Coordination of aproximations in secondary school students’ understanding of limit concept

The aim of this research is to characterize the coordination of the processes of approximation related to the understanding of the limit of a function. We analyze the answers of 64 post-secondary school students to 7 problems considering the dynamic and metric conception of limit of a function. Results indicate that the metric understanding of the limit in terms of inequality supports that the student is capable of coordinating the approximations in the domain and in the range when lateral approximations coincide. However, the student is not capable of this coordination when lateral approximations do not coincide. This indicates that the metric understanding of the limit begins with the previous construction of the dynamic conception in case of coincidence of the lateral approximations in the range.

Concept and measurement: the cultural borders of meaning

Paper submitted to the Sixth International Conference on Social Science Methodology, Amsterdam, The Netherlands, August 16-20, 2004.

Social anxiety and self-concept in adolescence

This study analyzes the relationships between social anxiety and dimensions of self-concept in a sample of 2022 (50.1% males) Spanish adolescents, ranging in age from 12 to 16 year-olds. The social anxiety was assessed by the Social Phobia and Anxiety Inventory (SPAI), and self-concept was measured with the Self-Description Questionnaire II (SDQ-II). Logistic regression analyses show that adolescents with social anxiety are more likely to negatively perceive their relationship with opposite sex peers and have lower scores in self-esteem than students without social anxiety. Furthermore, in most logistic models, students with social anxiety also show a higher probability of perceiving their relation with peers of the same sex in a negative way, considering worse student, less attractive and athletic, and more emotional instable than students without social anxiety. The relevance of sex and grade in the relationship between social anxiety and self-concept in adolescence is discussed.

An explanatory model of academic achievement based on aptitudes, goal orientations, self-concept and learning strategies

As a result of studies examining factors involved in the learning process, various structural models have been developed to explain the direct and indirect effects that occur between the variables in these models. The objective was to evaluate a structural model of cognitive and motivational variables predicting academic achievement, including general intelligence, academic self-concept, goal orientations, effort and learning strategies. The sample comprised of 341 Spanish students in the first year of compulsory secondary education. Different tests and questionnaires were used to evaluate each variable, and Structural Equation Modelling (SEM) was applied to contrast the relationships of the initial model. The model proposed had a satisfactory fit, and all the hypothesised relationships were significant. General intelligence was the variable most able to explain academic achievement. Also important was the direct influence of academic self-concept on achievement, goal orientations and effort, as well as the mediating ability of effort and learning strategies between academic goals and final achievement.

Developing pre-service teachers’ noticing of students’ understanding of the derivative concept

This research study examines the development of the ability of pre-service teachers to notice signs of students’ understanding of the derivative concept. It analyses preservice teachers’ interpretations of written solutions to problems involving the derivative concept before and after participating in a teacher training module. The results indicate that the development of this skill is linked to pre-service teachers’ progressive understanding of the mathematical elements that students use to solve problems. We have used these results to make some suggestions for teacher training programmes.

Goal Orientation Profiles and Self-Concept of Secondary School Students

The objective of this study is to identify possible combinations of multiple goals that lead to different goal orientation profiles and to determine whether there are significant group differences in self-concept dimensions. The Achievement Goals Tendencies Questionnaire (AGTQ) and the Self-Description Questionnaire-II (SDQ-II) were administered to a sample of 2,022 students of Compulsory Secondary education, ranging in age from 12 to 16 years (M = 13.81, SD = 1.35). Cluster analysis identified four profiles of motivational goals: a group of students with a generalized high motivation profile, a group of students with generalized low motivation profile, a group of students with a predominance of learning goals and achievement goals, and a last group of students with a predominance of achievement goals and social reinforcement goals. Results reveal statistically significant differences among the profiles obtained regarding self-concept dimensions.