Bush Mathematics: Geometry in Native Plants

Learning Outcomes

After engaging with this content, students will be able to:

• Identify basic geometric shapes and patterns in native Australian plants
• Understand the connection between Indigenous knowledge and mathematical concepts
• Create drawings and recordings of natural geometric patterns
• Apply geometric principles through hands-on outdoor activities
• Develop appreciation for mathematics in nature

Indigenous Mathematical Knowledge

Indigenous Australians have long understood the mathematical principles present in the natural world. Their deep connection to Country has led to sophisticated understanding of patterns, sequences, and geometric shapes found in plants. This knowledge has been passed down through generations and continues to provide valuable insights into how we can learn from nature.

The Cultural Context

Indigenous mathematical knowledge is deeply embedded in cultural practices and understanding of the environment. When exploring these concepts with students, it’s important to:

• Acknowledge the traditional owners of the land
• Respect Indigenous perspectives and knowledge systems
• Understand that mathematics exists in many forms across different cultures

Geometric Patterns in Native Plants

Symmetry in Leaves

Many Australian native plants display remarkable symmetry in their leaves. The Eucalyptus leaf, for instance, can be folded perfectly in half along its central vein, demonstrating bilateral symmetry. This natural example helps students understand:

• Line symmetry
• Mirror images
• Equal parts

Spiral Patterns

Banksia cones and some native daisies follow the Fibonacci sequence, creating beautiful spiral patterns. These patterns demonstrate:

• Number sequences
• Natural spirals
• Mathematical ordering

Fractals in Ferns

Native ferns like the Rough Tree Fern display fractal patterns, where smaller parts mirror the shape of the whole. This demonstrates:

• Self-similarity
• Pattern repetition
• Scale relationships

Practical Activities

Activity 1: Bush Mathematics Walk

Materials Needed:

• Drawing paper (A4 or larger)
• Pencils and colored markers
• Magnifying glass (optional)
• Collection bags (paper or cloth)
• Camera (optional)

Instructions:

1. Preparation
   1. Scout a safe location with diverse native plants
   2. Check weather conditions
   3. Prepare safety briefing for participants
2. During the Walk
   1. Look for symmetrical leaves
   2. Find spiral patterns in flowers or seed pods
   3. Observe repeating patterns in ferns
   4. Document findings through drawings or photographs
3. Recording Observations
   1. Draw the shapes discovered
   2. Measure angles where possible
   3. Note the names of plants (both common and scientific)
   4. Record any Indigenous names if known (with proper cultural respect)

Activity 2: Create a Pattern Journal

Materials Needed:

• Blank notebook
• Coloured pencils
• Ruler
• Protractor
• Plant specimens (collected with permission)

Instructions:

1. Journal Setup
   1. Create sections for different types of patterns
   2. Label pages with date and location
   3. Include space for drawings and measurements
2. Pattern Documentation
   1. Press and attach plant specimens
   2. Draw geometric shapes found
   3. Note mathematical properties
   4. Write observations about pattern repetition

Common Challenges and Solutions

Challenge 1: Plant Identification

• Solution: Use plant identification apps or field guides
• Alternative: Partner with local Indigenous educators or botanists
• Tip: Focus on common, easily identifiable species initially

Challenge 2: Weather Constraints

• Solution: Plan indoor alternatives using collected specimens
• Alternative: Use high-quality photographs or digital resources
• Tip: Create a flexible schedule that can adapt to weather conditions

Safety Considerations

1. Plant Safety
   • Always check for toxic plants in the area
   • Wear gloves when handling unknown plants
   • Never taste or eat any plants
   • Supervise children closely
2. Environmental Awareness
   • Obtain necessary permissions for plant collection
   • Follow “Leave No Trace” principles
   • Respect protected species and areas
   • Take only photographs where appropriate

Additional Resources

Australian Educational Resources

• Australian Academy of Science’s Indigenous Knowledge
• CSIRO’s Indigenous Mathematics Education Program
• Connecting Indigenous Knowledges (IK) with mathematics curriculum

Local Connections

• Botanical gardens education programs
• NSW environmental education centres
• Australian plant societies

Bush mathematics offers a unique way to connect mathematical concepts with the natural world while honoring Indigenous knowledge. Through careful observation and engaging activities, students can discover how geometry exists all around us in the Australian landscape. This approach not only develops mathematical understanding but also fosters appreciation for Indigenous wisdom and our natural environment.

Educational Standards Alignment

This content aligns with the Australian Curriculum Mathematics Standards for Years 3-4, specifically:

• Geometry and spatial reasoning
• Pattern recognition and analysis
• Measurement and data collection
• Cultural perspectives in mathematics