Indigenous Knowledges in PNG

!! Recognising variables and relationships visuospatially "! Canoe making (Matang; Owens & Kaleva)

"! String figures (Vandenriessche; Sth Africa)

!! Indo-European mathematical equivalents "! Graphs & calculus (Matang; UOG)

"! Knot theory & series of polynomes (Vandenriessche)

!! Position "! Orthogonal axes versus place-based (Senft et al.;

Bishop; Owens)

Linguistic Studies of Position

!! Location & direction - deixis "! Prepositions & postpositions (at, behind) "! Locative adverbs (here, there) "! Verbs (to go, to bring) "! Directionals (to, into) "! Presentatives (there is) "! Spatial or dimensional adjectives (high, wide) (Senft et al)

!! Large variety across languages !! Gestures !! May be society with more man-made objects has fewer terms

"! as the object determines position e.g. lock and key "! Context

!! Common "! three positions: distant place, medial distance and close by "! and/or three directions: at, going to or going from given as postpositions and postdirectionals (suffixes)

Culture, Language and Measurement

!! Position may impact on measurement "! Kilivila, PNG have vertical and horizontal but

horizontal may move from ground to arms (Lawton, Wado)

!! May be few words but may have qualifiers providing flexibility

!! Empty may indicate expectation

!! Comparison may be measured but approximations are adequate "! Anindilyakwa, Groote Island, Aust (Worsley)

Measurement practices

!! Vary with "! activity,

"! relationships of people involved in the activity & related activities determined by culture,

"! tool availability,

"! body parts,

"! attribute being measured and

"! purpose for measuring

"! context such as environment/supply

Language and measurement

!! Lack of equivalence of English adjectives and PNG language

!! General terms like size and use of verbs for making bigger

!! Metaphors

!! Reduplication

!! Impact of other languages and western education curriculum

!! Classification may have different word for our one adjective

Policy recognition of Indigenous knowledges

!! Australia "! Systemic change especially in funded

projects

"! Often project based rather than on-going

"! Involvement of community in decision making and in the school at planning, delivery and evaluation

"! Format of partnerships and means of engagement considered

"! Consideration of available community personnel

"! Open, trusting, authentic partnerships

"! Still need for more structural support

Australia cont. – Western NSW (Yunkaporta)

!! “building learning around deep understandings of Aboriginal pedagogy;

!! Designing learning through intercultural collaboration;

!! Allowing quality cultural context to emerge through Aboriginal pedagogy and intercultural collaboration”

!! Cultural metalanguage rather than western linear logic; holistic; cultural connections from different sources

!! Reflection and

!! representation

Smarter, stronger learning

communities

!! Past to future to present

!! What do we do well now?

!! What would we like to change?

!! How might we change?

Moving Forward

!! Decolonising the curriculum

!! Employment of Indigenous staff

!! Reduction in turnover of other staff

!! Gaining knowledge through yarn-ups

!! Viewing child in a culture way and as part of culture with Elders having a role in community, in knowledge building, in school decision making (Dubbo community)

!! Place-based, outdoor education with Elders

!! Democracy with Indigenous rights and respect in meaningful, engaging and self-determined education

Content (Frigo, literature review)

!! Value diverse cultural and linguistic heritages

!! Make explicit the differences between home and school, value both equally

!! Make explicit links between community, home and school based mathematics

!! Provide realistic and real-life classroom contexts for mathematical activities

!! Plan with community

!! Modify content and pedagogy to reflect students’ interests and needs

!! Engage with suitable resources and materials

Examples

!! Garma Project for Yolngu in Nth Territory of Australia "! complex relationship of position and every

other aspect of culture of Yolngu

"! Patterns of relationships and patterns of school mathematics

!! Reform agenda in PNG "! Elementary curriculum: Culture and

Mathematics emphasises principles like counting words and their relationships, principles and purposes for counting or ways of measuring, units,

Matang’s Research

!! The use of the vernacular language and mathematics resulted in stronger arithmetic skills in their home language and in English than those who used Tok Pisin and English in elementary school.

!! Paraides also found vernacular language resulted in good results in PNG.

