Grab that kite!

Teaching mathematics in te reo Māori

Uenuku Fairhall, Tony Trinick, and Tamsin Meaney

Abstract

This article uses the story of Whakatauihuihu to help describe how the teaching of mathematics in te reo Māori (the Māori language) has developed. It begins by recounting the enthusiasm of the teachers who worked on the development of the mathematics vocabulary in the 1980s, and then moves on to show how the teaching of mathematics in te reo Māori is no longer seen as an innovation that will solve all problems for Māori students. Instead, like a teenager going through the initial phase of self-reflection, teachers are now considering what teaching practices can support students and how these practices can be developed. The article concludes by looking at recent research carried out in Te Kura o te Koutu (Te Koutu School).

Long ago, well before our ancestors arrived here in Aotearoa, while they were still living in Hawaiki, there was a woman named Apakura.

To her surprise she miscarried, without even knowing that she was pregnant. She gathered up the clot of blood and gristle, wrapping it in her flax kilt. She walked down to the water’s edge, and after singing her lament Apakura threw the bundle into the ocean waves.

The tide carried the bundle out to sea, where it slowly sank below the surface. As it dropped down to the sea floor, blood seeped through the sodden kilt. The kilt unravelled and bits of gristle were carried away by the current.

The bundle and its red plume came to the notice of Rongotakawhiu, a denizen of the deep. He opened the kilt and realised that the disintegrating clot was an undeveloped baby. Chanting spells he collected what he could from the ocean current in order to reassemble the baby. Unfortunately, some blood and gristle had been lost and so he formed the baby, a boy, with no genitals, deciding that all the other parts were more necessary for survival.

The baby was named Whakatauihuihu by his adoptive father, and Rongotakawhiu took it upon himself to teach the young child all that he knew, both practical and magical. He also gave Whakatauihuihu a kite, which was to prove his favourite pastime.

Introduction: a brief history

It has always been possible to describe and discuss traditional ethno-mathematical practices, such as navigating and weaving, using te reo Māori, and since the 19th century the Māori language has also been used to discuss Western mathematical ideas (Barton, Fairhall, & Trinick, 1995). However, during the 20th century active discouragement of its use in all aspects of New Zealand life resulted in te reo Māori no longer being used in educational settings. The situation changed in the 1980s with the movement for the revival of te reo Māori, focusing on kōhanga reo (Māori immersion preschools) and kura kaupapa Māori (Māori immersion primary schools). Teaching mathematics in te reo Māori, like the birth of Whakatauihuihu, was not a simple process.

The inspiration for the use of te reo Māori to teach mathematics came from teachers’ strong belief that the Māori language could be used in all circumstances. However, it was soon recognised that teachers needed to be proficient in te reo Māori as well as being competent, knowledgable teachers of mathematics.

In the 1980s the most pressing need for teachers of mathematics in kura kaupapa Māori—which by this time also included wharekura (secondary programmes), including those in secondary school bilingual units— was for the development of a specialised mathematical vocabulary. Transliterations of expressions and terms from English into Māori were of limited value because they neither expressed the mathematical concept nor had appropriate connotations that came with using a term derived from cultural experiences. However, sometimes the needs of Western mathematics overcame the desire to develop a culturally appropriate mathematical lexicon. For example, in traditional te reo Māori, numerical prefixes are context specific and/or determined by a person’s relationship with the objects that are being quantified. Thus, a mountain can be quantified using the same descriptors as those for people only when there is a relationship between the speaker and the mountain. This relationship is more important than the quantities of the item being discussed. Yet the advantages in having numbers as nouns, as is done in English, for teaching Western mathematics resulted in this change becoming incorporated in te reo Māori. With this change also came a recognition that it was likely to have an impact on other aspects of te reo Māori, and on the culture as a whole (Barton et al., 1995).

