GEOMETRIC SHAPES AND PATTERNS IN THREE REGIONS

Steven Hariec, Caspar Kona, Agasten Tabi.

Introduction

This lesson is about geometric shapes and patterns. Shapes and patterns can be found all over Papua New Guinea and other Pacific Countries. Here, we will investigate some of the patterns and shapes using traditional mathematics, i.e. what materials we can find traditionally that have patterns which are similar or the same as the ones in the Secondary School Mathematics texts.

The objective of this lesson is to make students aware that:

1. They can extract geometric shapes and patterns from traditional and cultural items or materials.

2. Patterns exist around them, and future applications such as in carpentry and architecture are important.

3. They can make materials using patterns and shapes.

Therefore, this lesson will contrast and compare traditional patterns and shapes present in traditional materials with the patterns and shapes in SSM texts (7A & 8A). The content of the lesson will be patterns and shapes from the three different cultural backgrounds, that is, KARKAR ISLAND, BOGIA and PENTECOST (VANUATU).

DESCRIPTION OF THE TRADITIONAL MATHEMATICS

1.) COMMON PATTERNS FROM KARKAR

There are many patterns in our traditional societies. Different societies have their own styles of making patterns. Most of the patterns can be found on the handicrafts. Nevertheless, the patterns are made from whatever available resources exist in that society. For instance, there are numerous patterns on walls made from bamboo. This can only be found in the coastal areas due to the availability of bamboo.

Below are some traditional items which contain patterns (= ‘Damag’).

1. Gadab – Mat made from coconut leaves.
2. Bidar – Walls made from bamboo.
3. Dob – Pig trap made from bush strings.
4. Paspas – Armbands made from strings.
5. Kotouk – String bag.
6. Suduk – Windows made from bamboo.

2) DESCRIPTION OF TRADITIONAL MATHEMATICS ON PENTECOST ISLAND (VANUATU).

Pentecost Island possesses some interesting items where traditional mathematics can be found. Shapes and patterns are among the most distinctive and predominant types existing in any artifacts or materials that people make.

Different shapes and patterns can be found in:
1. Baskets
2. Walls of buildings
3. Mats
4. Traditional/custom stories
5. Head bands
6. Arms bands
7. Pig strings

3) DESCRIPTION OF TRADITIONAL MATHEMATICS OF BOGIA.

BOGIA, just like the other two societies, has some foundations of mathematics present. The obvious one of course is, shapes and patterns. Congruent shapes can be found on carvings, on walls, mats, baskets and many other items. Patterns are formed from these shapes through weaving in such a way as to form a particular pattern. For instance, weaving one up and one down using pandanus leaves makes a set of small congruent rectangles forming a grid. These different patterns that exist on cultural items have different names depending on the ups and downs of the weaving pattern of the pandanus leaves or bamboo strips. Although the society is changing rapidly towards modernization, these traditional ways of making patterns are still predominant and active amongst the people of BOGIA.

The table below shows names of some common patterns of the three areas. The names are also in the different languages.

ENGLISH KARKAR BOGIA PENTECOST MATERIALS

2 up-1 down Forfor paipai Ivuntu Hala-wib walls, mats, floor, window

1 up – 1 down Idu Isida Ivi Waa dindi mats

Star shape Patue Agar Hala-wamso walls

Three strings Lasau Brovo Hala-iilin pig string

Serial figure 8 Gum-ngan nda Halan-wakatii bilum

Cross-shaped
paddles utic Nimpu Halan-boga custom stories

LESSON PLAN

SUBJECT: Mathematics

TOPIC: SHAPES AND PATTERNS

GRADE: 7 & 8

REFERENCE: SSM 7A, CHAPTER 2, pp. 16….SHAPES
SSM 8A, CHAPTER 1, pp. 1……. INVESTIGATIONS IN GEOMETRY

MATERIALS: Baskets, bilums, leaves, paper,… etc

OBJECTIVES: By the end of the lesson the students should be able to:
1. Identify patterns and shapes present in the cultural items.
2. Make a tessellating pattern from the items.
3. Differentiate between congruent and similar shapes.

INTRODUCTION:
1. Hold a basket and ask this question:
What can you see on the basket?

2. Identify two baskets from KARKAR and PENTECOST, and briefly describe the traditional mathematics found in these societies, i.e., the names of different patterns in KARKAR, BOGIA and PENTECOST language. Also outline what and where in traditional culture these patterns and shapes can be found.

3. Ask the students where they can find shapes and patterns in their own society.

4. Explain the relationship to modern mathematics and state the reference in high schools texts, i.e., SSM 7A pp. 16 and SSM 8A pp.1.

BODY:
1. Identify 1 up and 1 down, 2 up and 1 down, 2 up and 2 down on the basket and sketch on the blackboard how it is woven.

2. Show how 1 up and 1 down can be arranged or woven differently on a drawn grid. State that it’s like arranging congruent squares/rectangles.

3. Give an EXERCISE:
(a) In how many ways can 2 up and 1 down, 2 up and 2 down by drawn?
(b) Draw a triangle and ask what shape is it and where on the basket they can find it. Ask the students to write the pattern down in terms of ups and downs.

CONCLUSION
1. Draw two grids and ask a student to come up and shade in 1 up and 1 down in the first grid and 2 up ad 2 down in the second grid.

2. Explain where these patterns can be found, i.e., on walls, floor, mat, basket, bilums, etc..

3. Relate the lesson to modern math’s and its applications like in buildings, tiles, carpets and other designs.

CONCLUSION
Our lesson is based on the topic: SHAPES AND PATTERNS. We explain it in terms of how the basket is woven to show the shapes and patterns present on it. The main aim of our lesson is to make students aware that shapes and patterns exist everywhere around them and even in their lifestyle. The lesson that is presented should easily achieve its goals, because examples of shapes and patterns can be easily seen around them; many traditional artifacts have patterns in them too and are easy to construct. Therefore, our lesson should achieve its goals since “MATH’S IS ALREADY IN THE SYSTEM”.

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