Tony Trinick

Developing a Māori language mathematics lexicon: challenges for corpus planning in indigenous language contexts

Over the last 25 years, there has been significant modernisation and elaboration of the Māori language mathematics lexicon and register to support the teaching of (Western) mathematics as a component of Māori-medium schooling. These developments are situated within the wider Māori language revitalisation movement in Aotearoa/New Zealand, of which Māori-medium education is a central component. A feature of the initial development of a Māori mathematics lexicon was the informal approach taken, involving elders, teachers and community working together to establish a corpus of appropriate terms, rather than any formal language planning approach. Subsequently, two state agencies, Te Taura Whiri i te Reo Māori (the Māori Language Commission) and the New Zealand Ministry of Education assumed a formal role in the standardisation and elaboration process. Due to limitations in resources and expertise, the Commission eventually withdrew from the process of developing the specialised lexicon for schooling and, in their absence, ongoing lexical development was entrusted to a group of Māori-medium mathematics educators (Te Ohu Pāngarau) and closely linked to the Ministry of Educations numeracy strategies. However, the process of linguistic modernisation of the Māori language to support the teaching of school subjects such as mathematics has since raised a number of conflicting tensions and linguistic issues, particularly among the older generation of Māori language speakers. This paper explores the process of development and the at-times conflicting linguistic ideologies which influenced the lexication and codification of the Māori-medium mathematics terminology. It also specifically examines the roles, policies and beliefs of the agents, including the two state agencies, involved in the process, charting the connections between micro, meso and macro language policy and practices in this context.

Cultural and Mathematical Symmetry in Māori Meeting Houses (Wharenui)

This chapter draws on the symbolism found in various artefacts in wharenui (meeting houses), with a particular focus on Rauru, a traditional Māori meeting house located in Hamburg, Germany, the location also of ICME 13, to illustrate an aspect of ethnomathematics: cultural and mathematical symmetry. This addresses a gap in Māori-medium education whereby much of the focus to date has been on revitalising the endangered Indigenous language of Aotearoa/New Zealand, te reo Māori. In contrast, reviving the associated cultural knowledge has been somewhat stymied for three key reasons: the dwindling number of elders with the knowledge, the tension associated with transposing traditional tribal knowledge to contemporary learning environments and resistance on the part of state agencies to acknowledging Indigenous knowledge. After 100 years of cultural and linguistic assimilation, reviving cultural knowledge is a big challenge for marginalised groups. Fortunately, aspects of both cultural and mathematical knowledge remain embedded in highly valued artefacts such as the meeting house, and are thus able to be reconnected in the contemporary Indigenous mathematics classroom. However, there is a need to better understand how the cultural significance can be connected to mathematical understandings in a way that gives value to both.

Impact of Differing Grammatical Structures in Mathematics Teaching and Learning

We show that languages express mathematical ideas in diverse ways that provide an opportunity to enrich the mathematical experiences of learners in multilingual contexts, but that can also introduce ambiguities or misunderstanding between teachers and students and impede the process of mathematical learning. While at times, multilingualism and/or teaching mathematics in the medium of indigenous languages has been considered from deficit perspectives, we consider these challenges as more enabling and enriching. We also show that languages such as English and French, with long traditions of developing a mathematics register, nevertheless contain some grammatical features which are not always ideal mathematically. If opportunities arise for linguistic-mathematical innovations in these world languages, language planners might like to consider innovating for features which research has shown facilitate mathematics learning.

Distribution, Recognition and Representation: Mathematics Education and Indigenous Students

The research undertaken in the last four years on the learning and teaching of mathematics connected to Indigenous students is evaluated using Fraser’s model for social justice, which consists of three elements: distribution (economic), recognition (cultural) and representation (political). Although at least one element, usually distribution, was the focus of the research papers, the occurrence of all three was rare—with representation seldom visible. Yet, evidence suggests that representation is an important element if Indigenous student achievement is to improve. As a consequence, there is a call for a moral change in how mathematics education research is promoted and undertaken with Indigenous students, with a need to include greater Indigenous community representation.

Writing to Help Students Think Mathematically

This chapter explores writing in mathematics. It looks in depth at students’ and teachers’ perceptions of the contribution of writing to students’ ability to think mathematically. It begins with the description of the genres that were used in the mathematics classrooms. The three genres are description, explanation, and justification. Mastery of each of these genres is linked to specific learning experiences. For example, justification requires students to engage in reflection about what they have done and why. The chapter also explores the issue of quality mathematical writing and how teachers recognise and promote it within their classrooms. Interviews with students revealed how they perceived writing in mathematics to be primarily for themselves and only secondarily for their teachers.

