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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.

Age Range

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

  1. Weather Station: Track daily weather for a week
  2. Pattern Book: Create a book of patterns you find
  3. Counting Collection: Collect 100 of something
  4. 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