Frame of reference in Iwaidja: towards a culturally responsive early years mathematics program

Most Indigenous Australian language speaking students in remote Northern Territory locations are taught in English by non-Indigenous teachers. Their first languages are inadequately accounted for in mathematics curricula and assessments. Hypothesizing that better understanding the conceptual and linguistic framework of their students would enable teachers to teach a more culturally responsive mathematics program, this thesis considers mathematical implications of the way Australian languages encode spatial concepts. The study focussed on understanding linguistic and cognitive elements of the students’ culture as necessary precursor to responding. It used a socio-constructivist perspective of education and the theory of linguistic relativity. Differences in preferred uses and acquisition of spatial frames of reference between Indo-European and Australian languages show a discord between the sequencing of location in Early Years mathematics curricula and the understandings of Indigenous students. Phase I was a linguistic investigation of spatial frames of reference in Iwaidja, an endangered Australian language spoken on Croker Island, using tools from the Max Planck Institute for Psycholinguistics. Paired speech tasks were conducted with senior adults, adults and their children or grandchildren, and with children. The findings confirmed cross-linguistic variation in the everyday language of spatial location. The study found Iwaidja uses all three frames of reference: absolute, relative and intrinsic. Adult-to-peer speakers used a range of absolute terminologies including a sunset-sunrise axis, wind directions and an ocean-land axis. Iwaidja has a relative ‘left’ and ‘right’ and a strongly intrinsic ‘front’ and ‘back’ that can contradict the relative frame of reference in both lateral and transverse axes. It has a focus on verbal processes rather than nominal objects, raising a questioning of the perceived necessity of nominalisation of mathematical abstraction for speakers of verb-focussed languages. Adult-to-child use showed less use of absolute frame of reference and greater use of relative. Australian languages such as Iwaidja and Kunwinjku appeared to have influenced the intrinsic frame of reference in the dialect of English spoken by the children. Phase II was an ethnographic case study of Early Years mathematics teaching including teacher perceptions at Mamaruni School, Croker Island. Interviews and observations showed language difference between themselves and their students was a major issue in mathematics teaching for the teachers. With little or no training in English as a Second Language (ESL) methodologies, most of them felt challenged to teach mathematics in the context. The school’s focus on teaching literacy and Standard Australian English sometimes appeared to be at the expense of mathematics. System pressures on teachers to teach Indigenous language speaking students at an “age-appropriate” curriculum level can lead teachers to implement ineffective mathematics programs. With time and training, the teachers became more responsive to the linguistic needs of their students

Spatial metaphors of the number line

This paper examines spatial metaphors in the English language associated with the number line, in particular metaphors of direction and motion, and how these are manifested in actual spatial practices associated with number. It considers how these metaphors are culturally influenced, and how the influences of other cultures, such as Arabic, produce inconsistencies that can contribute to confusion in the classroom. It also considers how the metaphors of number vary in some other languages, and how this leads to both different spatial representations of numbers and more challenges in multilingual and multicultural classrooms. In particular, it pays attention to the implications of variety in these metaphors for the mathematics education of Indigenous students in Australia being taught by English speaking teachers

Locating the Learner: Indigenous Language and Mathematics Education

Indigenous language speaking students in remote Northern Territory schools are expected to learn mathematics in English and are assessed in English. Most teachers in these schools have little knowledge of the mathematical concepts with which their students start school. This paper reports on the initial findings of a project which is investigating spatial concepts in Iwaidja, an Indigenous language spoken in the NT. Examples of spatial frame of reference preferences in Iwaidja and related languages are compared with those taken for granted by English speakers. Implications for mathematics teaching are explored in the context of an Australian Curriculum

The everyday language of mathematics: Investigating spatial frames of reference in Iwaidja

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What comes before? Understanding spatial reference in Iwaidja

This paper reports on initial findings of an investigation into spatial frame of reference in Iwaidja, an Indigenous Australian language spoken in a multilingual community. It considers spatial language in mathematics where students are being taught and assessed in a language not spoken at home and where their teachers do not speak the students` first languages. It finds that Iwaidja speakers use different frames of reference to English speakers in small scale space. The meanings and scope of key spatial terms in Iwaidja differ from English in ways that appear to be related to preferred frames of reference. It proposes that teacher awareness of these differences can help in mathematics teaching