Decisions such as this were made in the 1980s in a series of hui (meetings) held with primary and secondary teachers who were teaching mathematics in Māori. Two of the authors, Tony Trinick and Uenuku Fairhall, attended these hui. Teachers and others shared the terms they were using and compiled a list of terms for particular mathematical concepts (see Barton & Cleave, 1989). This early stage of the development of the mathematics vocabulary was not unlike the reconstruction of Whakatauihuihu, the demigod, by Rongotakawhiu, in as much as this group worked without all the necessary material and expertise.

Eventually Te Puni Kōkiri (the Māori Language Commission) became involved and a set of 600 terms and some grammatical structures were agreed upon (Barton et al., 1995). These included some of the terms coined by teachers, but on the recommendation of Te Puni Kōkiri traditional terms whose meanings were no longer used for modern living were given a related mathematical meaning. These were presented first as Ngā Kupu Tikanga Pāngarau: Mathematics Vocabulary (Māori Language Commission, 1991). Subsequently an expanded version was included as a glossary at the back of the new pāngarau curriculum document (Ministry of Education, 1994). The latest development is the publication of a dictionary of mathematical terms in 2004, which has been made available to all schools (Christensen, 2004).

Current issues in teaching mathematics in te reo Māori

One day, the children from Apakura’s village were sitting on the sand hills looking out to sea when, to their surprise, they noticed a kite flying back and forth, high above the ocean. The string to which it was tethered rose up out of the waves. They watched in fascination as the string came closer and closer to shore until a young lad ran out of the water on to the beach.

The children raced towards Whakatauihuihu, determined to secure his kite, but they couldn’t catch him—he was far too fast. If they managed to corner him, Whakatauihuihu would simply turn towards the sea and disappear once again, only to come out further along the beach. He jeered at his pursuers and called out, ‘You are all too slow! Go and get Apakura, only she can catch me!’

This surprised them because they had never seen Apakura run fast. However, a child raced back to the village to get her. A reluctant Apakura, along with other curious adults, went down to the beach and joined in the chase of the strange kite flyer. And, as Whakatauihuihu had said, Apakura was the one who finally managed to catch him. When she asked who he was, he said, ‘I am yours, the clot that was wrapped in your kilt and thrown into the sea.’

Apakura wept and begged him to return home with her. This he agreed to after consulting his guardian, Rongotakawhiu. It was arranged that Whakatauihuihu would spend six months on land with his newfound mother, and six months under the sea, where he could continue to learn the magic of Rongotakawhiu.

In some ways, the idea of successfully teaching mathematics through te reo Māori turned out to resemble the children running back and forth trying to take hold of the kite that Whakatauihuihu was flying. The development of a mathematics vocabulary encouraged teachers to feel that the kite was at hand. However, as they reached out, the kite changed direction and flew further away, the issue proving more complex than they had foreseen. Having a mathematics vocabulary has raised a number of other issues, including students learning mathematics through their second language (te reo Māori), the standardisation of the mathematics vocabulary, teachers’ knowledge of te reo tātaitai (the mathematics language), and teachers’ knowledge of mathematics content.

In particular, having te reo Māori as a second language was having an impact on the learning of mathematics in kura kaupapa Māori. Analysis of student data from Te Poutama Tau (the Māori-medium numeracy project) found that language proficiency was a significant factor in student achievement in the higher stages of the number framework (Christensen, 2003). Many students who attend kura kaupapa Māori have learnt Māori, or are in the process of learning it, as a second language. They have entered kura kaupapa with some level of fluency, mostly gained from attending kōhanga reo. However, the language spoken at home is usually English, and many of the students’ parents have limited te reo Māori. Few students have any contact with te reo tātaitai (the mathematics register) outside of the classroom and are aware of this limitation in their speaking opportunities.

