The Art of Mathematics
A Brief History of the Ndebele
The Ndebele are descended from the Nguni settlers who, it is believed, arrived in Southern Africa around 200 AD. In the early 1600s, King Msi settled among the low hills around which present day Pretoria is built. After his death, his two sons Manala and Ndzundza fought over the chieftainship and the Ndebele split into two main factions. Manala and his followers went northwards, towards present day Pietersburg. Ndzundza and his followers, who today are known as the Southern Ndebele, went east and south and they have remained distinctly Ndebele and culturally independent of their neighbours.
In 1849 and 1863, the Ndebele successfully warded off attacks by the white Boer invaders and settlers. However, in 1883 they were defeated and the tribal structure of the Ndzundza Ndebele was broken up and all of their tribal lands confiscated and divided among the Boers.
From the early to mid-20th century, the Ndebele were in the wilderness, and as a result, maintained a strong tribal identity in the face of the government forces that sought to destroy them. Their mural art and beadwork and their strict adherence to culturally based rules of personal adornment maintained their cultural unity and reinforced their distinctive Ndebele identity. These expressive symbols were used as a type of communication between sub groups of the Ndebele people. They stood for their continuity and cultural resistance to their current circumstances. The Boer farmers did not understand the meaning and only viewed it as cultural art that was not harmful, so it was allowed to continue. Ndebele artwork is impressive because of the designs and colours used.
In the early days, clay, ash, plant pigments, and cow dung were used to create earthy colours. Today however, bright colours adorn the modern home. The married women are responsible for the decoration used in both the beadwork and mural art.
The photograph shows the painted wall of a home. Parallel lines create horizontal strips in which designs can be created. Each of the panels contains a design that reveals a high level of symmetry. Each design has both horizontal and vertical symmetry.
Ndebele Botshabelo by Girolame, some rights reserved
To begin a wall-painting, the artist divides the wall into sections and then chalks lines diagonally across each section.
Next, the artist paints the black outline of the design for each section. Painting is done freehand, without the use rulers or set-squares. Somehow symmetry, proportion and straight edges are exactly maintained.
Then, the black outline is filled in with colour, and white spaces offset painted areas.
You can see photographs of the painting process on the Evergreen State College (US) website.
The obvious stating point for examining Ndebele art is to ask the children to describe what they see. This activity and the language used can be matched to their age and stage of development. This is a really good opportunity to develop the use of mathematical language.
National Curriculum attainment targets addressed
NC AT3 – Pupils classify 3-D and 2-D shapes in various ways using mathematical properties such as reflective symmetry for 2-D shapes.
The Ndebele image is available as a downloadable activity sheet.
- What shapes can they see?
- What are the properties of these shapes?
- Can you find any shapes that are not polygons? How do you know?
- Are they regular/irregular shapes?
- Can you find any shapes with right angles?
- Can you find any shapes with angles smaller/greater than a right angle?
- Can they find any shapes that have reflective symmetry?
- Can they identify lines of symmetry?
- Can they find any examples where shapes have been translated or rotated?
- Can they see any patterns?
This activity could also be extended so that children devise their own design on squared paper satisfying NC AT3 – Pupils draw common 2-D shapes in different orientations on grids. They reflect simple shapes in a mirror line. They find perimeters of simple shapes and find areas by counting squares.
This could be made more or less difficult by opening out or closing down the criteria for the design. The more criteria, the more challenging the activity, eg:
- Devise a design that:
- has a repeating pattern
- includes an irregular pentagon
- has two lines of reflective symmetry (horizontal/vertical)
- has a shape that has been rotated
- has a shape that has been translated horizontally/vertically
- Can you find the area of the…?
This activity could also be carried out using Microsoft Paint or, for a real challenge, writing instructions for Logo:
Key Stage 1
Using the Ndebele method, children in KS1 children can describe and identify properties of 2D shape.
- Using a ruler draw eight lines across the square – each line must go from one side of the square to one of the other sides
- When you have finished you will have made a number of polygons (straight-sided shapes)
- Use a different colour for each shape
- How many triangles did you find?
- Can you describe them?
- How many rectangles?
- How many are squares?
- What other quadrilaterals did you find? Can you find their names?
- How many pentagons did you find? Are they regular or irregular?
- How many of the shapes have lines of symmetry?
This idea can also be developed using Paint for children in KS2.
The children could create a display of their work. They could develop their thinking and language by posing their own questions for their designs.
Upper Key Stage 2
Select one of the symmetrical designs and ask children to measure the area and perimeter of the irregular polygon/compound shape. An example of one such design is shown below. By providing dimensions, the students can use the formulas they are familiar with to measure the area of the whole shape.