Children’s negotiation of meanings about geometric shapes and their properties in a New Zealand multilingual primary classroom

Abstract

New Zealand is a nation of superdiversity in terms of ethnicities and languages spoken. This superdiversity is reflected in New Zealand multilingual classrooms. In the New Zealand primary school mathematics curriculum, the teaching and learning of early geometry focuses on recognising and understanding shapes, their properties, and symmetries, and on describing the position and movement of shapes. The Achievement Objectives suggest that the children at Curriculum Level 3, which roughly translates to Year 5/6 (9 to 11-year-old), are expected to identify, describe, and classify two-dimensional (2D) and three-dimensional (3D) shapes by spatial features. Acknowledging the multilingual context of a New Zealand classroom, this study investigated how children negotiate their meanings about 2D shapes, 3D shapes, and their properties as they engage in whole-class and/or group interactions in a New Zealand primary classroom. Accordingly, following research questions (RQ) guided this study: 1. What discursive constructions do 9 to 11-year-old children use to represent their understanding of 2D shapes, 3D shapes, and their properties in a New Zealand multilingual primary classroom? 2. How do 9 to 11-year-old children interact to construct their understanding of 2D shapes, 3D shapes, and their properties in a New Zealand multilingual primary classroom? 3. What characteristics of dialogic space influence 9 to 11-year-old children’s negotiation of meanings about 2D shapes, 3D shapes, and their properties in a New Zealand multilingual primary classroom? A qualitative study informed by the Discursive Psychology perspective (Edwards & Potter, 1992) within the Critical Inquiry research paradigm was undertaken. Edwards and Potter (1992) argue that language-in-use is construed as an action in itself and, as a result, knowledge is taken as situated and constructed through language-in-use as people interact. Bakhtin’s (1981) Dialogic Theory and Garfinkel’s (1967) Ethnomethodology informed the theoretical framework of this study. Data were gathered from a Year 5/6 classroom in a New Zealand English-medium school. The participants were fifteen children (nine multilingual, six monolingual) and their mathematics teacher. Six geometry lessons on shapes and their properties were observed and audiovisually recorded. Additional data were gathered from a variety of sources, including semi-structured teacher interviews, four focus group interviews with children, a short questionnaire filled by the parents, children’s work samples, and teacher’s unit plan. Data from different sources allowed me to establish the reliability and validity of the findings. Data were analysed in three phases: thematic analysis, micro-level analysis, and macro-level analysis. Five themes were identified from thematic analysis of data to explore the discursive constructions that the children used to represent their understanding of shapes and their properties (RQ1). These themes are: (i) making sense of 2D shapes, (ii) making sense of 3D shapes, (iii) relating 2D shapes with 3D shapes, (iv) mathematical construct of dimension, and (v) naming shapes in Te Reo Māori (the Indigenous language of New Zealand). For the purpose of managing and presenting analysis, two Key Moments within each of the five themes were identified for further analysis at the micro-level and macro-level. For the micro-level analysis, I used selected Conversation Analysis (Schegloff & Sacks, 1973) techniques to explore what is said and how it is said (RQ2). Based on the micro-level analysis findings, the macro-level analysis was conducted using Bakhtinian concepts of speech genres, discourses, heteroglossia and unitary language, double-voicedness, and chronotopes to explore the characteristics of dialogic space that influence children’s negotiations of meanings about shapes and their properties (RQ3). The study reveals four novel findings. First, the analogy of “flat vs fat” may not be useful in developing children’s geometric understanding of dimension. Second, the study indicates that multilingual children use prosodic repertoires from their multiple languages as they engage in whole-class or group interactions, and these prosodic repertoires may be interpreted differently by monolingual English-speaking children. Third, the study reveals the presence of several speech genres available to teachers and children within the dialogic space of a multilingual classroom. Fourth, the study shows that multiple meanings could be drawn out for each utterance, and the meaning of an utterance is dependent not only upon the interaction of unitary language and heteroglossia between the discourses but within the discourse as well. The findings of this study suggest, first, that a comprehensive definition of dimension needs to be included in the school curriculum. Second, teachers may benefit from learning about prosodic features that multilingual children may use to show their confidence or doubt about their learning, along with several speech genres available within the dialogic space. Several ideas for further research in the mathematics education field with a focus on developing an understanding of geometry concepts such as dimension are also suggested. Overall, the study highlighted the need for teachers and teacher educators to recognise subtle yet powerful aspects of language use that influence children’s negotiation of meanings about geometric ideas as children engage in classroom interactions.