In the extract below, from the senior mathematics class in 2005, Uenuku acknowledges that learning about the components of the equation of a straight line is difficult. One student follows this up with a comment that it is too difficult to discuss this at home. The implication is not just that the content is too hard, but that being able to express it to others at home is too difficult:

The limited number of people who can discuss mathematical ideas in te reo Māori has also had an impact on the standardisation of te reo tātaitai. The small number of teachers who teach mathematics in te reo Māori are spread over a large area of New Zealand. As a result, few terms have become solidly integrated into the lexicon, with many kura—and even individual teachers within a particular school or unit—using local expressions. Words that are used less frequently, such as whenu (cosine), are more likely to be standardised, but more frequently used words, such as for multiplication, are less likely to be. For example, in the 1980s, “whakarau” was coined for multiplication. In recent years there has been a shift to using “whakarea”, but some teachers have resisted this change. The risk is that exploring mathematical ideas with nonstandardised language will lead to the development of nonconventional understandings.

In order to ensure this does not occur, teachers need a strong understanding of both mathematics and te reo Māori. A good example of this comes from Uenuku’s senior class. The class changed the expression used for “like terms” in algebra when considering how to identify them in expressions such as the following: -4× – 3× + 3×2 – 5×2. The term used in the new dictionary of mathematical terms, Te Reo Pāngarau (Christensen, 2004) is “rōpū”, meaning “grouping”. Students in Uenuku’s senior class coined the term “whakawhānau”, meaning “making families”. It was through discussion of what was happening when like terms were gathered together that the students felt that whakawhānau was more appropriate. This is because the connotations this term evoked better fitted their understanding of what was happening. Discussion of Western mathematics in te reo tātaitai needs to be done in such a way that makes use of the cultural connotations of the Māori words. However, traditionally whānau (family) was rarely used to describe inanimate objects, and the term “whakawhānau” may need to be considered as a stepping-stone to helping students understand the mathematical idea, which will then be replaced with the standardised term “rōpū”.

Very few current teachers learnt mathematics in te reo Māori and so many are learning the mathematical terms in Māori at the same time as they are teaching the concepts to the students. This is complicated further because, as is the case with primary teachers in New Zealand generally, kura kaupapa Māori teachers may themselves have limited knowledge and skills in mathematics. It may be that teachers will revert to how they themselves were taught when teaching content they are not confident with. Consequently, it is possible that those who would generally be considered fluent in te reo Māori will revert to a more English-sounding reo when teaching mathematics, because they are struggling with the ideas they are presenting.

Another issue with teachers not having been taught mathematics in te reo Māori is that they are unlikely to know the mathematical terms their students will need to use in the following years of study. The casual use of more advanced terms, which is often the way these are introduced in mainstream classrooms, simply cannot occur. Although this situation will improve as more teachers have been educated in kura, it is difficult at the present time for many teachers to utilise the full resources of te reo Māori.

Most teachers who teach in kura kaupapa Māori do so because they have a strong commitment to the language. As a result, there is ongoing discussion about how to keep the language strong. A teacher from Te Kura o te Koutu, a kura kaupapa Māori located in the central North Island, responding to a question on how te reo Māori is changing as a result of using it to teach mathematics, stated: “Mā tō rourou, ma taku rourou, ka ora te iwi” (Two heads are better than one). This suggests that the resources of both languages, English and te reo Māori, can be made use of. However, as with the early development of te reo tātaitai, it must be done in a considered way that reduces the unintended impact on the culture. It is possible that non-Māori assumptions, values, and world views are normalised in te reo Māori (Barton & Fairhall, 1995).

In recent years, teachers and researchers have moved beyond the development of an appropriate vocabulary towards thinking about some of these other issues—why the kite remains out of teachers’ grasp. This has led to a call for research to once again focus on issues relating to the teaching of mathematics in te reo Māori (Christensen, 2003; Christensen, Trinick, & Keegan, 2003). Since the beginning of 2005, research has been conducted at Te Kura o te Koutu. This research has been undertaken using funding provided by the New Zealand Ministry of Education’s Teaching and Learning Research Initiative grants. The next sections briefly describe progress so far.

Te reo tātaitai

On shore, Whakatauihuihu found that, unlike many of the men of the village, he could not go about naked because he had no genitals. His mother made him a kilt to hide what the villagers already knew was not there!

As time went by, Whakatauihuihu became renown for his magical powers and many sought his help. One of those was Tinirau, whose son, Tūwhakararo, had been brutally killed. He sent his wife, Hineteiwaiwa, to seek Whakatauihuihu’s help to avenge his son’s death.

