Probability & Mātauranga Māori
Patterns, Chance & Decision-Making Through Dual Knowledge Systems
Understanding probability through both modern mathematical concepts and traditional Māori approaches to pattern recognition, prediction, and collective decision-making.
Two Ways of Understanding Chance & Patterns
Mathematics uses numbers to understand probability and predict outcomes. Mātauranga Māori uses careful observation of natural patterns, environmental signs, and collective wisdom to understand likelihood and make decisions. Both approaches help us navigate uncertainty and make better choices about the future.
"He mata whaiaro"
An inquiring mind sees patterns in all things
Ngā Tahua Rangahau - Two Approaches to Probability
Mātauranga Māori - Pattern Recognition
- Environmental Signs: Reading natural indicators to predict weather, seasons, and resource availability
- Cyclical Patterns: Understanding long-term cycles in nature, stars, and tides
- Collective Wisdom: Using group knowledge and experience to assess likelihood
- Holistic Assessment: Considering multiple factors and their relationships
Mathematical Probability
- Numerical Calculation: Using formulas to calculate exact probabilities
- Data Analysis: Using past data to predict future outcomes
- Statistical Models: Creating mathematical models of uncertainty
- Precise Measurement: Quantifying exact chances and risk levels
Integration Strength
Traditional pattern recognition provides context and meaning; mathematical probability provides precision. Together, they create powerful decision-making tools.
Matakite - Traditional Prediction & Pattern Recognition
Reading Environmental Probability
Traditional Māori knowledge includes sophisticated methods for predicting outcomes based on environmental patterns. These aren't superstitions - they're based on centuries of careful observation.
Weather Prediction Examples
- Cloud Formations: Specific cloud patterns indicating high probability of rain
- Wind Patterns: Direction and intensity predicting weather changes
- Animal Behaviour: Bird flight patterns indicating storm likelihood
- Ocean Signs: Wave patterns and water colour predicting weather
Resource Availability Prediction
- Seasonal Timing: When plants and animals are most likely to be available
- Environmental Health: Indicators suggesting high probability of good harvests
- Migration Patterns: Predicting when fish and birds will be present
- Ecosystem Relationships: How one species' behaviour predicts others
Mathematical Probability Concepts
The Probability Scale & Formula
Probability Scale
Impossible
0
Unlikely
Even Chance
0.5 or 1/2
Likely
Certain
1
Probability Formula
P(event) = Number of favourable outcomes ÷ Total number of possible outcomes
Example: Probability of rolling a 4 on a six-sided die = 1 ÷ 6 = 1/6 ≈ 0.167
Whakatōpū - Integrated Practice Activities
Activity 1: Environmental Pattern Probability
Scenario: You are planning a outdoor school camp. Use both traditional knowledge and mathematical probability to assess weather likelihood.
Traditional Indicators
Observe and describe:
- □ Cloud formations and movements
- □ Wind direction and strength
- □ Bird behaviour patterns
- □ Ocean/water conditions
Prediction: Based on these signs, how likely is good weather?
Mathematical Analysis
Weather data shows:
- In the last 20 days: 14 fine days, 6 rainy days
- Calculate: P(fine weather) = ___ ÷ ___ = ___
- Express as percentage: ___ %
- Mark on probability scale above
Question: Do both methods give similar predictions?
Activity 2: Sustainable Resource Decisions
Scenario: A community needs to decide how much fish to harvest sustainably. Use both knowledge systems to make the decision.
Traditional Knowledge Assessment
Consider these traditional indicators:
- Fish size and health appearing smaller than usual
- Fish behaviour seems more cautious
- Seabirds are fishing closer to shore (less fish offshore)
- Traditional harvest season timing
Assessment: What do these signs suggest about fish population health? Should harvest be: High / Moderate / Low / Rāhui (no harvest)?
Mathematical Probability Analysis
Scientific data shows:
- Fish population estimated at 10,000 individuals
- For sustainable fishing, harvest should not exceed 20% annually
- Calculate maximum sustainable harvest: 10,000 × 0.20 = _____ fish
- If harvest exceeds this, probability of population decline = 80%
Integration Decision
Combine both assessments: What harvest level protects the fish population for future generations while meeting current community needs?
Activity 3: Traditional Games & Probability
Kī-o-rahi Ball Game
In this traditional Māori game, players try to hit 7 different pou (posts).
- Calculate: P(hitting any specific pou) = ___ ÷ ___ = ___
- If a player is more skilled at hitting pou 1-3, how does this change the probability?
