Maori Kowledge, Language and Participation in Mathematics and Science Education

Literature Review

Introduction

Debates about Maori knowledge, language and participation in mathematics and science education can be located within an international literature that explores the relationship between both indigenous and minority relationships with Western scientific and mathematical knowledge in a Western educational context. There is a large body of literature about the nature of science and mathematics with respect to culture. There is significant debate about the conception of science between ‘universalists’ and ‘multiculturalists’, with a systemic positioning at whatever point on the ‘universalist’/‘multiculuturalist’ continuum having significant pedagogic implications. A positioning on this continuum must be informed by a conception of the scientific and mathematical nature of traditional knowledge. There is a significant literature which considers the similarities and differences between Western Modern Science (WMS) and traditional indigenous knowledge bases. This debate is significant in terms of understanding the nature and extent of cognitive conflict for those who might experience a cultural conflict between the cultures of the home and school. It is also important when set alongside the relationship of the physical to the metaphysical in indigenous thought and the suggestion that conflict between the physical and metaphysical could make WMS threatening to indigenous cultures.If it is accepted, as it is by several Maori scholars, that the threat of WMS to indigenous cultures is overstated and that Maori scientific and mathematical education is desirable issues of language, culture and pedagogy arise. There is a literature which argues strongly that Maori participation and performance in mathematics and science is undermined by low teacher efficacy and low student self-expectation, inadequate teacher subject, pedagogic and cultural knowledge and conflict between the culture of home and school. This Maori experience is consistent with those of both indigenous and other ethnic minority groups elsewhere and contributes to an explanation of why Maori achievement in the National Education Monitoring Project (NEMP) and the Third International Mathematics and Science Study (TIMSS) was poorer than that of other cultural groups in New Zealand.There has been some research on successful teaching and professional development practices both in New Zealand and overseas which has implications for this project as well as work considering the impact on classroom practice of the language of instruction, indigenous knowledge and cultural stereotypes. It is strongly argued that when cultural stereotypes influence classroom practice there is created a significant barrier to Maori achievement.Finally, there is a small but significant literature concerning what Maori want from mathematics and science generally in terms of the disciplines’ connections to Maori development and specifically what Maori want from mathematics and science education.This review focuses specifically on Maori interests with supporting material from international contexts. It notes however the substantial review of Hipkins et al (undated) which considers New Zealand science education in a much wider sense than is the purpose of this review.

Indigenous Knowledge and Science and Mathematics Education

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Universalist versus multiculturalist conceptions of science

Debate about the nature of science and whether it can properly be understood as a universal body of knowledge arises from ‘competing accounts of natural phenomena’ (Cobern and Loving, 2000: 50). Irzik (2000: 71-72) explains that the debate between universalists and multiculturalists consists, on the one hand, of the universalist position that both scientific inquiry and scientific knowledge have a universal nature, found in Western Modern Science (WMS), which is ‘a far more superior form of knowledge than any other traditional sciences’. On the other hand, Irzik points out, is a multiculturalist position which dismisses the universalist assumption on philosophical, but also political and moral grounds, because it serves the ‘politics of exclusion’, and rejects any notion of alternative sciences ‘which suit the purposes of a “good life” better than WMS’ (Irzik, 2000: 71). Multiculturalists do not accept that science must by definition maintain a ‘universal common core’ and argue for the inclusion of Indigenous Knowledge (IK) and Traditional Ecological Knowledge (TEK) in science curriculum, and it is Irzik’s view that there are sufficient similarities between TEK and IK and WMS to justify the inclusion of both in science curriculums (2000: 72).Semali and Kincheloe (1999: 29) argue that it is the ability of WMS to present its findings as universal that gives it an imperialistic power dismissive of indigenous knowledge as ‘inadequate and inferior’. WMS has this effect because it produces

universal histories, defines civilisation, and determines reality… such capabilities legitimate particular ways of seeing and, concurrently, delegitimate others (Semali and Kincheloe, 1999: 29).

In contrast, multiculturalists believe that all knowledge, including that of WMS, exist within a cultural context and that

the language, issues, methods and meanings used by a scholar to depict a reality both reflect and constitute the cultural values, ideas and beliefs and practices familiar to the author (McGovern, 1999: 188).

Semali and Kincheloe (1999: 29) therefore argue that the cultural context of WMS makes it ‘white’ rather than ‘universal’ science and that the conception of a universal science only arises when one fails ‘to appreciate the ways modernist scientific universalism excludes “white science” as a cultural knowledge, a local way of seeing’. Semali and Kincheloe’s position is dismissed by Taylor and MacPherson (1997: 194) who outline Shahn’s (1990) questioning of a ‘white’ science argument on the grounds that women and non-white non-Europeans have made significant contributions to scientific knowledge. He also suggests that as a group white men are ‘alienated, confused and intimidated’ by science to the same extent as other groups. Shahn’s position is supported by Ezeife’s drawing on the work of Hatfield, Edwards and Bitter (1997) in the field of mathematical knowledge. Hatfield et al illustrate the range of cultural contexts from which contemporary ‘Western’ mathematics has developed. They note that it was Africans who first used numerals and invented rectangular coordinates. It was the ancient Egyptians who first developed symbols for 10 and 100 and who first used unit fractions. Negative numbers were first understood by Chinese mathematicians and Native Americans first used a symbol for zero. Further,

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the word algebra is Arabic in origin.... The first concepts of congruence were developed in Africa and Asia.... Cotangents and similar triangle principles we used in the building of Africa pyramids... Mozambicans built rectangular houses by using equal-length ropes as the diagonals. The Babylonians used the right angle theorem 1500 years before Pythagoras was born... and the modern method of using the so-called Pascal’s triangle was actually invented in Asia by the Chinese and the Persians 500 years before Pascal was born (Hatfield, Edwards and Bitter, 1997 quoted in Ezeife, 2002: 181).

The co-option of such knowledge into a ‘universal’ paradigm has concerned Cobern and Loving (2000: 50) with respect to contemporary indigenous scientific knowledge. Coburn and Loving suggest that although

good science explanations will always be universal... Western science would co-opt and dominate indigenous knowledge if it were incorporated as science. Therefore, indigenous knowledge is better off as a different kind of knowledge that can be valued for its own merits, play a vital role in science education, and maintain a position of independence from which it can critique the practices of science and the standard account.

For Coburn and Loving IK is therefore not science. That they argue, does not devalue IK, just as art, history, economics, and religion are not devalued by their exclusion from the scientific domain. Exclusion from science protects indigenous knowledge from co-option and manipulation which is important because ‘truth is never under the sole proprietorship of any single domain of knowledge - not even science’ (2000: 65). Yet Taylor and MacPherson argue that the very notion of a Western science is a ‘debatable point’ because the modifier Western suggests that it is practiced and culturally rooted only in the West – ‘neither of which are true’ (Taylor and McPherson, 1997: 202). Whereas, Zaslavskey (1994) suggests that students should understand that in non-Western cultures mathematical practices developed from the ‘real needs and interests’ of people and that a great deal of the mathematical knowledge that is taught as Western knowledge in schools was in fact developed in Asia and Africa

centuries before Europeans were aware of more than the most elementary aspects of mathematics.. Students of many different backgrounds can take pride in the achievements of their people, whereas the failure to include such contributions in the curriculum implies that they do not exist (Zaslavsky, 1994: 6).

Corsiglia and Snively (2000: 82) note Cobern and Loving’s (2000: 50) acknowledgement of the place of TEK in the science classroom, but observe that it is an acknowledgement made with reservation. It is an acknowledgement only to the extent that some of the insights of science can be arrived at by other ‘epistemological pathways’ (Cobern and Loving, 2001: 16). In contrast, it is Corsiglia and Snively’s (2000: 235) view that

indigenous science offers important science knowledge that WMS has not yet learned to produce, and that IK and TEK are being increasingly researched in Africa because they can contribute to the eradication of poverty, disease and hunger where modern techniques are deficient.

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If IK and TEK can make valid observations then it is not legitimate for the science classroom to present conventional science as the only way of

contemplating the universe... The point is not to establish that one form of science is superior to another, but to develop scientific thinking and to enable students to examine their own assumptions by distinguishing between the relative merits of different sciences to understand science concepts, and allow the existence of alternative perspectives (2000: 84-85).

It is however the tendency for Western science to establish itself as the only way of knowing that Jegede argues denigrates IK and creates difficulties for the ‘thought processes of African learners’ ((Jegede, 1995: 97).Waiti and Hipkins (2002: 232) argue a need to align ‘Western science with other knowledge systems’. They suggest that New Zealand’s ‘inclusive’ science curriculum may in fact produce stereotypes, appropriate minority cultural backgrounds and thus alienate students from the learning that might encourage science related careers and participation in public science debate. They support McKinley’s (McKinley, 1999: 39) view that social cohesion and a knowledge-based society requires the enabling of Maori children to participate fully in science. They reaffirm Waiti’s previous (McPherson Waiti, 1990: 185-186) assertion that ‘Maori people do not want to live in the past... this provides a challenge for educators to get beyond indigenizing Maori education’. Waiti and Hipkins note

a growing awareness of the need to take account of diverse cultural views and community concerns about the products of science, especially ‘cutting-edge’ biological and biotechnology research. This points to the need for greater participation of those from other cultures and science, as scientists and as actively involved citizens in the community.

The relevance of whakapapa to genetic engineering and indigenous ideas about sustainable management ‘when managing for biodiversity’ are examples of the interaction between cultural values and possibilities of WMS (Waiti and Hipkins, 2002).The relevance of the universalist/multiculturalist debate is that it is the universalist understanding of science that informs the assumptions school curriculums make about the nature of science and how science should be taught (Stanley and Brickhouse, 2000: 44). These assumptions include the notion that WMS provides a superior understanding of the natural world and overlooks the impact of cultural influences and assumptions on teaching and learning (Stanley and Brickhouse, 2000: 36). Atwater and Crockett (2003) argue against the tendency for WMS to understate the significance of culture in conceptions of science:

people interpret the world and their experiences differently. Their worldviews are explicit culturally dependent internal models found in their cognitive structures and are the result of their life experiences (Borden, 1991).... Therefore, the views of people about reality are socioculturally constructed and are given personal meaning by their sociocultural experiences. Their world views are the very skeletons of concrete cognitive assumptions on which their decisions and actions are founded (Kearney, 1984; Wallace, 1970). It is in this ‘socioconstructed world’ that the ‘agency of schooling’ is located (Atwater, 2003: 56-57).