Hineteiwaiwa travelled to Apakura’s village and asked where she could find Whakatauihuihu. A man pointed to the hill that stood behind the village, ‘There he is up there, flying his kite.’

She climbed to the top of the hill and asked the young kite flyer if he was Whakatauihuihu. He said that he wasn’t and that Whakatauihuihu was probably down in the village. Hineteiwaiwa returned to the village and asked another where she could find Whakatauihuihu. The response was the same, ‘There he is up there, flying his kite.’

When she got to the top, Hineteiwaiwa challenged the kite flyer that he was indeed Whakatauihuihu. He replied, ‘How would the person who told you know? The village is too far away to tell who I am. Stop bothering me!’

By the beginning of the 21st century the passion for teaching mathematics in te reo Māori was still there, but teachers were also aware that, like Hineteiwaiwa, more information was needed so that they could really understand what they were dealing with. Without this information, their ability to bring about what they wanted to achieve was limited. However, not everything could be investigated, and so choices were made about what to research and how to go about it. During 2005 and 2006 the project gathered information on the acquisition of te reo tātaitai by documenting and evaluating the scaffolding and modelling of students’ mathematical language by the teachers. It involved a partnership between the teachers of mathematics at Te Kura o te Koutu and the three researchers who are the authors of this paper.

The kura teaches mathematics to students from Year 0 to Year 13. The teachers in the primary section of the school were also participating in Te Poutama Tau, a professional development course that provides background and support in developing students’ numeracy strategies, and the teachers felt that our research would complement that project. Having all the teachers involved means the results are seen as more representative and useful in discussions about the mathematics programme.

The final stage of the research investigated how this knowledge affected the teaching practice of those involved, which in turn enabled an evaluation of the research for its practical value. Better understanding of how the mathematics register is acquired is likely to benefit not just kura kaupapa Māori teachers and their students, but also others considering language issues in other content areas.

Data were primarily collected by videoing each of the seven teachers’ mathematics lessons in 2005 and 2006. The classroom interactions were transcribed and the teachers then watched the videos with a university researcher. The joint analysis involved identifying the modelling and scaffolding strategies the teachers used in the classroom. These were arranged around the stages in the Mathematics Register Acquisition (MRA) model (Meaney, 2006). Meetings were held regularly to discuss the results of the analysis and realign the project to meet the kura’s changing needs. Teachers were interviewed and surveyed in August 2006 about how they felt about being involved in the project. More details about the methodology and findings of this project can be found in Meaney, Trinick, and Fairhall (forthcoming).

Findings

Our original research question related to identifying the strategies used by teachers to support students in acquiring aspects of the mathematics register. However, it soon became clear from our analysis that a scaffolding or modelling strategy could not be judged as effective or ineffective in isolation from the whole lesson or, in fact, from classroom practices in general. The next sections describe the strategies used at each of the four stages of the MRA model: kitenga (noticing); akoranga (intake); taunga (integration); and putanga (output).

The four stages of the MRA model

Kitenga

The kitenga stage is when the teachers introduce new terms or expressions, or add extra meanings to ones that students are already familiar with. The aim of this stage is to make students aware of new aspects of the mathematics register, whether these are new layers of meaning for already known terms or previously unheard terms or expressions. The stage is characterised by the teacher doing almost all of the cognitive work. They engineer the activity so that the new terms are needed, and ensure that the words are used frequently—mostly by themselves but also by the students.

It would seem that for a strategy to be effective at this stage, it must contribute to students hearing new vocabulary or grammatical expressions frequently and gaining meaning from them. At this stage the understanding that students are expected to acquire is usually a definition. However, the teacher giving a rationale also provided another kind of meaning to the new aspect of the register they were highlighting.

