Stage 0: Early Foundations (Pre-K → Grade 2)
Overview
This stage builds the fundamental cognitive skills that underpin all future learning. Focus on developing number sense, pattern recognition, and observational skills through play and exploration.
Info: Typically ages 4-8, but suitable for anyone beginning their mathematical journey.
Learning Objectives
By completing this stage, you will:
- Understand numbers and counting up to 100
- Recognize patterns and relationships
- Make careful observations about the world
- Follow sequential instructions
- Begin computational thinking
Mathematics Foundations
Number Sense & Counting
What you'll learn:
- Counting from 0 to 100
- Number recognition and writing
- One-to-one correspondence
- Greater than/less than concepts
Why it matters for research:
- Foundation for all quantitative analysis
- Understanding of magnitude and scale
- Basis for data collection and measurement
Recommended Resources:
- Khan Academy Early Math
- PBS Kids Math Games
- Physical manipulatives (blocks, counting bears)
Self-check: Can you count to 100? Can you identify which of two numbers is larger?
Basic Operations
What you'll learn:
- Addition and subtraction within 20
- Understanding of "combining" and "taking away"
- Using fingers, objects, or drawings to solve problems
Why it matters for research:
- Foundation for all mathematical operations
- Understanding change and comparison
- Basis for experimental measurements
Recommended Resources:
- IXL Math Practice (free samples)
- Math Playground
- Everyday counting activities (cooking, shopping)
Self-check: Can you solve 7 + 5? Can you solve 15 - 8?
Shapes & Patterns
What you'll learn:
- Basic 2D shapes (circle, square, triangle, rectangle)
- Pattern recognition (AB, ABC patterns)
- Sorting and classifying objects
Why it matters for research:
- Pattern recognition crucial for data analysis
- Classification skills for organizing information
- Spatial reasoning for visualization
Recommended Resources:
- Pattern Blocks Activities
- Tangram puzzles
- Nature pattern walks
Self-check: Can you continue the pattern: red, blue, red, blue, ___?
Introduction to Fractions
What you'll learn:
- Understanding halves and quarters
- Equal sharing concepts
- Parts of a whole
Why it matters for research:
- Foundation for ratios and proportions
- Understanding partial quantities
- Basis for probability concepts
Recommended Resources:
- Fraction Circles
- Pizza and pie sharing activities
- Paper folding exercises
Self-check: Can you show what half of a pizza looks like?
Language & Communication
Reading Foundations
What you'll learn:
- Alphabet recognition and phonics
- Sight words and simple sentences
- Reading comprehension basics
Why it matters for research:
- Reading scientific literature
- Understanding instructions and procedures
- Communicating findings
Recommended Resources:
- Starfall Learn to Read
- Reading Eggs (free trial)
- Library story time programs
Writing Basics
What you'll learn:
- Letter formation
- Simple sentences
- Basic storytelling
Why it matters for research:
- Documentation skills
- Clear communication
- Organizing thoughts
Recommended Resources:
- Handwriting Practice Sheets
- Story journals
- Drawing and labeling activities
Science Foundations
Observation Skills
What you'll learn:
- Using five senses to explore
- Describing properties (color, texture, size)
- Recording observations with drawings
Why it matters for research:
- Foundation of scientific method
- Data collection skills
- Attention to detail
Recommended Resources:
- Nature journals
- Mystery Science (free lessons)
- Weather observation charts
Self-check: Can you describe 5 things about a leaf using your senses?
Living Things
What you'll learn:
- Plants and animals
- Life cycles (butterfly, frog)
- Basic needs of living things
Why it matters for research:
- Understanding biological systems
- Observation of change over time
- Introduction to experimental subjects
Recommended Resources:
- National Geographic Kids
- Growing seeds experiment
- Pet or classroom animal observations
Simple Experiments
What you'll learn:
- Sink or float predictions
- Magnet exploration
- Mixing colors
Why it matters for research:
- Introduction to hypothesis testing
- Cause and effect relationships
- Recording results
Recommended Resources:
- Science Buddies K-2
- Kitchen science experiments
- Steve Spangler Science
Computer Science & Logic
Sequential Thinking
What you'll learn:
- First/then/last ordering
- Following multi-step instructions
- Creating simple algorithms (like recipes)
Why it matters for research:
- Algorithm development
- Experimental procedures
- Logical thinking
Recommended Resources:
- Cooking and baking activities
- LEGO building instructions
- Daily routine charts
Introduction to Coding
What you'll learn:
- Directional commands (forward, back, turn)
- Simple loops (repeat actions)
- Basic debugging (finding mistakes)
Why it matters for research:
- Computational thinking
- Problem-solving strategies
- Automation concepts
Recommended Resources:
- ScratchJr (free app)
- Code.org Pre-reader Courses
- Unplugged coding activities (human robots)
Self-check: Can you give instructions to make a peanut butter sandwich?
Logic Games & Puzzles
What you'll learn:
- Pattern completion
- Simple mazes
- Matching and sorting games
Why it matters for research:
- Problem-solving skills
- Logical reasoning
- Persistence and debugging
Recommended Resources:
- Jigsaw puzzles
- PBS Kids Games
- Board games (Sequence for Kids, Rush Hour Jr.)
Practical Applications
Real-World Connections
At this stage, learning happens everywhere:
- Grocery Store: Counting items, comparing prices, sorting produce
- Kitchen: Measuring ingredients, following recipes, observing changes
- Nature: Collecting and sorting leaves, observing weather, tracking growth
- Games: Board games for counting, card games for patterns, building blocks for spatial reasoning
Mini-Projects
Try these projects to apply your learning:
- Weather Station: Track daily weather for a week
- Pattern Book: Create a book of patterns you find
- Counting Collection: Collect 100 of something
- Plant Diary: Grow a seed and document changes
Assessment & Progress
Ready for Stage 1?
You're ready to move on when you can:
- ✓ Count to 100 confidently
- ✓ Add and subtract within 20
- ✓ Recognize and continue patterns
- ✓ Read simple sentences
- ✓ Make and record observations
- ✓ Follow multi-step instructions
- ✓ Create simple sequences in ScratchJr
If You're Struggling
Remember:
- Everyone learns at their own pace
- Use multiple senses (see, touch, hear)
- Practice with real objects before abstracts
- Make it fun with games and stories
- Celebrate small wins
Parent/Educator Notes
Supporting Early Learners
- Keep sessions short (10-20 minutes)
- Use hands-on materials
- Connect to daily life
- Encourage questions
- Praise effort over results
Common Challenges
- Number reversals: Normal at this age, practice with sandpaper numbers
- Attention span: Break into smaller chunks, use movement
- Abstract concepts: Always start with concrete objects
Next Steps
Congratulations on building your early foundations!
Ready to continue? Move on to Stage 1: Primary Foundations where you'll build on these skills with multiplication, more complex science, and beginning programming.
Not quite ready? That's okay! Review any sections you need, and remember - strong foundations take time to build.
"Play is the highest form of research." - Albert Einstein