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Stanley and Brickhouse (2000: 39) extend the significance of social construction to suggest that it ‘plays a role in the scientific account of physical reality’ and endorse Harding’s (1998) assertion that the ‘cognitive content of the sciences is shaped by culturally different forms and social organisation of research’ (Harding in Stanley and Brickhouse, 2000: 39). Stanley and Brickhouse also note the significance of cultural and economic factors in determining the type of scientific question asked and therefore the nature of the knowledge that is gained (2000: 44). Stanley and Brickhouse therefore adopt ‘a more “local” view of science than a universalist position would admit’ (Stanley, 2000: 39).If WMS is not in fact universal but deeply rooted in the cultural norms of the West then it is likely to influence how non-Western peoples view school science. In an African-American context Key argues that school science may even be seen as ‘something foreign’ to ‘students, who study science for years before reading about a scientist or inventor of their own ethnic group’. Key goes on to add a further dimension to the universalist/multiculturalist argument by suggesting that science processes are ‘generic’ or ‘culture free’, yet

if students cannot and do not identify with those who are “processing,” they may internalise the notion that they cannot perform science or are not expected to process scientific information and thus negate the content being taught (Key, 2003: 88).

Multiculturalists generally accept that WMS is an unusually effective and reliable knowledge system, but it is not the same as saying it has a reality independent of human conceptions (Stanley and Brickhouse, 2000: 40-41).

If WMS is an ‘effective and reliable knowledge system’ and ‘independent of human conceptions’, then there is an assumption that it should be part of the school curriculum for all peoples. But questions arise from that assumption as Lewis and Aikenhead (Lewis and Aikenhead, 2000: 4) indicate. ‘How should non-Western ideas be viewed in relation to Western science’? If non-Western ideas are not inferior should they be ‘accepted in science classrooms’? In contrast for the universalist there is no place for indigenous knowledge unless it has been subsumed into the body of knowledge referred to as Western Modern Science.

The Scientific Nature of Traditional Knowledge

Multiculturalists maintain that there is a place in science curriculums for indigenous knowledge, which poses questions about the scientific nature of traditional indigenous bodies of knowledge. Roberts takes the view that indigenous knowledge can be taught alongside Western science ‘as distinct but not entirely dissimilar knowledge systems within a single curriculum framework’ (Roberts, 1996: 59). This is not withstanding Rikihana’s view that ‘there is a disparity between Western science and Maori science’ because as Rikihana himself notes

Western science and Maori indigenous knowledge overlap but are not identical. Education should start with the common elements and move out from there (Rikihana, 1996: 25).

Lomax argues that the difference between traditional Maori knowledge and Western science is one of methodology

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which does not render [Maori]… knowledge invalid, but may require that we re-interpret the knowledge using new technology and in light of knowledge obtained from Western science (Lomax, 1996: 12).

Roberts’ approach to indigenous knowledge and Western science is to compare the similarities and differences from the perspective of Pacific knowledge bases. Aikenhead undertakes a similar project with respect to Canadian First Nations knowledge bases (Aikenhead, 1997: 15-16). Roberts maintains that both have an empirical data base with observations of the natural world having provided information which has been ‘accumulated over time, systemised, stored and transmitted, either orally or in written form’. There are however differences in the creation of empirical data bases between the two forms of knowledge. In many cases IK data bases have been built up over thousands of years and include qualitative as well as quantitative information because ‘all observations and interactions are considered relevant’. In contrast, Roberts argues

Western science data bases are comparatively short term (e.g., a one-year master’s degree, or a three-year PhD); primarily quantitative, and frequently obtained and/or supplemented by experimental data gathered under controlled rather than natural conditions, whereby only certain variables are observed, manipulated and measured (Roberts, 1996: 62).

Roberts continues to suggest that while Western science and indigenous knowledge share ‘an ability to construct theories (models) and make predictions’ there are similarities and differences in approach. Both systems make predictions but there are differences in the framing and testing of predictions and in the treatment of results (Roberts, 1996: 63). Both sets of databases are subject to verification by testing over time, although in the case of Western science

generally only after having successfully undergone controlled experimentation, peer review and publication. Tests of IK primarily involve ‘trial and error “experiments” under natural, uncontrolled conditions

while Western science generally tests its predictions under laboratory conditions, involving manipulation of certain variables only and including the use of a control or, if in the field, involving preselected parameters (Roberts, 1996: 63).

Explanations of cause and effect are also important features of both knowledge systems. Unlike Western science, which Roberts points out, abandoned the supernatural as a source of information and explanation in the 17th century, IK systems frequently use the supernatural, religious ‘and other subjective sources’ of information to assist in the understanding of natural phenomena (Roberts, 1996: 64). Although Roberts notes significant similarities between indigenous and Western knowledge systems she suggests that there are few such similarities with respect to the function of each system. Western science, she argues, places great importance on its claim to be objective and ‘value free’, while IK is

overtly value laden. Its role is not to provide neutral information which individuals are then free to use and interpret as they see fit, but instead to impart along with that information, the values, ethics and all other cultural mores of that society (Roberts, 1996: 63-64).

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In this way, indigenous knowledge systems have a functional significance beyond that of WMS.

By providing standards of conduct for each individual in that society, it [Indigenous Knowledge] helps maintain social stability, order, self and cultural identity (Roberts, 1996: 65).

Further, Kawagley explains that indigenous thought sees science as a quest for knowledge... as well as a means to live a long and prosperous life. By assessing the physical phenomena of the present and juxtaposing it against past experience, we gain an idea of what the future holds (Kawagley, 1995: 58).

Roberts’ position in a Pacific context is consistent with the views of Castellano (2000) on indigenous knowledge more generally. Castellano concurs with Roberts’ assessment of IK being derived from multiple, and not strictly controlled sources including traditional teachings, empirical observation, and revelation. Castellano argues that empirical knowledge is obtained from careful observation and represents ‘a convergence of perspectives from different vantage points, accumulated over time’ (Castellano, 2000: 24). In spite of Roberts’ assumption that there are sufficient similarities between indigenous and Western bodies of scientific knowledge to justify the teaching of both within a single curriculum (Roberts, 1996: 59). George has identified several ways in which school knowledge and IK differ (George, 1999). She suggests that IK does not arise from ‘planned procedures and rules’. Instead, she argues, existing knowledge along with intuition and creativity are used to find solutions to everyday problems. Generally such knowledge is transmitted orally from one generation to the next but is not found in school curriculum because

that is a position reserved for academic knowledge that has been sanctioned by communities of scholars over the years (George, 1999: 80).

Although George emphasises difference, she also explains similarities between WMS and the indigenous knowledge of Trinidad and Tobago. She presents a four-fold categorisation of the relationship between the two knowledge systems. In George’s first category conventional science can explain indigenous practice. For example, the indigenous practice of using a mixture of lime juice and salt to remove rust stains from clothes, can be explained in conventional science in terms of acid/oxide relations. In her second category a conventional science explanation is unavailable but likely to be developed. For example the plant verine has pharmacological properties recognised in traditional medicine, ‘but appropriate usage’ has not been verified by conventional science, although conventional science does recognise its pharmacological utility. In category three there is a conventional science link with traditional knowledge

but the underlying principles are different. For example, the indigenous admonition that eating sweet foods causes diabetes links diabetes with sugars, as does conventional science. However, whereas the indigenous system claims that sugars cause diabetes, conventional science claims that when one is a diabetic, the ingestion of sugars can worsen one’s condition.

Finally in a fourth category George places those aspects of IK which conventional science cannot accept.

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For example, there is no conventional science explanation for the indigenous knowledge claim that if one cuts one’s hair when the moon is full, the hair will grow back to an increased length’ (George, 1999: 85).

George suggests that the knowledge in categories 1 and 3 could be used in classroom programmes to highlight similarities between indigenous and Western conceptions of knowledge and indigenous students could thus become

actively engaged in trying to provide a conventional science explanation for everyday practices. Such categories can serve to generate interest among students and to develop pride in the knowledge and wisdom of their ancestors (George, 1999: 85).

George’s proposition requires thinking about teaching and ‘academic practices vis-a-vis indigineous/subjugated knowledge’ in the fashion proposed by Semali and Kincheloe (1999: 33). Although Semali and Kinceloe direct their comments to the teaching of mathematics, their remarks are transferable to the context of science teaching. They maintain that there is

a form of Western elitism [which] permeates math teaching that considers mathematical discovery and knowledge production emerging only from a rigorous application “of deductive axiomatic logic”. Western math has traditionally dismissed African or certain Asian mathematical forms as “childlike” and “primitive” (Semali and Kincheloe, 1999: 35).

They argue that such a belief is challenged by ethno-mathematical research (see Gerdes, 1994: 20, Pinxten, 1994: 23-25 and Katz, 1994: 26-29)) and that a reconceptualised curriculum is required which goes beyond presenting indigenous/subjugated knowledges as ‘mere add-ons that provide diversity and “spice” to Western academic institutions’ (Semali and Kincheloe, 1999: 37). Instead they advocate the learning of ‘the different ways diverse cultural groups might define “logic” (1999: 35). Wane however, points to a potential barrier to the curriculum envisaged by Semali and Kincheloe, a barrier which would be particularly acute if existing mathematics curriculums are as profoundly hostile to indigenous knowledge as suggested. Wane states that

indigenous knowledge has been relegated to the periphery and that, as a result its custodians are reluctant to discuss it, especially with people who have acquired formal (i.e. Western-style) education (Wane, 2000: 54).

The suspicion arises, as Castellano points out in the Canadian context, from:

The imposition of assimilative education, economic dislocation, and government control from an external culture [which] interrupted for generations the transmission of knowledge from grandparents to children and youth. It also disrupted the normal work of adults applying traditional knowledge to the demands of daily living and adapting the knowledge to evolving conditions 2000: 34).

It is important, Kawagley argues thatto change the idea that knowledge and systems that are not from the Western tradition are no good. This hostile view has to change if native education is to succeed (Kawagley, 2001: 54-55).

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Castellano (2000) and Dei (2000) both draw attention to the significance of traditional knowledge to indigenous development. Castellano notes that the ‘ultimate test of the validity of knowledge is whether it enhances the capacity of people to live well’. She goes on to infer that the ability of indigenous Canadians to live well is inextricably linked with their traditional knowledge base because they are

confronted with externally generated problems of huge proportions - the contamination of the food supply in polluted ecosystems and the marginalisation of rural peoples in a competitive world economy, to name but two examples.

For Castellano

the knowledge that will support their survival in the future will not be an artefact from the past. It will be a living fire, rekindled from surviving embers and fuelled with the materials of the 21st century (Castellano, 2000: 34).

