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Building confidence and fostering engagement in Aboriginal Community schools Peter Sullivan

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Abstract One of the key strategies when teaching mathematics to Indigenous students is to connect the mathematics they are intended to learn to their experience. This session will illustrate one approach to connecting learning to students experience, using two lesson sequences focusing on geometry. The lesson sequences were taught by Niek van Riel.

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The intention was to use students' familiarity with geometrical concepts to build confidence, success, connections between mathematics and schooling on one hand and students lives on the other.

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The importance of building on what students know and expect There is substantial consensus that, regardless of educational context, – the content should build on what students already know – the pedagogies should connect with what students expect

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Perspective 1: sensitivity to culture Stanton (1994) – both ways or common ground approaches – the curriculum should: be negotiated; build on aspects of traditional culture; incorporate technology; recognize the interfaces with language; and utilize contexts. See also Howard (1997), Cooper, Baturo, and Warren (2005), Garma Mathematics Curriculum (2007)

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Perspective 2: Good teaching is good teaching everywhere Frigo, et al. (2003), – a study of schools with high proportions of Indigenous students, listed among key elements of effective numeracy teaching as teaching skills in real life contexts, and building on what the students know.

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But what does this look like in the classroom?

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Sequence 1: Connecting 2D and 3D shapes The capacity to interpret diagrams, drawings and photos is important for some topics in secondary level mathematics such as finding the volume of objects, and practical problems. It also helps in – reading maps, – interpreting drawing of buildings, – communicating directions, – describing objects and – understanding directions

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What do the students know? from NAPLAN items administered individually in an interview: – 13/15 of the middle primary students could choose the correct piece to go into a jigsaw – Given a horizontal view drawing of an ice cream cone, 5/15 could choose a circle as the top view.

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From items that we created Given a small cube, – 5/28 could name it, – 4/28 could count edges, – 18/28 could give the number of faces, and – 17/28 could count corners.

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Shown a photo of a structure made from cubes, 4/28 could state how many cubes were needed to make it, 1/28 could say how many faces would be painted (one said all of them), 25/28 could make it, 23/28 could place a yellow cube to the left of the structure, 14/28 could put a red cube north of the structure

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Asked to draw the birds eye view of the building they were in, – 12/27 could do this. Asked to draw the water tank from above – 17/27 could do this

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In summary, nearly all of these items were answered correctly by some students, and most students were able to do some of the tasks No student was able to answer all of the items.

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The lesson sequence Revising and introducing key terms Drawing and making to instructions How many cubes Taking a birds eye view Different representations of the same 3D objects Formalising the learning

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The suggestions on the card sorting The idea is that students, in pairs, match up the different representations of the objects, and then describe what they have done.

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Suggestions (continued) If you have blocks the students could be asked to make the structures shown, and then to see if that helps. After they have done that, there is a need to review their answers. One possibility would be to put the cards onto the smartboard. Another might be to have a large version of the cards. Another might be to have a set with Velcro on the back.

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You could perhaps ask a student to make a structure using blocks, then everyone can try to draw the birds eye view, a side view and say the number of blocks used to make it.

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Two videos The student in both is not one of the better ones, as evidenced by the shots of the other table where they were doing better, and this students is being helped by another students In the second clip the student is clearly thinking, considering alternatives, coming to grips with the ideas Note the interesting counting method

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The teacher is patient, focuses on the student rather than is distracted by the others, asks open questions and does not over prompt but does scaffold

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What this looked like Niek helping with cubes Working with cubes with materials

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The teacher reflection Students were briefed on their task. they began without blocks. Based on the pictures, students were able to accurately count how many blocks were in the 5 diagrams that showed the shape from a general perspective. The shapes that were shown from a birds eye view and side on view saw students count only the blocks that were visible to them. This saw students lay out a lot of the photo cards next to the i have 8 blocks card.

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To keep the ball rolling I introduced blocks to the students. Some were able to build the construction as it was by looking at the general perspective photo, while most of them picked up any photo and built what they saw. … Some students asked why there wasnt a card that said i have 4 blocks or i have 6 blocks.

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Teacher reflection continued Next I put on the board larger versions of the clue cards and drew 3 empty boxes next to each clue, telling the students that each shape has 3 photo clues each. Some students started to rearrange their photos with little success. Next I placed the general perspective photos next to each clue on the whiteboard and suggested students make the shapes with their own cubes that are on the whiteboard, and to look at your construction from different perspectives.

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There were two questions on the revision sheet that sought responses to associated questions. 9/16 students could state the number of cubes required to create a given structure. 16/16 students indicated which of two possibilities represented the front view of the structure

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Sequence 2: shapes and nets

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4/15 of the middle primary students could choose the correct response (5/15 counted only the faces that could be seen) How many faces? aiswa workshop 2011

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5/13 could state which face is opposite a nominated face aiswa workshop 2011

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no upper primary student could write the answer correctly. aiswa workshop 2011

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3/13 could choose the total The total number of faces, edges and vertices of this shape is 26 What is the total number of faces, edges and vertices of a square pyramid 13161820 aiswa workshop 2011

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Sequence 2: shapes and nets Revising and introducing key terms Exploring the cube Taking apart some boxes to show what they look like flat Making a cube from a net Imagining with nets Making a rectangular prism from a net Making other shapes from nets Card sort A worksheet

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What this looked like Decorated cubes Sorting cards withF:\kimberleys\niek\flip camera\sequence 2\day 4 sequence 2\sorting cards with shapes to match.MP4 shapes.. Two students shape cards

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Some more Faces etc

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Teacher reflection Students slowly started catching on and I left them for about 20 minutes to slowly figure out each structure in their pairs. You could see students faces changing as they started to realise the perspective of each photo.

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Students finished their matching of cards and a 10 minute review was done on the whiteboard with larger versions of the cards. Most of the students had success in the end but there were a number of prompts needed to push them in the right direction to combat frustration and giving up. This activity took 70 minutes to complete and ample time was given between prompts to allow students the best opportunity to solve the problem. So I just find it thrilling when I see kids, especially girls, who are good at that, have a natural aptitude.

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Fundamentally it is about connecting students to their experience, and it is suspected having a teacher willing to connect to those experiences. As the second author reflected: – …its amazing when I go hunting with them and theyll go out in the bush and theyll spot a bird neck this far out of the grass five hundred metres away, … their visual field and perspective is so much greater than what Im used to and they bring that into the classroom …

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