Kaupapa: This unit explores how mathematical models can help us understand ecological systems, integrating Western scientific approaches with mātauranga Māori (Māori knowledge systems) about environmental relationships.
Cultural Considerations: When discussing Māori ecological knowledge, emphasize that this is living knowledge still practiced today, not just historical information. Always acknowledge the iwi or source of any traditional knowledge shared.
Safety: Some students may have strong emotional connections to conservation issues. Be mindful when discussing species decline or extinction.
Let's model the relationship between kiore (Polynesian rat) and kākāpō populations:
The basic Lotka-Volterra equations:
\[ \frac{dx}{dt} = \alpha x - \beta xy \]
\[ \frac{dy}{dt} = \delta xy - \gamma y \]
Where:
Use this Desmos simulation to adjust parameters and observe population changes.
Question: What happens when you increase the predation rate (β)? How does this reflect historical observations of kākāpō decline?
Traditional Māori knowledge speaks of whakapapa (genealogical connections) between all living things. The concept of mauri (life force) helps explain why populations naturally fluctuate.
Whakataukī (proverb): "Ka ngaro te kākāpō, ka ngaro te kākā, ka ngaro te kererū, ka ngaro te tangata." (When the kākāpō disappears, when the kākā disappears, when the kererū disappears, mankind will disappear.)
Research traditional Māori practices like rāhui (temporary prohibition) and kaitiakitanga (guardianship). How might these concepts be represented mathematically in population models?
Modify the Lotka-Volterra equations to include:
| Assessment Type | Description | Weighting |
|---|---|---|
| Model Development | Create and justify a mathematical model for a NZ ecological relationship | 30% |
| Cultural Analysis | Explain how mātauranga Māori informs understanding of the ecological system | 20% |
| Computational Task | Use software to analyze and visualize population data | 25% |
| Reflection | Compare Western and Māori approaches to ecological management | 25% |
Develop a three-species model incorporating:
Research how Māori lunar calendars (maramataka) relate to species activity cycles and incorporate these periodic patterns into your model.
| Learner Need | Adaptation |
|---|---|
| Visual learners | Provide graphic organizers for equation components, use color-coding |
| Struggling with math | Use simplified difference equations before differential equations |
| ESOL students | Provide bilingual glossary of key terms (English/Te Reo Māori) |
| Advanced students | Challenge them to model more complex systems with multiple variables |
This unit demonstrates how mathematical modeling can bridge Western science and mātauranga Māori to better understand and protect Aotearoa's unique ecosystems. By combining these knowledge systems, we develop more holistic approaches to conservation challenges.
He whakataukī (proverb) to conclude: "Mā te whakaaro nui e hanga te whare, mā te mātauranga e whakaū." (With wisdom the house is built, with knowledge it is strengthened.)