Dei makes the same argument and extends it within the context of IK and African development:

Nowhere are the links between development and indigenous knowledge more prominent than when we examine the micro-level interactions of social, political, spiritual, cultural and economic activities and institutions in rural communities. Local peoples experience and interpret the contemporary world in ways that are continuous and consistent with their indigenous worldviews. For the purposes of discussing development issues and indigenous knowledges in developing countries... the search for general solutions to human problems (i.e. development) must proceed from an understanding of local specificities (Dei, 2000: 71).

The notion that IK is centred on local specificities is central to the discussion of Jhon Goes in Center who confirms that IK arises from the systematic collection and assessment of data over time. He argues that in North America experiential information was gathered ‘about cycles, seasons, connections, and strategies’ which was then incorporated into the culture. ‘Experience was evolved into knowledge, and knowledge was evolved into wisdom’ (Dei, 2001: 120). On this basis Jhon Goes in Center firmly rejects any questioning of the contemporary and continuing utility of IK. Rather than abandon traditional knowledge in favour of WMS he argues that

some parts of science can fit well together and we as native people [should] learn to use science in our own ways and for purposes that fit with our own world-view and value system (Jhon Goes in Center, 2001: 120).

Jhon Goes in Center cites Geographic Information Systems (GIS) as an example because it

has the potential to help us consider, all at once, traditional knowledge; scientific understanding; current issues, resources, and goals; and future obligations and possibilities (2001: 120).

He advocates an ‘Indianisation’ of GIS for its potential to combine harmonious values in order to obtain information about people and land, and for its ability to assist in the organisation of information and a fashion

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which incorporates native standards, goals, and tribal wisdom. In using GIS to meet needs such as managing natural resources or providing government services to a community, we incorporate tradition and culture and information systems and all aspects of the process by which is used (Jhon Goes in Center (2001: 121).

The use of GIS to develop indigenous knowledge is an example of the ‘dynamism’ to which Dei refers. It is an example of the ‘embedding’ of the ‘modern’ into indigenous knowledge and shows that such knowledges ‘also have moral and cognitive conceptions about nature and society that may be compatible with Western scientific knowledge (Dei, 2000: 72).Jhon Goes in Center describes a mediation of nature and culture; a concept discussed by Kawagley in his Yupiaq Worldview. Kawagley however argues that the Yupiaq experience is one of greater alienation from traditional culture because the increasing non-indigenous population in its traditional area has undermined traditional knowledge: ‘people set their nets at the assigned hour, even if the times may not be opportune for the best catch’ (Kawagley, 1995: 63)). Kawagley also points out the practical connection between culture and mathematics. In traditional Yupiaq society it was convenience not mathematical precision that determined approaches to mathematical questions. For example, the number of fish one had caught did not need to be counted with precision. Instead one would look at the space filled and ‘compare it to space filled in times past to judge whether one has enough to last the year’ (Kawagley, 1995: 58). Sophisticated observation of natural phenomena, such as the colour and formation of clouds to acquire meteorological knowledge was a feature of traditional Yupiaq science.

They did not have technical names for the different kinds of clouds, but they knew what each would indicate to determine the temperature, wind direction and speed, air pressure, and approximately how long that weather condition would persist (Kawagley, 1995: 59).

On the basis of resolutions of international indigenous meetings initiated by the Mataatua confederation on the cultural and intellectual property rights of indigenous peoples Viergever (Viergever, 1999: 336) concludes that for indigenous peoples there can be identified three most important elements of indigenous knowledge.

(i) it is the product of a dynamic system... (ii) it is an integral part of the physical and social environment of communities; and (iii) it is a collective good.

The physical and metaphysical in indigenous thought

Loving and de Montellano (2003: 148) assume that IK does not distinguish the physical from the metaphysical and argue that this requires IK to defend myths and religion as ‘scientific and actual’ which inevitably results in ‘antiscience and pseudoscience’. Yakabu (1994) also assumes a conflict, while Thijs and van den Berg (1995) share the inference of the Maori writer Durie (1996: 7) that Loving and de Montellano’s position is overstated.

We would think that in the perception of students the domains of science/physics and tradition/metaphysics do not overlap. In other words we do not believe that there is a serious interference between the contents of

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traditional/superstitious beliefs and the scientific understanding, since the two domains are separated in terms of the types of questions considered. There is the difference between the ‘how’ questions which belong to the science domain, and the ‘what purpose’ questions on values pertaining to the metaphysical realms (Thijs and van den Berg, 1995: 334).

Durie argues that the emphasis Maori thought places on the link between the physical and the metaphysical is not so much a point of absolute difference from ‘conventional science’, but a difference in balance, indeed the ‘similarities between Maori approaches to knowledge and Western scientific thinking are more striking than are the differences’ (Durie, 1996: 7).Others however argued that WMS and traditional thought are in conflict, for example Yakubu (1994) suggests that even when people in traditional societies have been well educated in science, they find it difficult to give up the traditional solutions to problems to consider new and better ones.

Certainly, in a non-Western context, it seems that attempting to replace traditional beliefs with the scientific view may not even be desirable let alone achievable (Taylor and McPherson, 1997: 193).

Is Western Modern Science a Threat to Indigenous Cultures?

Aikenhead (1997: 15) draws attention to Jegede and Okebukola’s argument that because WMS is often a ‘Western cultural icon of prestige, power, and progress’, Western culture ‘usually permeates the culture of those who engage’ in science, which can threaten indigenous cultures and thus cause Western science to be seen as a ‘hegemonic icon of cultural imperialism’. Aikenhead accepts Battiste’s (1996) argument that in the case of indigenous peoples of Canada ‘the threat is real’. Harding (1998) is more specific in her discussion through highlighting the political utility of science to indigenous subjugation.

Scientific and technological change are inherently political, since they redistribute costs and benefits of nature’s resources in new ways. They tend to widen any pre-existing gaps between the haves and have-nots unless issues of just distribution are directly addressed (Harding, 1998: 50-51).

Smith argues that the threat posed by WMS to Native American children is such that it may cause for them a loss of culture: ‘cultural genocide’. Smith believes that WMS devalues Native American science and as such causes a ‘progressive alienation from traditional values, family and community’ (Smith, 1996: 2). Lujan, however sees science education as a ‘tool for American Indian community development’ (Lujan, 2001: 79), while James (2001) argues that:

Indian people still need to learn all they can. Not only so that they can come to understand what whites are up to and help whites understand the impact of their own schemes but also so that Indian individuals and communities can finally reclaim their heritage and control the future (James, 2001: 1).

In contrast to Smith (Smith, 1996), James goes on to suggest that the educational problem for Indian communities is that the system has not provided what communities actually need. He cites a survey he carried out in 1995 among Canadian First Nations in which he found that

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in every province, the failure of education systems to teach the skills Indian communities need was the single most commonly cited problem for community development (James, 2001: 5).

The possibility that Smith’s pessimism is overstated is implicit in Corsiglia and Snively’s belief that most indigenous parents want their children to acquire the best available Western scientific knowledge, provided that such knowledge does not displace their own cultural understandings (Corsiglia and Snively, 2000: 85). Corsiglia and Snively thus offer a response to Stanley and Brickhouse’s suggestion that non-Western cultures be asked what concerns they have, or do not have about WMS and asked whether learning about WMS is ‘a threat to the survival of their culture’ and to what extent they wish to access Western scientific knowledge (Stanley and Brickhouse, 2000: 45). Durie provides an indigenous response. His emphasis on an ‘integrated approach to economic, social and cultural development’ leads to the position that there is an ‘imperative’ nature for full Maori participation in science. Durie comes to this conclusion because he emphasises an ‘interface’ between Maori knowledge and science which allows ‘an expanded understanding of ourselves and the world around us’ (Durie, 1996: 1). Further the Japanese writer Ogawa (1997: 3) suggests that comparative studies of WMS and IK give “science” education ‘its own value and a certain culture’.

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Language, Culture and Pedagogy

Teacher and Student Expectations

McKinley’s assertion that teacher expectations... have been seen as significant determinants of student performances, and research suggests that we must instil in teachers higher expectations than they currently have of Maori students (McKinley, 1996: 52)

is supported anecdotally by Te Puni Kokiri in its profile of ten Maori who have pursued careers in science, mathematics or technology. The individuals profiled cited the importance of the teacher and teaching as factors influencing their pursuit of such careers (Te Puni Kokiri, 1996). Holt also emphasises the importance of teacher expectation to Maori achievement.

Teachers who expect Maori children to achieve mathematically will provide programmes that are challenging, including motivational contexts that utilise their developing skills (Holt, 2001: 286).

The implication of this remark is that teachers who do not expect Maori children to achieve do not provide such programmes.McKinley, Holt and Te Puni Kokiri adopt positions consistent with Carter, Larke, Taylor and Santos’ (2003) identification of a ‘deficit model’ having brought the learning of ‘poor students and students of color to a point of paralysis. They argue that the ‘deficit model’ contributes to low teacher expectations and more importantly, Carter et al suggest, to the teacher’s sense of efficacy.

Teacher efficacy is the extent to which a teacher believes he/she can affect student learning... Teacher efficacy is intricately tied into the teacher’s belief system about students and the learning process. The deficit model paralyses many teachers, because they believe that circumstances in the student’s life prevent learning. Teachers who have no efficacy believe that trying makes little difference and situational factors in the lives of students will cause success or failure in the classroom.

The ‘deficit model’ assumes that it is only the middle-class who can be positively influenced by schooling. Teachers who reject that assertion believe that they can make a difference to all students and take responsibility to teach everybody in their classrooms. The efficacious teacher believes that there is a connection between his or her teaching and student success (Carter et al, 2003: 7). Poodry (2001) believes that North American Indian communities themselves have a destructive tendency to accept the deficit model which he describes as a ‘particularly evil myth’. It is a myth, Poodry suggests, that is based on acceptance of a view that ‘our abilities are more determined by our genes or by the nature of the system than by our efforts’. Poodry describes this attitude as ‘negative, stereotypic, and excuse making’ and suggests that it is ‘perhaps more pervasive among Indian people than among other groups’ (Poodry, 2001: 34). Dukepoo (2001) also challenges the ‘myth’ identified by Poodry. Dukepoo, a Native American teacher, dismisses deficit model theories and suggests that Native American achievement ‘is very much possible if we set high standards and help students live up to them’ (Dukepoo, 2001: 37). He does however identify barriers to achievement. In particular, he mentions stereotypical learning styles: ‘Indians are human… as such,

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they all have different learning styles’. Dukepoo notes that Indian people have accommodated different learning styles for thousands of years. He also argues against an emphasis on culture in the classroom:

Instead, I try to teach my Indian students good solid genetics so that they can make it into medical school, which they do. Culture is important to Indian students so that they are rooted in their communities and balanced in life. I do not integrate culture and classroom because information and techniques should be culture free, even if the application often is not (Dukepoo, 2001: 39).

