Patterning and algebra are deeply connected, with patterning serving as a foundational stepping stone to understanding algebraic concepts. Visual patterns, in particular, are powerful tools for introducing and developing algebraic thinking.
The Connection Explained
Algebra often involves generalizing relationships and expressing them using symbols and equations. Patterning helps build this skill by:
- Identifying Regularities: Students learn to spot repeating sequences or growth patterns in numbers, shapes, or objects.
- Extending Patterns: Predicting what comes next in a pattern encourages deductive reasoning.
- Generalizing Patterns: Expressing the pattern's rule in words or symbols is a core algebraic skill. This is where the pattern translates into a function or equation.
According to research, visual patterns are a way to introduce and extend students' understanding of algebra and functions. Using visual patterns allows educators to use the same structures as algebraic counterparts, enabling students to better grasp algebra.
Examples of Patterning Leading to Algebra
Consider the following examples:
Example 1: Linear Pattern
Imagine a pattern of squares where each step adds 3 squares.
- Step 1: 1 square
- Step 2: 4 squares
- Step 3: 7 squares
- Step 4: 10 squares
This pattern can be described algebraically as y = 3x - 2, where x is the step number and y is the number of squares. Recognizing this linear increase allows for the creation of a linear equation.
Example 2: Quadratic Pattern
Consider a pattern with dots forming squares of increasing size.
- Step 1: 1 dot (1x1 square)
- Step 2: 4 dots (2x2 square)
- Step 3: 9 dots (3x3 square)
- Step 4: 16 dots (4x4 square)
This pattern can be expressed as y = x2, where x is the step number and y is the total number of dots. Observing this quadratic increase allows for the creation of a quadratic equation.
Why is this Important?
Understanding this connection is important because:
- It makes algebra more accessible and less abstract.
- It helps develop problem-solving skills.
- It provides a visual and intuitive understanding of functions.
By starting with patterning, especially visual patterns, students can gradually transition to understanding abstract algebraic concepts more effectively.