- What strategy would give the best chance of success?
Group Decision Making
In traditional hui (meetings), decisions are made by consensus.
- If 12 people need to agree, and 9 currently support a proposal, what's the probability all 12 will agree?
- How might kōrero (discussion) change these probabilities?
- Why might consensus be better than simple majority voting?
Ā Muri, Ā Mua - Contemporary Applications
Climate Science
Traditional environmental indicators now help scientists improve climate change predictions and assess probability of extreme weather events.
Risk Assessment
Insurance companies use both statistical data and traditional knowledge to assess environmental risks for communities and businesses.
Public Health
Health authorities combine statistical models with traditional community knowledge to predict and prevent disease outbreaks.
Technology Design
App developers use both user data and cultural understanding to predict what features people will find useful.
Whakaaro - Knowledge Integration Reflection
Understanding probability through both mathematical formulas and traditional pattern recognition gives us more powerful tools for making decisions and predicting outcomes. Mathematics provides precision, while mātauranga Māori provides context and meaning. Together, they help us navigate uncertainty with both accuracy and wisdom.
"He mata whaiaro" - An inquiring mind sees patterns in all things, whether through numbers or through nature.
Curriculum alignment
- Statistics — Knowledge: - The response to a statistical question includes findings that are summarised and interpreted in context and using evidence. - The tapering sides of a data visualisation are …
- Statistics — Practices: - Planning and collecting data in order to respond to a statistical question (e.g. Are our feet the same length?) - Calculating the mean, median, and mode for numerical data -…
- Ecosystems — Practices: Explaining how humans benefit from other organisms and natural resources and evaluating the importance of biodiversity in daily life (e.g. using plants for food, water from ri…
- Statistics — Knowledge: - Categorical data can be visualised through dot plots and bar graphs. - Paired categorical variables can be visualised through a stacked bar graph or a clustered bar graph. -…
- Statistics — Knowledge: - A variable is an attribute or measurement of the people or objects being studied.A categorical variable classifies objects or individuals into groups.Discrete numerical vari…
📋 Teacher Planning Snapshot
Ngā Whāinga Ako — Learning Intentions
Students will engage with this resource to develop statistical investigation skills — planning inquiries, collecting and analysing data, interpreting distributions, and communicating findings. Tūhuratanga (investigation) is framed as a tool for understanding our communities and environment in Aotearoa New Zealand.
Ngā Paearu Angitū — Success Criteria
- ✅ Students can identify an investigative question, collect relevant data, and display it clearly.
- ✅ Students can interpret statistical findings and discuss what they might mean for a real-world community or environmental context.
Differentiation & Inclusion
Scaffold support: Provide structured investigation frameworks (PPDAC cycle templates) for entry-level access. Offer partially completed data tables for students who need additional support. Extend capable learners by asking them to critique a statistical claim from a news article, or to design their own community data investigation.
ELL / ESOL: Pre-teach statistical vocabulary (median, mode, range, distribution, sample, population). Pair visual representations (graphs, tables) with plain-language explanations. Allow students to discuss statistical ideas orally before writing. Encourage use of home language for initial sensemaking.
Inclusion: Statistical investigation offers natural differentiation — all students can engage with the same real-world question at different levels of mathematical complexity. Neurodiverse learners benefit from structured, step-by-step investigation processes. Use collaborative group investigation formats that distribute roles (data collector, recorder, analyst, presenter).
Mātauranga Māori lens: Tūhuratanga — the practice of careful investigation — resonates deeply with mātauranga Māori. The maramataka is a sophisticated data system: tracking environmental patterns, seasonal cycles, and ecological indicators over generations. Iwi environmental monitoring — counting kaimoana populations, tracking water quality, observing bird migrations — is applied statistical thinking. Framing statistics within community and environmental inquiry connects data to mana whenua responsibilities.
Prior knowledge: Students should have basic familiarity with data displays (bar graphs, dot plots). No prior statistical investigation experience required — the PPDAC inquiry cycle provides accessible scaffolding for first-time investigators.
Curriculum alignment
- Statistics — Statistical Investigation: Plan and conduct investigations using the statistical enquiry cycle — determining appropriate variables and data collection methods; gathering, sorting, and displaying multivariate category, measurement, and time-series data to detect patterns, variations, relationships, and trends; comparing distributions visually; communicating findings, using appropriate display.
- Statistics — Probability: Investigate situations that involve elements of chance by comparing experimental distributions with expectations from models of the possible outcomes, acknowledging uncertainty.