Siapo designExploring the Pasifika

Principles in Transformation Geometry

An evolving purpose

• As an HOD– raise Pasifika achievement – target Merit and Excellence

• Facilitation 1– Geometry and Measurement / ICT / Thinking

• Facilitation 2– Using geometry context to explore the new curriculum links

between front and back / KC’s / Effective Pedagogy

• Facililation 3– Pasifika Goals and Principles

Pasifika Education Plan Goals

• Goal 4 - Accelerate Pasifika students’ qualifications achievement.a) Increase the number of students achieving National Certificate of Educational Achievement Level 1 or higher by

2012 (from 67.8% in 2006 to 80% in 2012).

• Goal 5 - Continue increasing the effectiveness of teaching and learning for Pasifika students.iii) Increase teacher effectiveness across all curriculum areas.

SIAPO

• Siapo are the name given to the tapa cloth of Samoa.

• They are made from the bark of the mulberry tree.

• They employ many elements of transformation geometry in their designs.

Start with a paper mulberry tree branch

Cut along the length of the branch

Strip the bark from the branch

Remove the outer bark

Stretch the strip of inner bark

Scrape the bark with a clam shell

Remove the water

Flatten the bark with an i’e.

Leave to dry

Bind together spare bark

The upeti board with pattern to be transferred

Stretch the bark over the board

Use arrow root to reveal the pattern

Using ele (terracotta clay) to bring out design

Swab with bound together bark to further bring out the design

Patch the siapo

Repeat with additional layers

Paint the final design using a paogo (dried pandanus) brush

The finished siapo…

Siapo designs…

This design symbolises the nets used in catching pigeons and turtles.

Fa’a ’au’upega / Net

CHALLENGE 1• Work in pairs• Put up a screen between the two of you• Select four squares from the middle of

the table• Make a design with them on your side

of the screen• Describe your pattern so your partner

can try and create it on their side

Describe it…• Key words for describing your design…

– Asymmetrical a.k.a. – Linear pattern a.k.a.– Rotational symmetry a.k.a.

• Maths vs. Non maths vocabulary• Maths specific - Congruent• Different maths / non-maths - Similar

A bit unbalanced?

Very straight-laced?A bit twisted?

Identifying transformations

• “flip”

• “turn” “twist”

• “shift” “move”

• “larger” “smaller”

Reflection / Reflect

Rotation / Rotate

Translation / Translate

Enlargement / Enlarge

Describing transformations

• Reflection – Mirror line

• Rotation– Centre of rotation– Angle of rotation

(always anticlockwise)

• Translation– Left / right Up / Down– Vector of translation

• Enlargement– Centre of enlargement– Scale Factor

XX

A

B

Aiming for merit / excellence

DESCRIPTION• Shape A has been reflected

in line AB to give shape A’.• Shape A has been rotated

90 degrees about Point X to give shape A’.

• Shape A has been translated three to the right and one down to give Shape A’.

• Shape A has been enlarged by scale factor 2 about point X to give shape A’.

INSTRUCTIONS• Reflect shape A in the line

AB. Label this shape A’.• Rotate shape A 90 degrees

about point X. Label this shape A’.

• Translate shape A three to the right and one down, Label this shape A’.

• Enlarge shape A by scale factor 2 about point X. Label this shape A’.

Upping the thinking levels

• Tapa Transformations meets

Bloom’s Taxonomy

Principle Link to task Adaptations

Know the learner

Use the home language(s), knowledge, and experiences of Pasifika students as valuable learning resources in the classroom.

Ensure students’ prior knowledge and experiences are activated and used to build a bridge between what they already know and new knowledge.

Provide a range of culturally relevant texts, topics, contexts and perspectives.

Pasifika PrinciplesPrinciple Link to task Adaptations

Know the learner Diagnostic TaskNoticing Understanding Teaching

Use the home language(s), knowledge, and experiences of Pasifika students as valuable learning resources in the classroom.

Siapo patterns explanation

Comparing and contrasting with tapa from other Pacific nations.

Ensure students’ prior knowledge and experiences are activated and used to build a bridge between what they already know and new knowledge.

Teaching model: Materials Imaging Generalising

Language

Mapping current / first description to mathematics description.

Provide a range of culturally relevant texts, topics, contexts and perspectives.

Context and perspective

Further student input / perspective / voice to direct learning.

Principle Link to task Adaptations

Provide deliberate and explicit, transparent instruction about language as well as learning content.

Provide high challenge with appropriate level of support.

Provide multiple learning opportunities with a focus on learners using academic language.

Make productive links with family and community.

Pasifika PrinciplesPrinciple Link to task Adaptations

Provide deliberate and explicit, transparent instruction about language as well as learning content.

Vocab 1 - 3

Descriptions vs Instructions

Further incorporation of literacy strategies.

Provide high challenge with appropriate level of support.

Thinking skills progression to Merit and Exc

Transfer concepts and language into other design contexts.

Provide multiple learning opportunities with a focus on learners using academic language.

Teaching Model Use of manipulatives Written and oral language ICT

20+ uses of siapo cards.

Make productive links with family and community.

Sharing of designs

Knowledge swap – maths language / art design.

Kiwi icons

Further exploration…

• NCEA Analysis sheet– Standard– Requirements– Statistics– Reasons for not getting– Key teaching ideas

Making links…• Conceptual knowledge is assumed to

be constructed by assimilation of new relationships and is stored as a linked network of concepts.

• Procedural knowledge is gained by practice involving performing a routine in response to a certain stimulus (Galbraith & Haines, 2000).

Making links…• To develop conceptual knowledge teachers

provide opportunities for students to assimilate new relationships which are stored as a linked network of concepts.

• To develop procedural knowledge teachers explain the routine to be performed and the students practice performing this routine in response to a certain stimulus (Galbraith & Haines, 2000).

Further differentiation

ACCELERATION

DEPTHDEPTH

CHALLENGE

CREATIVITY

COMPLEXITY