| Figures | ||
| 1 | Ngkwarl (sugarbag) is gently coaxed out of the bloodwood tree with a probing stick. | 6 |
| 2 | Wild akatyerr fruit (Solanum centrale). | 8 |
| 3 | Bucketful of dried akatyerr. | 8 |
| 4 | Praxis in Indigenous mathematics education. | 10 |
| 5 | Utopia Alyawarr ranger (fifth from left, wearing a yellow shirt) sharing stories about caring for his country. | 14 |
| 6 | Constructing new measurement knowledge in an intercultural space (adapted from Northern Territory Department of Education, 2017b, pp. 15–21). | 16 |
| 7 | Example question to demonstrate disciplinary thinking of area of the region in green. | 31 |
| 8 | Quadrat survey design to solve problems involving areas of common shapes. Modelling a practical situation – akatyerr vegetation cover is surveyed along a 50-metre transect line to construct new mathematics knowledge. | 32 |
| 9 | Principles of Indigenous research. The three principles – voice, political integrity, and resistance – are bound by a framework of cultural respect. | 33 |
| 10 | The human dimension to mathematics learning. This image depicts the interactions between community members, the teacher, and students in a familiar social context, the yarning circle. | 41 |
| 11 | Jimmy Navie (right) from Wanta Aboriginal Corporation helps two students construct new mathematics knowledge about sustainable wild akatyerr harvest using the quadrat survey. | 42 |
| 12 | Knowledge concepts interrelated to akatyerr (adapted from Dobson et al., 2008), Merne Altyerre-ipenhe Reference Group et al., 2011, and Turner, 2005. | 49 |
| 13 | Proportional reasoning – solving the percentage of plant cover in the quadrat frame. | 53 |
| 14 | Akatyerr I noticed growing in disturbed roadside sandy red soils near where I lived. The yellow fruit are ripe, the green fruit are unripe. | 64 |
| 15 | Students prepare bush medicine plants for a Pop-up Shop as part of the Employment Pathways curriculum. | 69 |
| 16 | The teacher (me) eliciting a fair price from Year 8/9 students while displaying the first batch of bush medicine. | 70 |
| 17 | Sharmic (centre right) and Henry (centre left) consult the catalogue created for the Utopia Desert Art Pop-up Shop. | 71 |
| A Year 9 student is selling a bush medicine original artwork and completing the cash transaction while the customer (image cropped) stands alongside her. | 72 | |
| 19 | A Typhonium plant growing at the base of a river red gum tree (Eucalyptus camaldulensis) in an area downstream of the permanent water source. The broad leaves on this plant are unique for a desert ecosystem. | 73 |
| 20 | A student points to the direction the transect line will be laid. | 81 |
| 21 | A yarning circle conducted on the akatyerr growing site, showing the relational processes. Two elders, Jedda Purvis (blue beanie) and Judy Purvis (pink beanie), with the assistant teacher, Louisa Long (red shirt), and the teacher, Nicole Boyd (blue shirt), are interacting during the student-led inquiry. | 91 |
| 22 | Auto-coded themes generated from yarning circles at the akatyerr site. | 96 |
| 23 | The right way to conduct two-way dialogue on akatyerr. | 99 |
| 24 | Student interests in akatyerr knowledge concepts pooled by each student participant and classroom assistant teacher, Sharmic. | 104 |
| 25 | Student interests in akatyerr knowledge concepts related to people, country, and land management contextualised to the Australian Curriculum as question prompts for yarning circles. | 106 |
| 26 | Phases of the Goompi pedagogical cycle (reality, abstraction, mathematics, reflection) adapted for the akatyerr harvest context from Matthews (2006). | 111 |
| 27 | Dried akatyerr – a concrete referent packaged by students. The whole dried akatyerr pictured was harvested by students and staff. | 113 |
| 28 | Yarning circle at akatyerr harvest site: Students yarn with adults during the reality phase of the Goompi measurement pedagogical cycle. | 116 |