Akoranga

By this stage some of the cognitive load has shifted to the students. They now need to give definitions and examples, rather than just being expected to notice and interpret those provided by the teacher. However, the teacher is still very much in control and students’ contributions are usually short, thus providing them with little opportunity to provide inappropriate responses. The aim of the akoranga stage is for students to form an understanding of when and how new aspects of te reo tātaitai are to be used. Effective strategies, therefore, are those that support students exploring when and how to use these new aspects. This support includes providing students with both positive and negative feedback about their experimentation with the new aspects.

Taunga

By the taunga stage students have a good understanding of the new aspects of te reo tātaitai. The aim of this stage is to have students use these new aspects, but in a situation where the teacher is able to step in and provide support if necessary. Consequently, the teacher’s role has become one of reminding students what they know and can do. The students have the major responsibility for making use of the new language. If the student seems unable to operate at this level, the teacher is quickly able to supply more support, thus recognising that the student is still at the akoranga stage. Effective strategies are ones that allow students to have major control of their use of the mathematics register but enable the teacher to remind students what they know and can do.

Putanga

The final stage of the MRA model allows students to show their fluency in using te reo tātaitai. The aim is for students to be able to show what they know and can do without any support from the teacher. At this stage teachers do not choose from a series of strategies. The teacher’s role is simply to provide opportunities for students to make use of the fluency they have acquired. An effective strategy is, therefore, one that supports this provision.

Teacher reflections on strategies

Having looked at the list of strategies used in the mathematics classrooms at the kura, teachers agreed to trial strategies they had not used previously. These strategies gave an indication of what the teachers felt were effective. On the whole, these tended to be ones that supported students gaining a metacognitive awareness about their learning of the mathematics register. They were also strategies that tended to encourage students to move between modes of expression, such as from speaking to writing.

Combining strategies

When considered in isolation, some strategies employed by teachers at the various stages of the MRA model could be considered less effective than others. For example, having students repeat an answer after the teacher has gone through an explanation is perhaps not going to highlight for students new aspects of the mathematics register very effectively. However, when this is simply one strategy among many, all designed to support students to become aware of these new aspects, then its value can be more clearly seen. In each of the lessons, if the teachers used strategies from any of the MRA stages, they would always use more than one strategy. Combining a range of strategies, therefore, seems to be part of what makes effective support for students who are operating at the different stages.

Māori scaffolding and modelling strategies

In considering the modelling and scaffolding strategies for supporting the acquisition of te reo tātaitai, all of the strategies could be considered culturally appropriate. The question then becomes: Are some of these strategies unique to Māori immersion classrooms? Many of the strategies used by the teachers in this project are seen in English medium classrooms, both in New Zealand and in other countries, but the use of the linguistic resources within te reo Māori for scaffolding is one strategy that is unique. Words such as arā and kē, which warn listeners about the type of material that will follow, are not found in English, and are effective support mechanisms for students’ learning.

Another feature—although not unique to kura kaupapa Māori classrooms and one more strongly observed in the video recordings—was the amount of student contribution to the interactions. Even at the kitenga stage, which is where teachers have the most responsibility for doing the cognitive work, students took an active role in contributing to the discussions. It was quite clear that students were originators of interactions as often as the teacher. Video recordings of pairs of senior students show them working together as “teacher” and “learner”. The lack of reticence in taking up either role is considered to be an outcome of the valued tuakana–teina, older–younger sibling, relationship. Māori children do not traditionally segregate themselves into age-based peer groups; instead, there is the expectation that they will take responsibility for each other, whether younger or older.

For us, strategies that reflected a Māori world view were those that used the features of te reo Māori effectively and supported students to become active participants in interpreting and producing te reo tātaitai appropriately.

Changes in teachers’ classroom practices

The comments made by the teachers showed that they felt that being part of the project had had a positive impact on their teaching. This suggests that the analysis of their videoed lessons had contributed to them reflecting-in-action. Being involved in a two-year project was important because it gave them time to think about their current practices. It also provided them with the time to implement changes to their practices based on this reflection.