“Māori were Traditional Explorers”: Māori Pedagogical Practices

There has been much theorising about Māori pedagogical practices and how they differ from other pedagogic practices. In this chapter, we use the principles outlined in Te Aho Matua, the guiding principles for all kura kaupapa Māori, as a starting point for analysing whether the teaching of mathematics at Te Koutu was done differently and according to what had been theorised as Māori pedagogic practices. For the parents and teachers at the school there was a tension in believing that their children were different in the way that they learnt from other children because of their Māori background. Although they wanted the children’s Māori heritage to be celebrated in their mathematics learning, they were unsure whether specific Māori pedagogical practices were required. For teachers the tension was exacerbated by the fact that they had to operate within the rules and regulations for teaching mathematics of the Ministry of Education. Many of the pedagogical practices used at Te Koutu could be found in other classrooms. However, our contention is that the set of pedagogical practices fostered students’ learning of mathematics in a way which encouraged them to be Māori explorers of the modern world in which they lived.

Teachers as Learners of the Mathematics Register

The other chapters in this part examine the teachers’ own fluency in te reo Māori for discussing mathematics. Few teachers who teach in te reo Māori had themselves learned mathematics in this language. Although this situation will change in coming years, it is having an impact on how mathematics is discussed in the wider community. We discuss how teachers need both strong mathematical knowledge as well as strong language to find the most appropriate ways to teach mathematics. If teachers have this combination in them, then it is possible for them to support students to move from conversational language to the mathematics register more easily. The ways that the teachers work on improving their own language fluency around mathematics ideas are described. These include the provision of professional development by the New Zealand Ministry of Education as well as the school itself.

The Development of a Mathematics Register in an Indigenous Language

The Māori language, te reo Māori, increased its mathematics register at two distinct historical moments in time, and these are documented in this chapter, which begins the section on political challenges. The initial enlargement of the mathematics register occurred with the beginning of continuous contact with European trade and farming communities. Consequently, the vocabulary increased in respect to measurement and monetary interactions. At this time, transliterations proliferated, perhaps because most Māori did not see their language as being in conflict with English. Following the banning of te reo Māori in schools in the 1860s, there was no significant expansion of the mathematics register for more than a century. In the 1980s, kura kaupapa Māori were set up as a result of a political movement by Māori parents and the wider community. We outline the different challenges from expanding the mathematics register that arose at these different periods of time with very different political environments. For example, we describe in the most recent expansion how some archaic terms were given new, albeit related, mathematical meanings. We also show how the mathematics register continues to develop to meet the demands of new mathematical professional development programmes and curriculums introduced by the New Zealand Ministry of Education. In many ways this challenge can be considered as one where “normal” is now being redefined.

The History of Te Kura Kaupapa Māori o Te Koutu – The Politicisation of a Local Community

Most kura kaupapa Māori began outside the New Zealand–funded education system and were not recognised by the Ministry of Education until the 1990s. In this chapter, we describe the history of one of these schools, Te Kura Kaupapa Māori o Te Koutu. In particular, we focus on the parents’ aspirations for the children’s education which combined the need for their children to gain mainstream qualifications with the need for developing fluency in te reo Māori and supporting the students’ Māori culture. In the ten years between 1998 and 2008, parents continued to have similar aspirations. However, as more parents entered full-time work, their commitment to contributing to their children’s education had changed from active involvement to supporting what the teachers and the school decided. Another consequence of parents being in full-time employment is that the school is considering having to provide a long-day-care centre and preschool on site, in order to have children with sufficient Māori language to begin school. Consequently, the schools continuing work to meet the new environments in which they operate means that this is an ongoing challenge, which is recognised but is still in the process of being met.

The Resources in Te Reo Māori for Students to Think Mathematically

In this chapter, the first chapter in the section on mathematical challenges, we describe the features of te reo Māori that can support students to think mathematically. These features include both traditional ones such as logical connectives and new ones such as the newly coined terms that had transparent meanings. We draw on classroom transcripts to provide examples of different contributors to students’ mathematical thinking. For example, the importance of students providing justifications and explanations to support their mathematical thinking is introduced. As well, the importance of the interaction between teachers and students in developing students’ reasoning is discussed. An example is provided where a teacher taught young students body movements as one way of symbolising mathematical operations. This type of mathematics symbolisation was connected to the cultural practice of kapa haka (traditional team dance).