Atwater and Crockett’s argument that teacher attitudes and beliefs ‘drive classroom actions’ is supported by Hill and Hawk’s (Hill, 2000: 11, 56) research in New Zealand multicultural schools. Hill and Hawk found that successful teachers in multicultural schools in poor socioeconomic communities shared a positivity that translated into their setting of high standards for themselves. This was indicative of a high level of belief among these teachers that they could make a positive difference to their students. Hill and Hawk’s research supports the view of Ladson-Billings (1995) that

teachers who hold positive beliefs about students’ capability and success are teachers who create environment in which there is a sense of order accompanied by a sense of engagement. Such teachers remind students that they are capable and create learning situations in which children have an opportunity to succeed (Bryan, 2002: 827).

There is, therefore significance in the statement that: Many times, teachers’ reflections on personal and classroom events are filtered through the lens of world views, beliefs, attitudes and images; consequently, it is essential that science teacher educators and researchers examine these influences on science learning and teaching (Atwater, 2003: 59).

Further characteristics of successful teachers were identified in 2003 by Alton-Lee. Alton Lee found that ‘quality teaching is focused on student achievement (including social outcomes) and facilitates high standards of student outcomes for heterogeneous groups of students’. It adopts ‘pedagogical practices [which] enable classes and other learning groupings to work as caring, inclusive and cohesive learning communities’, it encompasses ‘effective links… between school and other cultural contexts in which students are socialised to facilitate learning’ and is responsive to student learning processes’. Alton-Lee also found that successful teachers create effective and sufficient opportunities to learn and align ‘curriculum goals, resources including ICT usage, task design and teaching’. Pedagogy which ‘scaffolds and provides appropriate feedback on students’ task engagement’ also characterises good teaching practice (Alton-Lee, 2003: 88-90).

Teacher Knowledge

In 2002 a Curriculum Stocktake undertaken for the Ministry of Education found that teachers generally have a confidence in their teaching ability that a range of other literature would suggest is unjustified. Although only one-fifth of teachers reported that they had undergone professional development in mathematics,

nearly all teachers have a medium or high level of confidence in their teaching of mathematics, about two-thirds of secondary mathematics teachers having a high degree of confidence (McGee, 2002: 291).

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Yet at the same time teachers expressed doubt and ambivalence about the usefulness of the [curriculum] statements to meet the learning needs of Maori students’. Teachers claimed to find the mathematics document ‘user-friendly’ but said that as with the other documents they have only ‘some flexibility’ in planning for individual needs and interests (McGee, 2002: 289-290). In a 1997 Task Force report the New Zealand Ministry of Education expressed concern about the impact of inadequate teacher subject knowledge on student learning (Ministry of Education, 1997). Later, in 2000 a report of the New Zealand Education Review Office cited improving teacher subject knowledge and science education pedagogical content knowledge among a range of proposals designed to improve the teaching of science, in primary schools in particular (Education Review Office, 2000).By 2002 the relationship between teacher knowledge and student achievement still concerned policy makers. In that year an Advanced Numeracy Project (ANP) was initiated to raise student achievement ‘by building teacher capability in numeracy teaching’. At the same time the Ministry stated that

ways of raising student achievement should be investigated, with particular emphasis on raising the achievement of Maori students’ (Higgins, 2002: v).

The Ministry argued that the project provided professional development opportunities which account for improvements in teacher knowledge and practice, which in turn accounts for improvement in student achievement (Higgins, 2002: v).There is a view among several Maori scholars that bureaucratic concern is well founded. Herewini (Herewini, 1998: 258) identifies recruitment of an adequate number of Maori teachers who are fluent in Maori and competent in the teaching of mathematics as critical factors in the development of the mathematical potential of Maori children. This goal, Herewini points out, is compromised by the limited pool from which potential teachers can be drawn. There is a limited number of Maori who are fluent in the language and there has historically been a ‘relative lack of achievement of many Maori in mathematics’, which means that many

Maori student teachers bring to their courses negative feelings about mathematics, and a lack of understanding of the major concepts and processes that primary children can be helped to develop (Herewini, 1998: 258-259).

Herewini points to an absence of significant numbers holding the attributes Ohia identifies as belonging to the ‘ideal teachers of Maori mathematics’. Those attributes are

fluency in the Maori language and culture; mathematical content and attitudes; demonstrated familiarity with Maori learning and teaching styles; ability to apply several resources to accompany the content and skills; a thorough appreciation of learning and teaching theory (Ohia, 1995: 37).

Ohia’s assessment is consistent with Fairhall’s position. Many believe that once Maori children are taught mathematics in Maori they will do much better. There are probably more important factors, such as sound teaching (Fairhall, 1993: 22).

Yet Maloney in part attributes the relative lack of Maori success in mathematics to negative self-esteem and attitudes to study. These barriers to success might be

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addressed ‘principally by promoting learning in Maori and by promoting and developing the Maori language itself’ (Maloney, 1993: 54).Maloney’s research on mathematics in bilingual classroomsdemonstrates the effect of inadequate teacher knowledge on classroom practice. In the classrooms Maloney observed teacher unfamiliarity with Maori language was evident in that mathematics teaching was done in English with Maori being used for ‘organisation and control’. The mathematical content did not substantially differ from that of mainstream classes other than in the use of Maori examples. Maloney notes however that there were differences in teaching procedures from those used in mainstream classes: namely the emphasis on group rather than class or individual work. Like Herewini, Maloney comments on the recruitment of suitable teachers. She argues that it is a difficulty for which there is no easy solution.

In the long run, what can be hoped is that the bilingual classes will generate Maori-speaking mathematics graduates who will take over the teaching role. But in the short term there are two possible courses of action. One is to give mathematics teachers the opportunity and incentive to become bilingual teachers. The other is to provide teachers who are proficient in the language with the opportunity and incentive to become mathematics teachers (Maloney, 1993: 55).

Although based on a small sample (six teachers in one school) Rogers’ (2003) study of the professional development needs of mathematics teachers in kura kaupapa Maori makes several observations about the improvement of teacher knowledge. In a rejection of a ‘deficit model’ Rogers emphasises the significance of the teacher:

Regardless of the socioeconomic status of their homes, and influences of both caregivers and peers, children’s mathematics achievement is very sensitive to teaching. Poor teaching leads to mostly low achievement whereas good teaching leads to mostly high achievement. Therefore, children’s mathematics achievement is closely linked to teachers’ mathematics teaching (Rogers, 2003: 2).

Rogers identified inadequate professional development opportunities as a significant barrier to the improvement of Maori teacher knowledge. Opportunities were inadequate because ‘the assumptions and theoretical frameworks the professional development facilitators worked from were outside the kaupapa Maori paradigm’ (2003: 56). Rogers categorised the teacher professional development needs into four main groups:

understanding the mathematical concepts (closely aligned to understanding the mathematics vocabulary that had been translated into te reo Maori). Catering for differences in mathematical ability within the class and making mathematics meaningful. Understanding the ‘progression’ of the mathematics both within the course of a year and from year-to-year (Rogers, 2003: 104).

The connection between subject knowledge and successful teaching practice was clear to Rogers who found that:

Those teachers [with whom he carried out his study] who did spend the time learning mathematical processes that were new to them were rewarded by a growing confidence in themselves as mathematicians and increased motivation to the mathematics from students (Rogers, 2003: 136).

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This observation lends support to a professional development model Rogers advocates on the basis of his own research as well as that of Castle and Aichele (1994) and Bishop and Glynn (1999). Castle and Aichele advocate a professional autonomy in which the teacher controls learning and makes choices which means that ‘individuals are more likely to see connections and engage in practice that reflects a cohesive view of learning’ (Rogers, 2003: 143). Rogers argues that this view is similar to Bishop and Glynn’s idea of Tino Rangatiratanga, which emphasises that participation on one’s own terms is a firmer basis for teacher learning. Rogers’ remark ‘that the first commitment a teacher needs to make is to take the time needed to plan and teach children effectively in mathematics’ (Rogers, 2003: 143) is however made in a context and tone which implies a belief that this motivation is not always found in the teacher.Arguments in support of notions of professional autonomy and tino rangatiratanga in the context of teacher professional development are evident in Stigler and Hiebert’s (1993) comparison of teacher professional development between the United States of America and Japan. They attribute Japan’s relatively greater gains in improvement in classroom practice to Japan having given teachers themselves primary responsibility for such improvement. Stigler and Hiebert describe the professional development process Kounaikenshuu. Kounaikenshuu is school based and run by teachers to achieve the objectives of a school improvement plan. One of the main aspects of this process is ‘lesson study’, which involves several teachers meeting regularly over periods ranging from several months to a year ‘to work on the design, implementation, testing, and improvement of one or several “research lessons”(Stigler and Hiebert, 1999: 110). ‘Lesson study’ is based on the assumption that the most effective place to improve teaching is within the context of a classroom itself. Stigler and Hiebert contrast the difference in approach which they argue explains a relatively more successful improvement to classroom practice in Japan where teacher knowledge has improved under that country’s professional development model.

Despite years of reform, research suggests that classroom teaching has changed little in the United States. In Japan, by contrast teaching practices appear to have changed markedly over the past 50 years... whereas US educators have sought major changes over relatively short time periods - indeed, the very word reform connotes sudden and wholesale change - Japanese educators have instituted a system that leads to gradual, incremental improvements in teaching over time (Stigler, 1999: 86).

Maori Pedagogy

Skill New Zealand (2001) describes research into Maori pedagogies by Hemara, which suggests that traditionally,

Maori educational practices and processes reflected the interconnectedness between the different spheres of Maori existence’. Traditional Maori education was characterised by the process being both student and teacher-centred. The learning process was seen as one of reciprocity ‘teachers and students learnt from each other, making the whole endeavour a cooperative venture in which all parties learnt something new’. Learning was lifelong and intergenerational. Education was often overseen by kaumatua who emphasise practical and social skills as well as teaching ‘ethical and esoteric principles’. Simple lessons on a complex subject were delivered at one time, with the student and teacher drawing out more complex meanings over time. After the

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children learnt to successfully complete a task they moved on to different and perhaps more complex activities. Curricula were mixed and complimentary. Students undertook gradual learning from a familiar starting point. Learning was incremental and familiar, with new knowledge, skills and activities related to preceding and following lessons. The basis for lessons was what children were already familiar with’. Gifted children were identified and selected to attend higher learning institutions. Particular talents were encouraged and developed ‘for the enhancement of mana and economic well-being’. Learning and teaching developed from student strengths. Small numbers of students was common and one to one instruction was important. Hemara argues that ‘Many of these characteristics are still relevant for Maori learners’ (Skill New Zealand, 2001: 60).

