Learning on the margins: Positioning and algebraic thinking of a Haitian student in a Chilean classroom

Abstract

Migrant students who speak a language different from that of the school often face barriers that limit their participation and recognition in the mathematics classroom, leading to lower performance compared to their peers. This study explored the learning experiences of Daniel, a Haitian third-grade student in a Chilean school, while participating in a didactic intervention designed to foster early algebraic thinking. By observing his interactions with his peer group, the study analyzed exclusion dynamics and learning opportunities in a monolingual setting. In this context, the primary objective was to examine Daniel’s algebraic thinking and his positioning within the peer group as he solved algebraic tasks focused on pattern generalization.

The study adopts a non-deficit perspective on potential bilingualism through an embodied cognition approach, which considers not only words but also gestures and movements as valid expressions of thought. Additionally, the concept of positioning was used to analyze the roles students adopt in their interactions with others and how these influence their participation. In mathematics education, research has shown that linguistic minority students are often positioned as less competent, restricting the validation of their ideas. Thus, the study’s conceptual framework allowed for an analysis of both the cognitive and social aspects that shaped Daniel’s interactions with his peer group.

Methodologically, a case study was conducted, focusing on Daniel and his interactions with three Spanish-speaking classmates. The research was carried out within the framework of a didactic intervention based on pattern generalization tasks to develop algebraic thinking. Sessions were video-recorded, students’ worksheets were collected, and individual interviews were conducted at the end of the intervention. The video analysis followed a categorical approach, incorporating categories to describe positioning within the group (expert, novice, facilitator) and algebraic thinking through Daniel’s semiotic activity, including gestural, spoken, and written records.

The findings indicate that, despite his difficulties in arithmetic and oral expression in Spanish, Daniel demonstrated advanced algebraic reasoning, particularly in identifying patterns, assigning correct meanings to letters, and proposing their use in simple algebraic expressions. His ideas were often best understood through gestures rather than spoken language, emphasizing the importance of considering non-verbal forms of expression in mathematics instruction for potential bilingual students. Despite his contributions, the analysis of positioning revealed that Daniel was mostly perceived as a novice, which limited his participation and the consideration of his ideas within the group. On several occasions, Daniel abandoned his own correct ideas in favor of incorrect ones proposed by classmates whose voices were perceived as more competent in the subject.

These results provide a basis for reflecting on how linguistic exclusion in the classroom can obscure students’ abilities, restricting their participation and mathematical learning development. Furthermore, this study highlights the importance of implementing teaching strategies that promote equity in the classroom by recognizing and valuing diverse forms of mathematical expression. In particular, it underscores the need to consider gestural repertoire as a legitimate means of communicating ideas, fostering a more inclusive and accessible approach to mathematics education.