine the teacher’s practice and ultimately the mathematical organisation actually taught.     

Dialogue between theories interpreted as research praxeologies: the case of APOS and the ATD

The notion of “praxeology” from the anthropological theory of the didactic (ATD) can be used as a framework to approach what has recently been called the networking of theories in mathematics education. Theories are interpreted as research praxeologies, and different modalities of “dialogues” between research praxeologies are proposed, based on alternatively considering the main features and proposals of one theory from the perspective of the other. To illustrate this networking methodology, we initiate a dialogue between APOS (action-process-object-schema) and the ATD itself. It starts from the theoretical component of both research praxeologies followed by the technological and technical ones. Both dialogue modalities and the resulting insights are illustrated, and the elements of APOS and the ATD that the dialogue can promote and develop are underlined. The results found indicate that a complete dialogue taking into account all components of research praxeologies appears as an unavoidable step in the networking of research praxeologies.     

Identity learning: the core process of educational change

The aim of this paper is to offer an additional perspective to the understanding of educational change processes by clarifying the significance of identity learning. Today’s innovations require changes in teachers’ professional identity. Identity learning involves a relation between social‐cognitive construction of new meanings and individual, emotional sense‐making of new experiences. This relationship between cognition and emotion asks for a strong learning environment: the question is whether schools provide these strong learning environments. To answer this question, the paper provides an overview of the existing knowledge about schools as contexts for teacher learning and change. It will become clear that the emotional side of the change process has been overlooked. A model for identity learning is presented, involving both meaning‐giving and sense‐making. Building on this model, it is discussed how school leaders can build strategies for the identity learning of teachers.     

Can teachers motivate students to learn?

Research on motivation has mainly concentrated on the role of goal orientation and self‐evaluation in conducting learning activities. In this paper, we examine the relative importance of teachers’ teaching and their efficacy beliefs to explain variation in student motivation. Questionnaires were used to measure the well‐being, academic self‐efficacy, mastery goal orientation, performance avoidance, intrinsic motivation and school investment of students (n = 3462) and the teaching practices and teachers’ sense of self‐efficacy (n = 194) in primary schools. Results of the multi‐level analyses show that connection to the students’ world and cooperative learning methods had a positive effect on students’ motivation, while process‐oriented instruction by the teacher had a negative effect on motivational behaviour and motivational factors of students. Finally, the results lend credence to the argument that teachers’ sense of self‐efficacy has an impact on both teachers’ teaching and students’ motivation to learn.     

PUBLIC EXPENDITURE ON HIGHER EDUCATION: A COMPARATIVE STUDY IN THE EC‐MEMBER STATES, 1975‐1990

This article is an exercise in cross‐national comparative research on the financing of higher education, the countries involved being the EC countries. Before relevant comparisons could be made, agreement had to be reached as to what “higher education” is and what “students” are. It was then necessary to find some way of making accurate comparisons of monetary units and of dealing with contradictory ways in which educational statistics were and still are collected and collated. A research strategy was developed using existing sources, a specially developed questionnaire, and consultation with national experts. The results displayed biases for which corrections had to be made. They also, however, displayed a wide variety in the level of higher education expenditure in the EC countries. The project gave rise to the creation of the first comprehensive database that covers public expenditure on higher education in the twelve member states of the EC. It can be regarded as the first step in the creation of the “perfect database” on higher education expenditure which in turn would be a most valuable tool for higher education policy‐makers.

     

The effects of contingent feedback on perceived control and performance

The purpose of this study was to examine the impact on students’ performance of three contingent feedback strategies used by teachers. Contigency means that the feedback strongly corresponds with task behaviour that can be controlled by the students. Elementary school students (N=296) received individualized feedback about their performance during a series of five lessons. Within this contingent feedback structure, three strategies were applied which were assumed to enhance the perceived controllability of the task situation: (1) enhancing the perceptibility of the contingency between feedback and task behavior; (2) explicit reference to effort as part of the feedback, and (3) setting of goals. As predicted, the three contingent feedback strategies had a significant positive effect on perceived controllability, and led to better task performance.     

Design and calibration of a drill-guided system by laser for structural strengthening of historic bridge

Restoring the spans of a historic bridge requires installing tensors to ensure the structural and mechanical stability of the rows of stones that form the resistant body of the bridge. Once the positions where the structure-crossing tensors should be installed have been determined, the entry and exit points of each drill hole must be marked on both sides of the bridge. However, the exit point of each drill hole is not visible from the entry point, making it impossible to drill precisely. Here, we present a method based on a calibrated system that combines precision topography with laser technology. Using this method, drill holes longer than 12 m can be achieved with centimetric precision.     

The effect of systematic academic instruction on behavioural and academic outcomes of students with EBD

This study aims to assess the impact of systematic academic instruction on academic progress and behavioural problems of students with emotional and/or behavioural disorders (EBD) in special education. Earlier studies have noted the importance of a systematic approach as well as the significance of focusing on academic instruction instead of on behaviour. On the basis of these studies, it was hypothesised that the amount of teachers’ systematic academic instruction positively influences the academic progress of students with EBD as well as their behaviour. The amount of systematic academic instruction by teachers in daily teaching (N = 88) and the behaviour and academic progress of a sample of their students (N = 234) were measured and analysed by means of multilevel analyses. The results show a significant relationship between systematic academic instruction and academic outcomes. However, academic outcomes taking into account previous academic performance and behavioural outcomes could not be related to systematic academic instruction. Implications for research on the daily practice of special education are discussed.