Dewe argues that the purpose of schooling is to empower, and that it is a recent development for Maori to be able to choose between ‘empowerment’ and ‘disablement’. For Dewe the choice is remarkably simple: ‘Schools with a kaupapa Maori base empower Maori students. Schools without a kaupapa Maori disable them’ (Dewe, 1993: 31). McKinley (McKinley, 1999: 39) offers a more substantial alternative and asks questions to which there are answers which might facilitate the realisation of empowerment for Maori. McKinley asks What makes teaching and learning effective for Maori children?’ and suggests that the question be investigated through research which considers:

learning and cognitive styles, effective teaching practices and classroom programmes, social and cultural factors (including role models and mentors) that enhance or inhibit motivation and learning, the circumstances that produce (and recognise) exceptional and gifted Maori children, effective interactions, communications, and relationships between Maori children and science teachers, how Maori children approach learning science.

Hill and Hawk (2000) begin to respond to McKinley’s question. Although their study was not carried out in an exclusively Maori context, the number of Maori students in the low decile multicultural schools in their investigation was significant. They found a number of factors which contribute to effective learning and teaching. Effective teaching includes learning activities designed to do more than ‘keep students occupied’. Among the teachers Hill and Hawk observed

There was logic to the timing and sequence of activities that suggested that teachers had put thought into how they would construct the learning for students (Hill and Hawk, 2000: 36).

Links were established with previous learning ‘through specially designed revision activities’ and while many teachers talked about the need to accommodate different learning styles

it was more common for teachers to talk about providing variety and making learning fun. Some of these teachers had not had formal training in this area but were instinctively making professional judgements about what worked and what did not work (Hill and Hawk, 2000: 39).

Hill and Hawk found that effective teachers ensure that new and important concepts are presented in a carefully structured way and that this “explicit teaching” comprises presenting material in small steps, pausing to check for student understanding and

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requiring active participation from all students’ (Hill and Hawk, 2000: 40). Consistently implemented and well understood routines were also found to characterise effective teaching (Hill and Hawk, 2000: 55). Effective teachers see themselves as learners and are

self-evaluating and reflective in an ongoing way. They are constantly aware of the reactions of their students and their own observations and intuition about how things are going. They have confidence to change a planned lesson part-way through if they feel it is important (Hill and Hawk, 2000: 13).

Holt (2001) points out the range of approaches required to improve mathematics education for Maori. These include: teaching and learning practices, classroom culture, assessment practices and teacher and student expectations. She suggests that perhaps these aspects of the teaching and learning process might best be developed in ways that ‘emphasise the oral, holistic and thematic learning of traditional Maori culture’ because ‘holistic learning experiences are context-based and meaningful material is not broken down into small discrete skills or chunks of knowledge’ (Holt, 2001: 21). Clarke (1999) shares this view, while Lee adds a further dimension to the discontinuity between the home and school cultures which may be relevant for Maori.

Although scientific inquiry is a challenge for most students… it presents additional challenges for students from cultures that do not encourage them to engage in inquiry practices of asking questions, designing and implementing investigations, and finding answers on their own… Cultural norms may also prioritize respect for teachers and other adults as authoritative sources of knowledge, rather than the development of theories and arguments based on evidence and reasoning (Lee, 2003: 466).

Carter et al (2003) associate the ‘development of theories and arguments based on evidence and reasoning’ with the field-independence learning style, which they claim is found mainly among mainstream, middle-class, white Americans.

The field-independent learner is individualistic, is good at abstract analytic thought, has keen perception of discrete parts, favors inquiry, prefers independent study, and is very task oriented. Educators favour students with this learning style, and their favour is reflected in most successes of field independent learners in schools (Carter, 2003: 7).

There is an inconsistency between field-independent learning and Jegede’s understanding of the sociocultural influences on non-Western students’ learning.

Studies have shown that there are five predictors of sociocultural influences in the classroom, especially within non-Western environments, which teachers must pay particular attention to. They are: authoritarianism, goal structure, traditional worldview, societal expectation, and the sacredness of science. Authoritarianism characterises the traditional society, where the belief is strongly held that the older person, having been exposed to more life experiences, should be in a better position to appraise a situation and pass “correct” judgement. The society frowns at a situation where the elder’s point of view is challenged or questioned. Accordingly, the elder asserts authority in decisionmaking. It behoves the younger individual to accept without question the directives passed down by the elder. This locus of authority of knowledge is

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transferred into the classroom, where the science teacher is seen as the elder who “knows all” in matters relating to scientific facts, processes, principles, and laws. Goal structure refers to the interaction pattern within most non-Western societies, a pattern that is predominantly cooperative in nature. In this cooperative setting, the goal structure of individuals is directed at the same objective, and there exists a high independence among the individuals working towards a common goal. This contrasts very markedly with the individualistic competitive orientation that school science portrays to learners. A traditional worldview relates to traditional beliefs and superstitions being used as a framework through which occurrences are interpreted. Many non-Western societies, especially in Africa, hold the notion that supernatural forces have significant roles to play in daily occurrences. The younger members of the traditional society are supposed to learn and believe these notions without questioning them. However, this creates conflict when the learner’s scientific knowledge is not in agreement with the traditional worldview. Societal expectations play a pivotal role when the success of individuals within a community is developed and interpreted through the nature of their interaction within a communal society. The behaviour of members in the community is invariably and intimately linked to, and governed by, the behaviour of the larger community. Hence, a school child always reviews his or her achievement in school as a reflection on his or her home, friends and community.The sacredness of science pertains to conceptual interpretations of science. There is a pervasive view held by a large proportion of African society that the study of science is something special, and that requires magical explanations incompatible with the thoughts of someone from a non-Western society (Jegede, 1996: 79-80).

Meaney developed a curriculum ‘support document’ to assist in the formation of a ‘community negotiated’ mathematics curriculum. The purpose of the document is to assist communities to narrow the gap between home and school cultures by supporting curriculum development (Meaney, 2000). Taylor and Stevens (Taylor and Stevens, 2002: 245) suggest ‘culturally relevant’ and ‘student centred’ mathematical activities for native Americans. Barta suggests further activities for the same purpose because:

Educators communicate thoughts and ideas through their cultural perspectives. The challenge for the successful teacher is to learn to understand better how his or her culture has influenced the way that he or she understands and uses mathematics. Empowered with this awareness, such a teacher may realize the necessity of using students’ cultural perspectives to communicate mathematical thoughts and ideas. When teachers help their students become aware of the many ways their ancestors have used and still continue to use mathematics they endow those students with the realization that as direct descendants, they too, possess mathematical ability (Barta, 2002: 73).

The language of instruction

Fairhall has argued in favour of the teaching of mathematics in Maori on the basis, among others, that:

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While the students learn mathematics they acquire Maori language. The anxiety of learning a second language is diverted to the learning of subject content... also, the language provides the students with an identity for what is often considered a foreign discipline (Fairhall, 1993: 23).

In an international context there has been little research on the effects of native languages on learning science. According to Atwater the research that has been done has provided inconclusive results (Atwater, 1994 in Rowland, 2003: 117). Barker however cites research from

situations as different as Alaska, Middlecamp and Baldwin (1995) Kawagley et al, (1995) and Samoa, Lee Hang and Barker (1996) that science learning in an indigenous language can reduce the poverty of students’ thinking (Barker, 1999: 58).

Nevertheless, Rakow and Bermudez (1993: 61 681) comment that ‘a multicultural view of science education research as it relates to Hispanic American students must include more than a simplistic view of this group as different merely by virtue of language’ is equally applicable in the Maori context. Rakow and Bermudez note that language is just one aspect of culture that could influence science learning.

It is only when researchers view this broader context of culture as one encompassing the values and beliefs, the learning styles, the influence of home environment, and the cultural influence of language that we will truly begin to understand the needs and barriers facing Hispanic American students as they attempt to succeed in an increasingly technologically oriented society (Rakow and Bermudez, 1993: 681).

The relationship between the culture of home and school: non-Western knowledge and the science classroom

Malloy and Malloy contrast African-American cultural values with the cultural norms of the school to argue that ‘the success of students in a class depends on the ability of the students to understand and participate in the culture of those who are in power’ (Malloy, 1998: 250). The ability of the student to ‘understand and participate’ is inextricably linked to the closeness of the relationship between the culture of school and home. Often there is a significant gulf rather than a closeness of cultures, which is the point Trodding makes with respect to North American Indian reservation children. Trodding suggests that school pressures reservation children to move away from tribal traditions but the effect of such movement is to isolate children from their families, communities and identities. Indeed, the cultural gap between home and school can be such that by the time they reach university ‘some Indian students fear traditional systems because they do not understand them’ (Trodding, 2001: 64).In the North American context Smith (Smith, 1996: 14) identifies points which should be incorporated into a First Nations’ curriculum so that the gap between home and school might be narrowed. Hill and Hawk (2000: 18) identify understanding of the ‘worlds of students’ as a significant contributing factor towards successful teaching in low decile multicultural New Zealand schools. They argue that successful teachers in these schools demonstrate

a very good understanding of the lives of the students and the students know that they have and value that highly. Teachers make an effort to ask and talk about

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students’ lives outside school and most of the students want to share that with them (Hill and Hawk, 2000: 18).

Hill and Hawk also found that successful teachers have strong interactions with students outside the classroom and place a high value on contact with parents which was more often for positive rather than negative reasons (Hill and Hawk, 2000: 26-27).Lessening the distance between the worlds of home and school is also an objective of the Tu Tangata programme which operates in some New Zealand schools with high Maori populations. Tu Tangata involves members of students’ communities working alongside them in classrooms because:

The daily presence of people who really care is a powerful force. It allows the students to be themselves as an important part of their own community. It reinforces the message that education really matters (Tu Tangata, 1998: 15).

Jegede and Aikenhead (undated) take the position that there are at least two types of culture which students experience when they study science in the Western classroom: ‘the culture of school science and culture of their life world’. Therefore, Jegede and Aikenhead argue, there is a need for students to make a cultural transition from their life world to the world of school science. There is a need to narrow the gap between the culture of home and the culture of the school. It is the ease with which this transition, or ‘border crossing’, is made that determines the student’s understanding of science (Jegede and Aikenhead, undated) . Jegede and Aikenhead suggest the border to be crossed can be particularly wide, which explains why ‘a large majority’ of them can not learn science in a ‘meaningful way’:

at home, non-Western pupils function within a life-world knowledge system diametrically opposed to the knowledge, skills, attitudes, values, language, etc taught in school science content that bears characteristics of a Western orientation. The eco-cultural environment of non-Western learners determines their social and cultural imprints of how knowledge is acquired and how it is used. At school, the science concepts taught as symbolic knowledge can become a source of “cultural violence” and non-empowerment, resulting in serious conflict between what people bring into the science classroom and what they are expected to take away from it (Jegede and Aikenhead, undated).

