What Do You See That You Can Name? A Chilean Lexicon of Middle School Mathematics Teachers

• In Event: The Lexicon Project: Examining the Content, Structure, and Implications of Pedagogical Naming Systems From Different Cultures

Abstract

Objective
The purpose of this study was to document the lexicon of Chilean teachers of middle school mathematics, as part of an international effort to identify and compare lexicons of nine countries in five continents.

Perspective
Communities of practice share, among other things, discourse that allows them to learn from each other (Kelly, 2006). The level of sophistication of this shared language might vary. It is thus reasonable to expect that the language researchers and teachers employ to describe the classroom differs. Nonetheless, teachers’ language does not often feature in research, becoming less visible than that of researchers (McIntyre, 2005). This study aimed to identify and describe, as a starting point, the professional lexicon of middle school mathematics teachers in Chile to reflect on the language of the local teaching community.

Methods and Data
The initial stimulus was a set of 8th grade mathematics lessons, one from each of the nine participating countries. A team of researchers and experienced mathematics teachers viewed these videos and listed short terms and phrases of things we could name, prioritising the teachers’ terms. Lexical items comprising a term, description and examples were later developed. Our lexicon was validated with Chilean teachers using an online survey that assessed familiarity and usage. The descriptions and examples were translated into English, and a close English approximation for the term was identified. The validated list was analysed employing systematic coding to address the main features of our Chilean lexicon.
The data in our Chilean lexicon consists of 74 terms. The systematic coding process focused on the expression of agency and their reference to forms versus functions.

Results
Results show that our Chilean lexicon features predominantly short phrases as opposed to one-word terms. Our lexicon’s focus is generic, since 49 terms are applicable across subject areas, and only 25 terms are specific to mathematics. The analysis of agency, that is, whose actions the terms depict, was applicable to 58 terms. Our findings show that most terms refer to teachers’ actions (37 terms), and only some focus on students (12 terms). Six terms could be enacted by either the teacher or a student, and only two terms refer to joint activities. Focusing on forms and functions, our lexicon appears to be a highly functional one, with 43 (58%) of terms portraying functions (e.g. ‘promoting diverse problem-solving strategies’), 12 terms referring to both form and function, and only 18 terms (24%) referring to forms (e.g. ‘use of manipulatives’).

Conclusions and Significance
Our analysis reveals that the lexicon of Chilean mathematics teachers in middle school has some degree of subject specificity, a focus on the functions of actions, and a strong emphasis on teachers’ actions. This shows that there is a level of shared professional terminology that teachers recognise and employ. The apparent secondary role of students in our lexicon can be linked to Chilean classroom studies, reporting that teaching emphasises teacher-led activities focused on transmitting information and practising skills, with scarce opportunities for students’ contributions (Preiss, Calcagni & Grau, 2015).

Authors

• Elisa Calcagni, University of Cambridge

• Valeska Grau, Pontificia Universidad Católica de Chile