| 29 | Example creative act: walking the transect line to locate the quadrat point. | 116 |
| 30 | Example student artefact recording two attributes: length (Quadrat point column) and area (% Cover column). | 118 |
| 31 | Student representation of area of the 1 m2 quadrat covered in akatyerr vegetation (also mass and capacity) in photographed image of quadrat point 49 (visual representation). | 119 |
| 32 | Student representation of area of the 1 m2 quadrat covered in akatyerr vegetation at quadrat point 49: no vegetation drawn on the graph paper (visual representation) and graph labelled 0% (numeric representation). | 119 |
| 33 | Example student artefact recording two attributes: length (Quadrat point column) and area (% Cover column) relating to transect line number 3. | 120 |
| 34 | Student representation of area of the 1 m2 quadrat covered in Typhonium (or pretty flower) vegetation in photographed image of quadrat point 39. | 121 |
| 35 | Grid reference for estimating percentage cover (adapted from Deakin University, School of Life and Environmental Sciences, n.d.). | 122 |
| Example student artefact: Student 1’s drawing of the area of the 1 m2 quadrat covered in Typhonium vegetation at quadrat point 39. Student 1 worked in a pair with Student 2. | 122 | |
| 37 | Example student artefact: Student 2’s drawing of the area of the 1 m2 quadrat covered in Typhonium vegetation at quadrat point 39. | 124 |
| 38 | Example student artefact of a creative act: photographing the area of the 1 m2 quadrat covered in grass vegetation at quadrat point 37. | 125 |
| 39 | Semi-permanent soak (freshwater discharge) at the akatyerr site: a place to reflect the reality. | 126 |
| 40 | The RATIO pedagogical model phases: Reflect, Act, Trial, Interact, Opportunity. | 149 |
| 41 | Example question to demonstrate disciplinary thinking of area of an array (and procedure). | 150 |
| 42 | Example trial of the Goompi pedagogical cycle – reality, abstraction, mathematics, and reflection (explicitly adapted for the akatyerr quadrat survey; Goompi pedagogical cycle adapted from Matthews, 2006). | 154 |
| 43 | Creating opportunities for students to conduct a quadrat survey. Assistant teacher Sharmic is pictured standing, and I am pictured crouching with the quadrat survey instrument held up to demonstrate to students. | 156 |
| 44 | Map illustrating the location of Alyawarr, Eastern Anmatyerr, and neighbouring languages. | 172 |
| 45 | Aligning the quadrat frame at a quadrat point demonstrated by Student 3 (left). Placing the quadrat frame along transect line demonstrated by Student 4 (right). | 177 |
| 46 | Culturally inclusive Year 8 work sample – solving problems relating to the volume of prisms. | 181 |
| 47 | Aerial image of akatyerr harvest site with parallel transect lines (red lines). | 182 |
| 48 | A section of the aerial image of akatyerr harvest site transformed and represented to solve area of rhombus (by applying trigonometry formula as Area = S2 sin A or Area = S2 sin B). | 183 |
| 49 | Geometric reasoning (congruent angles) and solving area of a rhombus (Area = S2 sin B). That is, if S (side length) is 50 and angle <ABD is 100° then Area = S2 × sin(100). | 183 |
| Tables | ||
| 1 | Indigenous culture content in NTILC curriculum for first languages maintenance. | 17 |
| Curriculum adjustments for contextualising measurement learning to sustainable wild akatyerr harvest: Integrating Indigenous languages and cultures, science cross-curriculum priorities, and mathematics for Years 8–9 students. | 75 | |
| 3 | Summary of each trial of the Goompi pedagogical cycle adapted for contextualising measurement attributes to akatyerr harvest. | 127 |
| 4 | Rich description of the participants in each participant group. | 137 |
| 5 | Summary of the influences filtering through my narrative of my lived experience. | 142 |
In: Decolonising Mathematics Education
Author:
Nicole Boyd
Nicole Boyd
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