Jegede (1995: 17) argues that successful border crossing can occur through a process of collateral learning which allows a student in a non-Western classroom to construct ‘side by side with minimal interference and interaction, Western and traditional meanings of a simple concept’. Elsewhere Jegede, (Jegede, 1996: 80-86) gives a detailed description of collateral learning of which he suggests four main types: ‘parallel, simultaneous, dependent and secured’. His summary of the concept explains collateral knowledge as the ‘declarative knowledge of a concept which such a learner stores up in the long-term memory for strategic use in either a Western or a traditional environment’ (Jegede, 1996: 117).Jegede (Jegede, 1995: 122) argues that the cultural clash and difficulties associated with border crossing and collateral learning creates an educational imperative:

Unless the teaching of science and mathematics bears very clear and unmistakable relationships to the immediate environment, both social and otherwise, and until we firmly establish and understand the cultural basis of

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learning within indigenous non-Western cultures of Africa, efforts at educating Africa... might not be as effective as desired.

The solution, Jegede maintains, involves restructuring science and mathematics education and refocusing teacher education programmes to ensure that their philosophical foundations are located ‘and guided by, African imperatives’ (Jegede, 1995: 123). In practice this requires an education that is ‘accommodating, practical and positively oriented’. Atwater and Crockett believe that because culture ‘shapes the world views of students’ it is important that teachers have the cultural knowledge to teach all students. Teacher education must therefore encourage prospective teachers ‘to take risks, to look into the future and imagine a schooling world where all students are successful’ (Atwater and Crockett, 2003: 79). The ambitious nature of such a goal is implicit in Atwater and Crockett’s listing the requirements of teacher education programmes with that objective at the forefront. They argue that multicultural teacher education programmes must include:

(a) a social justice agenda; (b) a “cradle-to-grave” approach to science teacher education programs; (c) collaborations across institutions and communities; (d) a focus on professional development school reform in science classrooms, and on reinventing the university’s role in K.-12 science schooling; (e) a blending of science education research and practice; (f) a serious and sustained engagement in science learning and teaching by focusing on science knowledge, powerful pedagogies, and school culture; and (g) a self-renewing organisational structure (Atwater and Crockett, 2003: 79-80).

Malloy and Malloy (1998) argue for a ‘culturally based pedagogy’ in mathematics education because without that pedagogy teachers will have difficulty sharing a mathematical ‘code of conduct’ with all students. They suggest as positive measures towards that end ‘inquiry-based approaches, real-world problems, varied forms of grouping, alternative assessment, and multicultural and gender-bias-free materials’ (Malloy and Malloy, 1998: 248). Nevertheless these listed measures ‘do not address the interaction between the culture of the student and the culture of the classroom’ (Malloy and Malloy, 1998: 250). There is thus a need to examine fully ‘the role of culture on cognition and thus the use of a culturally based pedagogy in mathematics instruction’ (Malloy and Malloy, 1998: 248). Another caution about inclusive educational programmes is that there is a possibility that they have assimilative tendencies. Barton and Osborne (2001: 13) hold a suspicion that ‘science for all [could involve) an all that becomes increasingly homogenous’. They suggest that instead education for ‘marginalised children’ might require ‘rethinking foundational assumptions about the nature of the disciplines, the purpose of education and our roles as teachers’.In contrast Taylor and MacPherson’s (1997: 197-198) study of the impact of traditional beliefs on the ability of Fijian students to accept and understand Western science found that:

Regardless of how firmly students held to their traditional beliefs, they claimed that these in no way interfered with their learning of science. They appeared to be able to contextualise their knowledge with the traditional meaning of a concept being applied only in a traditional setting and the scientific meaning being applied in contexts where it was appropriate, such as the science classroom.

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Taylor and MacPherson also note that one aspect of science - matter - offered the Fijian students ‘little potential for conflict with traditional beliefs, while in other domains there are clearly conflicting viewpoints which could result in confusion’. So the question is asked

Perhaps much of physical science comprises domains of knowledge that are not addressed in traditional cultures (and vice versa). Conflict only becomes a possibility when both systems focused on the same domain (Taylor and MacPherson, 1997: 202).

Taylor and MacPherson undertook a cross-cultural comparison of students’ alternative conceptions of science. The comparison across three cultures, including a group of Western cultural origin found the same misconceptions prevailed across the three cultural groups. The same misconceptions, Taylor and MacPherson suggest, occurred ‘possibly due to shortcomings in instruction’ (Taylor and MacPherson, 1997: 202). Taylor and MacPherson argue that many Western students are ‘turned off science’ because these alternative conceptions create a

perceived gap between the content of science lessons and their own everyday experiences... For many students in developing countries this gap must inevitably be greater because they are generally exposed to a less technological world.

It is useful therefore to gain an understanding of the alternative conceptions of students in developing countries (Taylor and MacPherson, 1997: 191). In the New Zealand context Ohia has argued that mathematics programmes need to be reorganised to reflect ‘Maori thought and philosophy’ in order that Maori might achieve outcomes similar to those enjoyed by other groups (Ohia, 1993: 37). He maintains that the assumption, which has informed curriculum development, that all students have the same opportunity to acquire mathematical knowledge does not hold. It does not hold because: ‘The teaching of mathematics is not culture free’. Instead mathematics programmes ‘inescapably reflect the dominant Pakeha tradition’ and do not recognise that differences in culture, linguistic experience and learning and teaching methodologies ‘can adversely affect the attempts of Maori to ‘succeed’ in mathematics’ (Ohia, 1993: 38).Ahlquist and Kailin (Loving and de Montellano, 2003: 49-51) identify several criteria for the teaching of science from a ‘critical multicultural perspective’. Their criteria include specific programmes to recruit and support people who have ‘traditionally been left out of science’, the teaching of science from historical, cultural and political perspectives which should include discussion of the contributions to science of non-Western peoples. They also advocate teaching science in social context in order that it be demystified. Teaching for equity and challenging science textbooks that are ‘Anglocentric and Eurocentric’ are also priorities for Ahlquist and Kailin. The view that students are more likely to be interested in learning science when its teaching is located within their own culture is supported by Key’s (Key, 2003: 98) research among African-American eighth grade science students. The study found that African American students much preferred STS science topics to traditional Western topics. Malloy and Malloy (1998) note research indicating that African-American students do well in mathematics when they can see its utility.

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Bishop (1994) has suggested a research agenda for the teaching of culturally ‘relevant’ mathematics. He suggests that among others the following questions be considered.

What theories could and should influence the “culturalizing of the formal mathematics cutticulum? How should, and could, a curriculum be restructured in relation to a local culture?... What values are developed within the current school mathematics curriculum? Values are rarely explicitly referred to in mathematics curricula, and research which reveals the hidden values is sorely needed. What other values can be emphasised… To what extent can a “culture-blind” intended mathematics curriculum be made less of an obstacle in the classroom?... What cultural conflicts are experienced by mathematics learners and how do they cope with them?... In what sense does bicultural mathematical learning differ from bilingual mathematical learning? (Bishop, 1994: 17-18).

Indigenous Knowledge, stereotypes, textbooks and classroom practice

Ninnes’ (2003) examination of four school science textbooks in Australia and Canada revealed limitations in ‘discourses and representations of culture and cultural difference’ and limitations in the books’ treatment of ‘diverse knowledges and ways of knowing, and of indigenous identities’. Ninnes found an absence of representations of indigenous ideas and identities and

the use of narrowly conceived notions of indigeneity, such as the discourses around traditionality; the construction of binaries that disguised adversity within indigenous populations and result in essentialist notions of indigeneity; and the various means by which science knowledge is privileged to the detriment of other knowledge forms (Ninnes, 2001: 181).

Ninnes suggests that these problems can be addressed through a reconsideration of how diversity is written about. Further, in spite of the weaknesses he identified Ninnes also found textbooks which did recognise diversity within indigenous groups. Diversity was recognised through the use of particular group names instead of generic terms and through

the use of modifying language to avoid overgeneralising; representations of a range of contemporary and historical indigenous identities and knowledges; and the incorporation of indigenous knowledges into the main textual narratives alongside but not subordinate to the ideas that are represented as Western scientific ideas (Ninnes, 2003: 182).

Ninnes points out that there are social and political processes that influence textbook development as societies respond to competing interests

concerning who controls the process and to what extent the process of multicultural science curriculum development acts as a means of controlling and disciplining indigenous and other minority groups (Ninnes, 181-182).

Ninnes wrote elsewhere that he found that the most important reason for including ‘multicultural material’ in school textbooks was to give effect to state requirements. Philosophy, relevance and perceptions of the nature of science were further reasons (Ninnes, 2001: 20).

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One respondent to Ninnes’ survey noted the absence of ‘indigenous ownership’ of material used in textbooks (Ninnes, 2001: 24). Another expressed concern that

to sidetrack into multicultural views would require time-time that could result in students being disadvantaged in their understanding of current science (Ninnes, 2001: 24).

Ninnes suggests that there is a need for further research regarding the sources of knowledge pertaining to indigenous peoples, the extent of involvement of indigenous people in the production of texts that purport to represent their knowledges and that construct identities for them, and the effects of including material of this kind in science curricula of indigenous and other students’ approaches to learning science (Ninnes, 2003: 182).

Loving and de Montellano (2003: 14) suggest that suitable teaching materials ‘that tie culture with science’ are not available in great number because there has been a ‘refusal of scientists and science educators to develop accurate and valid materials of this type’ (Loving and de Montellano, 2003: 14), which has ‘fostered the development of alternative of alternative science materials of dubious quality’ and indeed some examples of ‘blatantly bad science’ (Loving and de Montellano, 2003: 15). Loving and de Montellano’s remarks are consistent with Rogers’ conclusion that

the best resource was only as good as the teacher's ability to facilitate the resource for the learning of the students. More beneficial than any textbook written Te Reo Maori was a teacher competent in the main mathematical ideas and processes within each strand of the mathematics curriculum, and equipped with a variety of strategies to advance student learning of these ideas and processes (Rogers, 2003: 105).