We also decided to investigate whether teachers’ perceptions about the changes they had implemented in their classrooms could be identified from an examination of the lesson transcripts. We assessed the number of words the teachers and students repeated more than seven times in the 2005 lessons compared to the 2006 lessons. Seven uses of the word was chosen because it has been argued that second-language learners need to hear a word seven times, at spaced intervals, to acquire it (Thornbury, 2002, cited in McNaughton, MacDonald, Barber, Farry, & Woodard, (2006).

We had anticipated that the proportion of mathematical words repeated in the 2006 lessons would be greater than the nonmathematical words. This was the case in the junior classes, but not the case for the intermediate and high school classes. It may be that the most experienced teachers were operating in these senior classes and their teaching involved more written recording of mathematical activity. This recording would contribute to the repetition of words, of course, but because it was not kept it cannot be included in the counting of words. It may also be that analysis of the words repeated seven or more times in the lessons is not a very useful way of determining whether changes had occurred in teachers’ practice. Further investigation needs to be undertaken to see how change in how teachers support mathematics register acquisition can be measured.

Mathematics: she’ll be write!

One of the outcomes of this research was to realise that only limited writing is occurring in mathematics lessons. This made us re-evaluate our research aims. We felt that, like Hineteiwaiwa, as soon as we approached what we felt would be answers to our questions, we had to rethink our questions. Consequently, further funding was sought, and gained, to investigate teachers’ support of students’ writing in their mathematics lessons. This project is still very much in its early stages, and a later research report will provide a more comprehensive description of its findings.

There were several reasons why it was felt that increasing students’ writing in mathematics is important. For a start, writing can be a vital part of learning mathematics, because the written products can be referred to again and again, and so can support students’ reflection on their learning (Southwell, 1993). The actual act of having students write about their mathematical understanding can also help students to solidify their mathematical understanding. National Certificate of Educational Achievement (NCEA) assessments, which are done in the final years of high school, also require students to be able to write mathematical explanations and justifications (Meaney, 2002). Having a whole kura policy for the development of mathematical writing will support students to gain the necessary writing skills to complete these NCEA assessments. It will also support their ongoing understanding of mathematical concepts.

Any text, whether oral or written, is influenced by three components: what is being discussed; who is producing and interpreting the text; and the form the communication is taking (written, oral, or gesture). Halliday described these as field, tenor, and mode (see Meaney, 2005). Changes to any of these will result in changes to the type of text produced (Halliday & Hasan, 1985). Types of texts will therefore reflect the purposes they serve. For example, demographic data are commonly presented in graphs, especially if used in reports designed for statistically literate adults. If texts are continually produced to fulfil the same set of field, tenor, and mode requirements, then the linguistic features of the texts will become stabilised over time. These texts can then be categorised into genres. Not to structure text in terms of the same conventional set of field, tenor, and mode can result in their meaning being misinterpreted. Consequently, it is important that students learn during their schooling experiences how to write in the genres that are used in particular content areas.

Marks and Mousley (1990) have identified several genres that mathematicians use and that should be included in students’ repertoire of mathematical writing. These genres are:

However, when they investigated the genres that were used in 11 classrooms (seven primary and four secondary), they found instead many instances of recounts, incorporating symbols and visual representations, but very few examples of other genres. Given that the purpose of writing is different for mathematicians compared with other students, it is perhaps not surprising that students were being asked to write in different kinds of genres. However, by the time students are in their final years of high school it could be expected that they would have the skills to produce all of these genres.

In March 2007 the teachers at the kura classified samples of students’ writing into three distinct genres: whakaahua (description); wharakamarāma (explanation); and parahau (justification). Each pair of teachers looked over a range of students’ writing. They then classified the students’ writing according to the categories they felt were appropriate. Two pairs then shared their categories and decided on one set they felt was most appropriate. Then the whole group came together and had a more extended discussion about the genres.

The samples came from different-aged students and were on a range of topics. The quality of the writing also varied, and whether descriptions, explanations, or justifications were used. The formats of writing students could use to produce these genres included pictures, iconic representations, graphs, geometric representations, symbols, and narratives. It was felt that genres would commonly require a combination of formats rather than being exclusively one or the other. This is particularly the case in explanations and justifications.