!! Lipka & Adams found better mathematical results for Yu’pik with culturally based units of work being used

Value of appreciating Indigenous cultural

mathematics

!! Explicating visuospatial reasoning in early childhood education

!! Alternatives resulting from cultural linguistic contexts emphasise cultural context "! geocentric concepts before egocentric

concepts of position (Bali:Wassmann & Dasen; NT: Harris)

"! route descriptions with descriptive landmarks or directions (British & Iranian: Spencer & Darvizeh)

"! representations of space e.g. Australian Aboriginal maps (Harris, Klich); Yupno, PNG (Wassmann); Micronesian star maps and games (Penn Museum)

Explicit content links

!! Tinatatuna counting (Paraides)

!! Kâte cutting bamboo (Matang)

!! Many groups using groupings of different numbers to form a composite unit for counting e.g. hand for 5 until 20 (Lean, Owens)

!! Combining numbers in different ways to represent a number is common especially for systems with a 2 cycle (and higher cycles) (PNG) (Owens)

!! Body part tally systems like a number line for comparing, adding and subtracting numbers (PNG) (Owens; Kaleva)

!! Mathematics is a changing system in languages which are rapidly changing (PNG) (Muke)

Appropriate Pedagogy !! The outcomes and the journey are closely linked in

Indigenous pedagogy (Yunkaporta & McGinty)

!! Learner autonomy with a balance between self-direction and social support (Dubbo community; Yunkaporta & McGinty)

!! High Indigenous expectations (not school expectations) in terms of identity and engagement in local knowledge protocols – major recognitive social justice issue

!! Use of stories by teachers and students; modify models or examples given by teachers to meet local needs; recreate own visual versions of processes; share with community

!! Build on cultural activities like weaving (Cherinda; University of

Goroka student projects; Owens); bridge and house construction to develop mathematical concepts

!! Use artifacts e.g. bridges like mathematics trails that establish concepts that link to the real environment

The traditional Cane Bridge on

Yalo River at Mambuanda

Village – Kagua, Southern

Highlands Province

by Kita Yambi, Kewabi

language area

To start to build this kind of bridges, a group of man led by the village chiefs usually take an initiative… bush materials such as bush canes, vines, ropes, long sticks from young trees, branches and posts… left on the sides of the river…, they start by erecting four huge posts into the ground, two at each side of the river.

When that is done, they tie 3 to 4 cross bars to make immovable; long, strong tied a special way to each post equally distant at top and bottom; trees spread between for footpath and tightened with bush rope. Hand bars and ropes to also support footpath like a wave; ropes from top to footpath so it does not move.

Prepares a series of examples e.g. on

angles based around the syllabus

Example 1:

Kota Yarisi was at the top of the posts tightening the bars together during a cane bridge making. Sualo Nakisi was on the bridge, 10 meters away from the posts on the opposite side of the river. The distance from the bridge to the top of the bars is about 5 meters. Kota Yarisi looks down on Sualo Nakisi at an angle.

!! What is the angle of depression that Kota Yarisi looks down at Sualo?

Constructing Telefol Traditional Door

Board” (AMITUNG) Telefomin, Sandaun Province by Clement Oggi

The height and the width are measured using bush ropes. A bush rope is used to measure around the waist of the fattest man in the village … is used again to measure the doorway of the door board. The circle is drawn on the wood for easy carving. Then designs are carved

three different traditional colours to paint the designs that have been carved: maroon called ‘Baagaan’, white called ‘Buuguung’ and black colour from carbon called ‘Amsiring’.

To make the paint shiny and bright some grease pig [liquid pig fat] is mixed according to the correct proportion with the three traditional colours.

Links to Grade 8 syllabus: Ratio Anivatok and Naatum decided to paint their newly constructed door board designs. They both had the three traditional paints to paint their designs on the door board. Before painting the door board, Naatum suggested that they should mix the three traditional colours with some grease pig before they can paint their door board. This is because when the paints are mixed evenly with the grease pig, the colours on the door board will be shiny and bright. And so they both agreed and started to mix the paints with the grease pig.

!! The three colours are made bright and colourful by mixing each one of them with the grease pig in the ratio of 2:1 (two is to one). We are mixing all the three paints with the grease pig in the ratio given above to produce the correct brightness.

!! The ratio 2:1 is in its simplest terms because there is no whole number that will divide exactly into both sides.

!! If Naatum and Anivatok decided to increase the ratio of paints to grease pig up to 9:6.The ratio 9:6 is not in its simplest terms. What is it in its simplest term?

Conclusion

!! Social justice issues and Indigenous rights in schooling (O’Sullivan)

!! New perspectives on learning

!! Different mathematical relationships

!! Different views of mathematics in society

!! New ways of engaging students and teachers

!! Valuing and involving the expertise of Elders

!! Better ways of introducing western mathematics

!! Deeper understanding from alternative perspectives, alternate mathematics, place-based education, but globalised perspectives

!! Values education - valuing diversity