Resource materials for the teaching of mathematics in Maori need to balance traditional Maori mathematical knowledge, the mathematics curriculum, and modern technological concepts. Trinick argues that the contexts that are ‘relevant’ for the teaching of Maori mathematics include ‘themes from traditional Maori society or from sport and leisure activities’ (Trinick, 1993: 44) and that

assessment procedures should make use of concrete examples... should be holistic and cut across curriculum boundaries; assessment involved cooperative work and interactive learning (Trinick, 1993: 50).

In this way Trinick argues ‘the reality’ of the Maori child might be reinforced. There is a connection between teaching resources and assessment and Kent (1996: 95) argues that assessment methods and equitable outcome are linked to the extent that kura kaupapa Maori will be ‘ineffectual... unless there is acceptance... of the assessment practices preferred by Maori’. Kent carried out an investigation which compared Maori third and fourth form student responses to written based assessment with student responses to individual and class interviews. The knowledge being assessed was that acquired from a study of the phenomenon of heat using the hangi as the context (Kent, 1996: 95). Kent concluded that ‘although the degree of validity varied among students’ the interviews were a ‘more valid method of assessment’ because the interviews made it possible ‘to elicit a greater depth of scientific understanding... that was apparent in the written responses’ (Kent, 1996: 100). Gregory (Gregory, 2001: 41) advocates ‘authentic assessment’ which is a form of

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assessment ‘that is as close to children’s reality as possible’. Authentic assessment helps to overcome ‘one of the biggest difficulties’ for children learning mathematics, which is language that is too complex. In North America Quattromani and Austin-Manygoats (2002) suggest a ‘mathematics portfolio’ as a tool for valid assessment because it can serve as a

vehicle for organizing students’ artefacts that aid in the assessment of performance, creativity, participation, group interactions, decision-making skills, product development, and other essential learning experiences that are otherwise difficult to consider in any other holistic manner (Austin-Manygoats 2002: 84).

Davison and Miller (1998: 262) note the suggestion that the inclusion of ‘culturally relevant situations’ in science and mathematics curriculums can help to raise American Indian achievement. This objective however, raises a concern for Davison and Miller about the effect of ‘the tendency to overreact in trying to be culturally sensitive to specific populations’. The tendency they believe is particularly likely to be found among teachers who are not grounded in the culture of the people whom they teach: ‘being culturally sensitive is difficult for those outside the culture’. (Davison, 1998: 262). McKinley (1996: 51) makes the same point in relation to the Maori context. While McKinley sees merit in locating science programmes within the student’s own cultural context she warns against the possibility of teachers who are not familiar with Maori culture causing offence as a result of that unfamiliarity. A further warning McKinley issues is that teachers avoid the assumption that all Maori students have been ‘exposed to the same cultural knowledge’. In spite of her endorsement of culturally relevant contexts in 1996, by 1999 McKinley remained unconvinced of adequate research to demonstrate that a broader “culturally relevant” pedagogy ‘can improve achievement by matching teaching approaches to the learning styles found in specific cultures’ (McKinley, 1999: 36). McKinley expressed reservation about drawing conclusions on the basis of ‘simplistic assumptions about cultural learning styles’ which ‘assume that teaching practice should mimic some of the surface characteristics of cultures, as described by anthropologists’ (McKinley, 1999: 36). McKinley points out that cultures change and that group characteristics do not apply to all individuals:

for example, we know that Maori children as a group have lower scores on standardised intelligence tests than do Pakeha children as a group, but this tells us nothing about the next Maori or Pakeha individual who walks into our classroom (McKinley, 1999: 37).

Rowland and Adkins (2003: 118) maintain that the same problem of stereotyping exists in North American Multicultural Science Education and Native American Science Education. They argue that the stereotypes are based on limited research and experience and cannot accommodate ‘within group variance’.Rogers (2003: 46) suggests that kaupapa Maori ideology dismisses stereotypes and ‘supports the assumption that Maori youth are not all “at risk” nor are they all “academic superstars”, they are positioned instead to determine their own academic destiny... by promoting Maoriness as normative. Rogers points out that Bishop and Glynn (1999: 169-170) ‘argue that through... kaupapa Maori theory a context is offered whereby “children can determine their own positions in classrooms” rather than “a teacher pedagogy that perpetuates teacher images” which are not from the culture of the child’ (Rogers, 2003: 46). The perpetuation of teacher images extends

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to perceptions of suitable careers for students of a particular group, as Ford (1984) and Mestre and Robinson (1984) found with respect to Hispanic Americans, whom they found received remarkably different kinds of career counselling from those provided to Euro-American students. Stereotypical views of indigenous students have led to assumptions about how they should and should not be taught. Ezeife (Ezeife, 2002) suggests that for aboriginal students in particular,

teaching mathematics by the use of methods and instructional designs that glorify the familiar explain-example-exercise pattern of expository teaching has led to the high dropout rates for mathematics and associated science courses’ because of the approach’s emphasis on ‘rules without reason’. Instead he advocates approaches which are ‘consistent with how students learn’, which he argues include emphasising the concrete rather than the abstract and the real rather than the imaginative (Ezeife, 2002: 182).

Ezeife also advocates the use of tactile visual approaches and the presentation of material ‘in a culturally relevant manner, using situations the students find interesting and familiar’ (Ezeife, 2002: 181). Stereotypes aside Were (Were 2003) argues that there is a benefit in visual approaches because the ‘material qualities of objects can mobilise mathematical thinking and act as vehicles for learning’(Were, 2003: 25). Were also argues from experience of the Papua New Guinean mathematics curriculum that where knowledge from local cultural contexts can be applied to Western mathematics teaching than ‘a concrete link between abstract mathematics and local everyday life’ is established.

It is based on the theory that certain properties of objects can harness mathematical thoughts, and it is these thoughts that can be used fruitfully as a vehicle for learning. So for example, concepts of numeracy and spatial reasoning are tapped directly from the mathematics embedded in various phenomena with shape, symmetry, time, pattern, colour, set theory, number, angle length, and capacity illustrating some of the specific mathematical concepts the curriculum programme harnesses (Were, 2003: 30),

McLean (2002: 184) is supportive of teaching through the use of ‘culturally-based information’ including such things as non-standardised methods of measurement. In 1988 McKenzie developed a teaching resource which used kowhaiwhai as a context for mathematics teaching. In 1999 he evaluated the resource, arguing that he had in fact put ‘the cart before the horse’ (McKenzie, 1999: 261). Instead of using kowhaiwhai to teach mathematics he now advocates the reverse: the use of mathematics to teach kowhaiwhai. McKenzie’s reasoning was that:

Activities from a cultural base carry ideas other than mathematical ones and these may not be easily carried along with the mathematics. If the cultural ideas are omitted, what remains is not true to the whole; if they are included, then a whole new set of issues arise... The rafter panels carry too many values to be seen as just mathematics, but they can be used as an example of the places and which mathematical ideas can be found (McKenzie, 1999: 261).

The utility of this kind of mathematical learning is that contextual mathematics has ‘intuitive meaning for children’ (Owens, 2001). The argument continues to suggest that teaching in contexts of cultural familiarity to children and contrasting their ‘life-worlds’ ‘with a critical analysis of the subculture of science... consciously moving back and forth between life-world’s and the science-world’ facilitates the type of

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border-crossings that Aikenhead argues are essential to the successful acquisition of scientific knowledge by non-Western students (Aikenhead, 1996). Turnbull Nelson-Barber and Mitchell provide examples of mathematical activities which are likely to have cultural familiarity respectively to Inupiaq and Yup’ik peoples of Alaska and the Navajo people of Arizona (2002). Davison, however points out that the connections between cultural activities and school mathematics may not be obvious to children who live in ‘two worlds’ – the world of home and that of school (Davison, 2002 ).Hilberg, Doherty, Dalton, Youpa and Tharp (2002) advocate seven ‘standards’ for the successful teaching of mathematics to American Indian students. They are: joint productive activity - teachers and students producing together, language development – developing language across the curriculum, contextualization – making meaning by connecting school to students’ lives, cognitive challenge – teaching complex thinking, instructional conversation – teaching through conversation, choice and initiative – encouraging students’ decision making and modelling and demonstration – learning through observation. Pallascio, Allaire, Lafortune, Mongeau and Laquerreis (2002: 57-68) study of the teaching of geometry among Inuit people led to six recommendations for teaching practice: use project-based teaching, use projects that require the use of geometric transpositions, allow studentas to choose with whom they will work, make ‘metacognitive activity’ explicit through frequent intervention, ensure projects have a relationship to school mathematics and ‘develop strategies of enculturation as a means to further the development of solid preprofessional training in spatial and geometric skills’.Aikenhead argues that border crossings would be further facilitated by the creation of a ‘cross-cultural science and technology curriculum: a science-technology-society (STS) curriculum’. An STS curriculum would include ‘the social, historical, and philosophical aspects of science as well as science-related societal issues’ (Aikenhead, 1996: 42).The significance of Aikenhead’s proposal for the substance of science teaching to indigenous students, and the point of contrast with conventional Western science teaching, is that:

Rather than insist that students develop knowledge, values, and skills for assimilation into the subculture of science, a cross-cultural STS science and technology curriculum will help students enrich their own life-world sub cultures by empowering them to draw upon the subculture of science in appropriate situations (Aikenhead, 1996: 43).

Maori Participation and Achievement in Science and Mathematics

What do Maori Want?

Several Maori authors have addressed the question of what Maori want from science and mathematics and from science and mathematics education. The Ministry for Research Science and Technology has met with different Maori communities and among other issues discussed Maori expectations. Roberts et al (Roberts, undated) and McKinley (1996) have identified a number of ‘key themes’ relating to what Maori want from the science industry. Those themes indicate a Maori desire

to develop their own economic assets, particularly forestry and fisheries; to maintain the quality of the environment as enshrined within the concept of kaitiakitanga (guardianship) and for Maori to take an active role in the research process and have the value of traditional local knowledge for this purpose

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acknowledged; equitable access to the science system that includes Maori input into, and influence on, the direction of research programmes which particularly affect the Maori community; to help retain traditional knowledge, particularly with respect to flora and fauna, other natural resources, traditional living skills, and the philosophical structures which support the knowledge paradigms; to address issues relating to the interface between science knowledge and matauranga Maori (McKinley, 1996: 53).

In 1993 Te Puni Kokiri stated emphatically, but cited no supporting research, that learning within the structures of Maori knowledge and teaching will enhance the cognitive and intellectual development of Maori children and so realise their full potential (Te Puni Kokiri, 1993: 10).