There was also some discussion about the audience for mathematical writing. Sometimes the writing may be exclusively for the student, and may therefore convey limited (if any) meaning to others. Predominantly it was believed that most writing done in mathematics classes is done for the teacher so that they can assess the students’ learning. In addition, students taking external exams are writing for examiners who they will never meet. On occasions, pieces of writing might be displayed for other students, or shown to parents or community members.

The next step in the research we are undertaking is to consider how to support students to become better writers of mathematics. This can be considered to be increasing both the quantity of genres that students are able to produce, and also the clarity and cohesion within each of the genres.

Looking under the kilt

A discouraged Hineteiwaiwa descended once more and asked yet another person where she could find Whakatauihuihu. On being told that it was he on the hill who was flying his kite, she complained, ‘But he has already denied twice that he is Whakatauihuihu.’

‘He does such things. He is strange. If he denies it once more then quickly pull up his kilt and you will surely know it is Whakatauihuihu!’ snickered the woman, and she left a bewildered and tired Hineteiwaiwa to once more climb to the top of the hill.

True to form, the kite flyer denied he was Whakatauihuihu. The extremely annoyed Hineteiwaiwa thrust her hand forward and quickly pulled up his kilt. Her anger turned to surprise as she could plainly see that the kite flyer had no penis or testicles. Whakatauihuihu dropped to the ground in shame and mumbled, ‘What is it you want from me?’

Whakatauihuihu was valued by the village for his magical incantations. Being able to do mathematics in te reo Māori has benefits that are not available to speakers of other languages (Barton, 2004). It may well be that in time it will also be valued by others for what it can contribute to mathematics generally. However, in order to reach this state of affairs, we need to consider what is under the kilt: to find out what else contributes to, or inhibits, students learning mathematics in te reo Māori. After 20 years it is perhaps too early to say that we have had more than just a peek. We are aware of some of the issues and we are working on some of the solutions. However, much more research with teachers working in the field is needed before we can say that we have a clear sense of everything that contributes to effective practice.

We are certainly very aware of the issues surrounding the development of te reo tātaitai, and we still face questions such as how to standardise the use of technical terms and whether this affects students’ learning. We are also aware that most students and their teachers are second-language learners of te reo Māori. We feel after our research of 2005–2006 that we have a clearer understanding of how to provide effective scaffolding for and model te reo tātaitai. This has enhanced our desire to better understand how teachers support students’ writing in mathematics. We hope to know more about this by the end of 2007.

This work has been carried out in one kura, and we still need to determine how applicable our understandings are to other kura. The students at Te Kura o te Koutu are already achieving good results, but it may well be that other factors in how the kura operates contribute to students’ mathematics understanding. We need to identify these factors. We anticipate that just as the lives of Hineteiwaiwa and Whakatauihuihu continued to become entwined in a further story, our research interests and the kura will also remain entwined with the learning of mathematics in te reo Māori for some time to come.

References

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Acknowledgements

This research was funded by the New Zealand Ministry of Education through a Teaching and Learning Research Initiative, administered by the New Zealand Council for Educational Research. Earlier versions of this paper were presented by Uenuku Fairhall as a keynote address at Symposium 2007 at the Marang Wits Centre for Mathematics and Science Education, University of Witswatersrand, South Africa, in April 2007, and by Uenuku Fairhall and Tamsin Meaney at the 30th annual conference of the Mathematics Education Research Group Australasia at the University of Hobart, in July 2007. Parts of this paper were also presented at the Third Ethnomathematics Conference held in Auckland in February 2006.

The authors

Uenuku Fairhall is the Principal of Te Kura Kaupapa Māori o te Koutu, an immersion school for Years 1–13 in Rotorua. Tony Trinick is the Associate Dean Māori in the Faculty of Education at the University of Auckland. Tamsin Meaney is a senior lecturer in the College of Education at the University of Otago. The three authors share an interest in the use of te reo Māori for teaching mathematics.

Emails:

uen_fai@koutu.school.nz

t.trinick@auckland.ac.nz

tamsin.meaney@otago.ac.nz