Working with mathematics teachers and immigrant students: an empowerment perspective

This article centers on a professional development project with a group of high school mathematics teachers in Barcelona. The eight participating teachers taught in low-income schools with a high percentage of immigrant students. Our model of professional development is based on the involvement of the teachers as co-researchers of their local contexts and practices. In this approach, our concept of social justice is tied to the notion of empowerment, both for teachers and for their immigrant students. Our analysis of data from twelve sessions with the teachers shows the development of a shared awareness of their local situation that leads to their questioning of their practices followed by a reconstruction of those. Teachers worked together to move from talking to action. Our analysis of data from the implementation of one lesson in a classroom shows that action, and illustrates signs of empowerment in the teacher and the students, such as students’ challenging of aspects of the task and taking on a more participatory role and the teacher’s reflection on the overall experience.     

Language as resource: a key notion for understanding the complexity of mathematics learning

Many mathematical concepts may have prototypical images associated with them. While prototypes can be beneficial for efficient thinking or reasoning, they may also have self-attributes that may impact reasoning about the concept. It is essential that mathematics educators understand these prototype images in order to fully recognize their benefits and limitations. In this paper, I examine prototypes in a context in which they seem to play an important role: graphical representations of the calculus concept of the definite integral. I use student data to empirically describe the makeup of the definite integral prototype image, and I report on the frequency of its appearance among student, instructor, and textbook image data. I end by discussing the possible benefits and drawbacks of this particular prototype, as well as what the results of this study may say about prototypes more generally.     

Teaching Mathematics in Multilingual Classrooms

In this paper we present the way in which language issues have become a relevant factor in research which aims to study the socio-cultural aspects of mathematics education in classrooms with a high percentage of immigrant students. Our research on language issues focuses on two aspects, namely the language as a social tool within the mathematics classroom and the language as a vehicle in the construction of mathematical knowledge. We introduce our problem within this area and provide a rationale for our research methodology, not avoiding its drawbacks,but rather giving examples of the kinds of difficulties we encountered. The paper highlights the integrated nature of the social, cultural and linguistic aspects of mathematics teaching and learning, and illustrates the fact that, even if the mathematical language can be considered universal, the language of ‘doing mathematics within the classroom’ is far from being universal. This revised version was published online in July 2006 with corrections to the Cover Date.     

One speaker,two languages: Learning opportunities in the mathematics classroom

The data reported in this article come from a large project whose goal was to explore how Latin American students in Catalonia, Spain use their two languages—Spanish and Catalan—to support their learning of mathematics in small groups with other students who are Spanish- or Catalan-dominant. For 5 years, lessons from bilingual mathematics classrooms in three public secondary schools were video-recorded and transcribed. In the presentation of findings, I discuss three language practices that emerged from the analyses of several classroom instances as follows: (1) caution with mathematical vocabulary, (2) invention of terms, and (3) word-for-word translation. One example is chosen to represent each practice and some of its situated effects. The first two examples support the view that the experience of language difficulties, either real or presumed, contributes to generating opportunities that may be beneficial to mathematics learning. The third example, where the focus on the mathematics is hindered, points to a contrasting finding. Unlike other studies in the field, which have reported the difficulties and obstacles that arise in learning and teaching due to bilingualism in the classroom, I propose a change of focus through the conceptualization of language as a potential for thinking and doing, and particularly for learning and teaching mathematics.     

Student perceptions of peer assessment: an interdisciplinary study

Peer assessment provides students with multiple benefits during their learning process. The aim of our study is to examine students’ perception of peer assessment. Questionnaires were administered before and after the peer-assessment process to 416 students studying 11 different subjects in four different fields taught at the University of Girona. Results suggest that students have a positive predisposition towards this methodology, both before and after its implementation. Students perceive it as a both motivating and recommended methodology that facilitates the acquisition of learning at different levels. As for its limitations, students highlight the responsibility that comes with it and a certain amount of distrust in fellow students’ abilities to peer-assess.     

Social representations as mediators of mathematics learning in multiethnic classrooms

Drawing on socio-cultural theory, we understand the norms regulating the practices within the mathematics classroom as resulting from the social representations of the socially dominant groups and of the school culture related to what constitutes learning mathematics. Immigrant studients, having their own personal histories as members of particular social groups, and having been in school traditions other than the one predominant in the host society, have their own images of what mathematics in school is about. Individuals interacting in the classroom are all re-interpreting the different episodes from the perspective of the social representations of the larger groups with which they identify themselves. In multiethnic classrooms different re-interpretations of the same norms clash. The lack of negotiation gives rise to obstacles to immigrant students’ participation in the mathematical conversations and, therefore, interferes with the students’ learning process.