Te Puni Kokiri then noted that such an approach required research ‘to identify and document traditional Maori mathematical concepts, words and processes’ and noted a need for teaching resources based on the outcomes of such research. Te Puni Kokiri also called for the examination of mathematical teaching methods to identify aspects which ‘are assimilative in nature’ as these obstruct Maori learning. Increasing Maori mathematical achievement was advocated because it ‘will help further develop an economic base for Maori and will assist New Zealand’s ability to compete internationally’ (Te Puni Kokiri, 1993: 10).Herewini (Herewini, 1998: 259) makes the related observation that the effect of relatively poor performance in mathematics among Maori is that Maori are denied access to professions and occupations, which are often of a high status, that require a strong mathematical ability. Instead ‘Maori people desire to achieve the same outcomes as non-Maori learners and to the same standards’ (Ohia, 1993: 113).Durie draws a connection between tino rangatiratanga, self determination, improved Maori wellbeing and an improved Maori skill base (Durie, 1996). Durie argues that an improved skill base requires ‘a positive approach to Maori human development’, and that such an approach requires an ‘integrated Maori focus’ that is able to ‘reinforce a Maori cultural identity’ He argues that without a Maori focus one might instead have ‘a Pakeha programme for Maori’ (Durie, 1996: 4) and one is likely, as the Maori Language Commissioner has pointed out, to clothe ‘Western thought with Maori words’ which ‘will erode the essence of the Maori language’ (Durie, 1996: 6). If increased Maori success in science is to be seen within the context of broader development, economic as well as cultural, the State’s closed education market may need to be relaxed. Durie argues that an approach to development reliant heavily upon a Maori knowledge base can ‘by drawing on centuries of experience... retain a sense of continuity in an otherwise fragmented world’ (Durie, 1996: 3). In Canada Dyck (2001: 28) makes the same point with regard to Aboriginal participation in science. This Castellano argues, creates a challenge to Aboriginal peoples

to open up space for Aboriginal initiative in schools and colleges, work sites, and organisations so that indigenous ways of knowing can flourish and intercultural sharing can be practised in a spirit of coexistence and mutual respect (Castellano, 2000: 23).

Durie’s aspirations are supported in an international context by Ahlquist and Kailin who argue that a ‘critically multicultural’ science curriculum should go beyond presenting multiple views of science to consider scientific solutions ‘to the critical and pressing daily life science issues that currently face global society, such as hunger and

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poverty, food production and distribution, genetic engineering, the users and abuses of energy, and the increasing forms of environmental pollution’. In this context one might link science and tradition (Loving and de Montellano, 2003: 51).The principal of the school studied by Rogers (Rogers, 2003: 61) wanted to ‘fill the gaps’ he perceived in the mathematical knowledge of his students. He wanted to establish ‘benchmarks’ from the mathematics curriculum which he believed 70% of students in each class should be able to master.

Maori School Performance in Science and Mathematics

Several investigations into Maori achievement relative to the achievement of other New Zealanders have been undertaken. They consistently reflect a gap in levels of achievement.In the 1994/95 TIMS (Third International Mathematcs and Science) study it was found that the most successful Maori students at Year 5 level achieved at the same level as the best Pakeha/European and Asian children. Yet more than three-quarters of Maori scored below the mean scores for these two other groups. In 1998/1999 the Maori and Asian groupings recorded the largest increase in mean achievement, while there was only minimal change for the Pacific and Pakeha/European groupings. In spite of the improvement there remained significant differences in achievement level and Pakeha/European children ‘achieved significantly higher means than Maori and Pacific students in all six science context areas’ (Hipkins et al, no date).In the 1994/1995 TIMS study Maori children at Year 4 achieved on average 12 to 13% behind Pakeha/European and Asian groups. On average Maori girls performed 5% better than Maori boys, while at Year 5 level the margin was 9%. All ‘girls achieved a higher level of growth in science [from Year 4 to Year 5] than the boys, especially students from Maori and Pacific Island backgrounds, with differences of 4 and 5% respectively (Garden, 1997: 123).TIMS showed that the greatest improvement by gender and ethnicity in mean mathematics scores between 1994 and 1998 was for Maori boys. There was no change for Maori girls, who in 1994 had performed significantly better than Maori boys, and the differential between genders had ‘all but disappeared’. The same pattern was observed in science (Hipkins et al: 16).The National Education Monitoring Project (NEMP) also found relative improvements in Maori performance at Year 4 and Year 8 levels across a similar time frame. NEMP found that in 1995 Maori children’s performance was less than that of non-Maori in 61% of the assessment tasks at Year 4 and in 57.6% of the tasks at Year 8 level. By 1999 the relative differences had fallen to 12% at Year 4 and 44% at Year 8 (Crooks and Flockton, 1999: 67). For Year 8 children the one area in which Maori performed better than non-Maori was one of Maori cultural context, namely kai moana. Year 8 Maori children claimed less experience connecting school science with everyday things and were less likely to believe that they would make good scientists themselves (Crooks and Flockton, 1999: 67).NEMP data showed significant difference between ethnic groups with respect to mathematical achievement in 1996. At Year 4 level non-Maori children scored higher than Maori on 40 of the 50 tasks, yet Maori were more positive about doing mathematics at school. They were also more positive about their ability in mathematics. At Year 8 level Maori achievement was lower than non-Maori on 41 of the 53 assessment tasks (Crooks and Flockton, 1997: 65-66).

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2001 NEMP mathematics data showed that Year 4 Maori children performed less well than other children on 58 of the 77 tasks. Maori did not perform better on any of the tasks. Maori were less positive than others in their mathematical self-belief. At Year 8 level Maori again performed less well than non-Maori. The negative difference was found on 61 of the 93 tasks. Maori did not perform better on any of the tasks, yet they were more positive than non-Maori about their enjoyment of school mathematics (Crooks and Flockton, 2001: 67).In 2001 NEMP compared the performance of Maori in general education with that of Maori in Maori language immersion education. It was found that both groups of children performed equally well on 34 of the 58 tasks. Children in general education performed significantly better in the remaining 24 tasks. Crooks and Flockton caution against reading too much into these comparisons because the methodology used to obtain the data had serious limitations. The limitations concernedthe Maori language competence of the children in immersion settings, and their ability to understand the language, rather than the mathematics, in the tasks they were asked to complete (Crooks and Flockton, 2001: 6).

Maori Responses

Maori responses to Maori education underachievement have taken place within the context of a state controlled closed education market. There are limitations to what Maori themselves can change. Within this environment however there appears agreement that

Kaupapa Maori educational initiatives based on the notion that language is the key to accessing the culture and together language and culture are the key to socio-political interventions; that is acquiring linguistic knowledge and acquiring socio-cultural knowledge are interdependent (Rogers, 2003: 26).

Maori have attempted to ‘align’ and ‘correlate’ Maori cultural, art, crafts, social, political and contemporary forms, as well as native fauna, marine and animal life, the remainder of the environment, and mystical understandings’ with ‘mathematical topics, concepts and exercises’ which ‘ensures that extra links are being made between mathematics and some aspects of the Maori world (Ohia, 1995: 34).

In this way Ohia believes it will be possible for Maori to achieve to the highest levels in mathematics. Barton and Fairhall (1995: 7-8) however, point to difficulties in developing the official Maori mathematics curriculum which suggest that Ohia’s aspirations are not reflected in the Maori classroom. Barton and Fairhall suggest that the Maori mathematics curriculum is not a radical change and that the main difficulty in working to develop the document was official pressure that it be no more than a parallel to the English document. Nevertheless Barton and Fairhall believe that the Maori mathematics curriculum is a ‘first step’ in the process of creating ‘a modern and recognisably mathematical curriculum while remaining in tune with Maori culture’ (Barton and Fairhall, 1995: 8).Barker (1999: 51) argues a similar difficulty in developing a Maori science curriculum, suggesting that it too is no more than a ‘first step’ in the creation of an authentic Maori curriculum. Barker argued that the bureaucratic parameters of the New Zealand Curriculum Framework meant that there was little room for ‘Maori

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knowledge structures or epistemologies’ (Barker, 1999: 51) and that as the Maori curriculum is ‘basically a translation from English and carried out under strict government oversight, it represents the co-option of Maori language for regulation and control’ (Barker, 1999: 55). But to go further than this, to ‘reconceptualise science’ requires

a coherent epistemology with which to do so. Until that issue is resolved, Maori cultural knowledge is unlikely to make it into the science curriculum, except to support existing ideas by providing “examples” and “starting points” or adding Maori touches to the historical background provided for various topics (McKinley, 1996: 36).

If there is to be a link between education and Maori development then the implications for the New Zealand context of Dei’s (2000) comments in an African environment, might well be considered.

For the idea of ‘development’ to have any credibility at all, it must speak to the social, cultural, economic, political, spiritual, and cosmological aspects of local peoples lives, as well as to their specific needs and aspirations. Debates about ‘development’ must be situated in appropriate social contexts that provide practical and social meaning to the actors as subjects, rather than as objects of development discourse. This is a critical perspective on development: that local communities should own and control the solutions to their problems. This critical perspective also recognises that real and effective control by the local community over the development process is possible only if the development agenda seeks to centre indigenous knowledge systems in the search for solutions to human problems. This means articulating conceptions and praxis of development that does not reproduce the existing total local dependency on external advice, knowledge and resources. Local input must be from the grassroots, should fully respect women’s knowledge, should be ecologically sound, and should tap the diverse views, opinions, resources, and interests manifested in the cultural values and norms of local communities (Dei, 2000, 73).

Conclusion

Recent NEMP and TIMMS data show that Maori are not achieving in mathematics and science to the same extent as members of other New Zealand ethnic groups and are not achieving to the extent required to meet Maori expectations of participation in mathematical and scientific industries. This can be attributed to several factors including: conflict between the culture of the home and the culture of the mathematics and science classroom, low teacher efficacy and expectation, low student self-expectation, inadequate teacher subject, cultural and pedagogic knowledge and a rigid curriculum framework which creates little space for Maori determined pedagogy. The effectiveness of classroom practice can also be undermined by cultural stereotypes. Maori scholars reject the notion expressed in some international literature that WMS is a threat to indigenous cultures and suggest that arguments surrounding conflict between physical and metaphysical conceptions of truth are overstated as explaining cognitive conflict arising from differences between home and school cultures. At the same time they advocate mathematics and science education that meets Maori cultural as well as economic needs. This cultural imperative raises the issue of language of instruction for cultural as well as cognitive reasons.

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While there is a small literature on effective classroom practice it focuses on ethnic minorities generally. There is consequently a need for substantial research on successful classroom practice specifically for Maori. Such research might consider effective classroom practice in the context of language, culture, traditional Maori knowledge, teacher knowledge and expectation, student expectation, cognitive conflict and Maori community needs and expectations.

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