How do we learn math?

Learning math is like building a house where each concept builds on previous ones. The brain processes math through specialized areas for number processing, working memory, pattern recognition, and spatial processing, while students develop skills in basic operations, number systems, measurement, geometry, and algebraic thinking through various teaching approaches ranging from traditional memorization to conceptual understanding to problem-based learning. It’s complex.

Early Mathematical Concepts

Number Sense is the foundation of all math learning. Young children develop this by:

  • Understanding that numbers represent quantities (three means three objects)

  • Learning to count in order and understanding that each number is one more than the last

  • Recognizing that the same quantity can be represented different ways (five dots in a line or in a circle)

  • Comparing amounts and understanding concepts like "more," "less," and "equal"

Spatial Awareness helps children understand shapes, patterns, and relationships:

  • Recognizing and creating patterns (red, blue, red, blue)

  • Understanding shapes and their properties

  • Developing concepts of size, position, and direction

  • Learning to visualize and manipulate objects mentally

Mathematical Language involves learning specific vocabulary and symbols:

  • Words like "add," "subtract," "equal," and "difference"

  • Understanding symbols like +, -, =, and numbers themselves

  • Learning to express mathematical ideas clearly

How the Brain Processes Math

Number Processing Areas in the brain help us understand quantities and perform calculations. Some people are naturally stronger in these areas, while others need more practice and different approaches.

Working Memory holds information while we solve problems. When doing 23 + 45, you need to remember the numbers, the operation, and any carrying while working through the steps.

Pattern Recognition helps us see relationships and make mathematical connections. This skill helps with everything from recognizing number patterns to understanding algebraic formulas.

Spatial Processing supports geometry, graphing, and visual problem-solving. It helps us understand shapes, measurements, and how mathematical concepts relate to the physical world.

Stages of Mathematical Development

Concrete Stage (Early Elementary) Children need to see and touch mathematical concepts:

  • Using blocks, fingers, or objects to count and calculate

  • Physically manipulating materials to understand addition and subtraction

  • Drawing pictures to represent word problems

  • Building shapes with blocks or clay

Representational Stage (Elementary) Students begin using pictures and diagrams:

  • Drawing dots or tallies instead of using actual objects

  • Using number lines to visualize operations

  • Creating charts and graphs to organize information

  • Using visual models for fractions and decimals

Abstract Stage (Late Elementary and Beyond) Students work with numbers and symbols without concrete supports:

  • Solving problems using only numbers and mathematical symbols

  • Understanding algebraic concepts and variables

  • Working with complex formulas and equations

  • Thinking about mathematical concepts theoretically

Key Mathematical Concepts and Skills

Basic Operations

  • Addition and Subtraction: Understanding these as opposite operations and developing strategies for quick calculation

  • Multiplication and Division: Seeing these as repeated addition/subtraction and understanding their relationship

  • Fact Fluency: Memorizing basic math facts so mental energy can focus on problem-solving

Number Systems

  • Whole Numbers: Understanding place value and how our number system works

  • Fractions: Representing parts of a whole and understanding equivalent fractions

  • Decimals: Connecting to fractions and understanding decimal place value

  • Negative Numbers: Expanding understanding beyond counting numbers

Measurement and Geometry

  • Units and Measurement: Understanding standard units and estimation

  • Geometric Shapes: Properties of 2D and 3D shapes

  • Area and Volume: Calculating space and capacity

  • Coordinate Systems: Graphing and understanding spatial relationships

Algebraic Thinking

  • Patterns and Relationships: Seeing mathematical connections and rules

  • Variables and Expressions: Using letters to represent unknown quantities

  • Equations and Functions: Understanding mathematical relationships

  • Problem-Solving Strategies: Systematic approaches to complex problems

The Importance of Learning Math

Learning mathematics is ultimately about developing powerful ways of thinking and problem-solving that extend far beyond numbers and equations. When students understand that mathematics is about patterns, relationships, and logical thinking, they can appreciate its beauty and usefulness in understanding our world.