# Algebraic Thinking

Algebra in the pre-k years involves primarily learning about patterns and relationships. What should you be teaching in pre-k programs? Patterns are at the cornerstone of algebraic thinking.

Children begin to sort, classify, and order objects into a variety of categories long before they enter a formal school setting. They also recognize, describe, and extend patterns and begin to analyze both how repeating and growing patterns are generated. (p. 128)

Perceiving patterns helps children understand mathematical structures. Mathematical thinking involves constructing relationships among ideas and concepts. Although not all mathematical relationships involve patterns, exploring patterns helps children learn to view items in relationship to one another rather than individually. Formation of these logical-mathematical relationships is the basis of future mathematical problem-solving. (p. 129)

Tennessee’s Early Learning Developmental Standards (TN-ELDS) identified Learning Expectations and Performance Indicators aligned to the math area of Algebraic Thinking as represented below.

Children begin to sort, classify, and order objects into a variety of categories long before they enter a formal school setting. They also recognize, describe, and extend patterns and begin to analyze both how repeating and growing patterns are generated. (p. 128)

Perceiving patterns helps children understand mathematical structures. Mathematical thinking involves constructing relationships among ideas and concepts. Although not all mathematical relationships involve patterns, exploring patterns helps children learn to view items in relationship to one another rather than individually. Formation of these logical-mathematical relationships is the basis of future mathematical problem-solving. (p. 129)

*From: Moomaw, Sally and Hieronymus, Brenda, (2011) More Than Counting: Standards-Based Math Activities for Young Thinkers in Preschool and Kindergarten. St. Paul, MN: Redleaf Press.*## Tennessee’s Early Learning Developmental Standards

Tennessee’s Early Learning Developmental Standards (TN-ELDS) identified Learning Expectations and Performance Indicators aligned to the math area of Algebraic Thinking as represented below.

**4 to 5 years (49 through 60 months)**

Component |
Learning Expectations(examples) |
Performance Indicators(examples) By the end of the age span |
Correlations |

Patterns and Algebra |
Explores and begins to sort and classify objects | Shows understanding of and uses comparative words | K.1.3 |

Groups common related objects: shoe, sock, foot; apple, orange, plum. |
K.2.1a K.2.2a |
||

Identifies, describes, and extends patterns | Copies repeating patterns and begins to construct own patterns. |
K. 4.2 |

*Excerpted from TN Early Childhood Curriculum Standards http://tn.gov/education/ci/earlychildhood/sec3math.pdf***A resource for thinking about what and how you should teach about patterns to 4-5 year old children is the Learning Paths chart below that aligns knowledge with sample teaching strategies.**

Content Area |
Examples of Typical Knowledge and SkillsFrom Age 3 |
Age 6 |
Sample Teaching Strategies |

Patterns/ algebraic thinking |
Notices and copies simple repeating patterns, such as a wall of blocks with long, short, long, short, long, short, long. . . . |
Notices and discusses patterns in arithmetic (e.g., adding one to any number results in the next “counting number”). |
Encourages, models, and discusses patterns (e.g., “What’s missing?” “Why do you think that is a pattern?” “I need a blue next”). Engages children in finding color and shape patterns in the environment, number patterns on calendars and charts (e.g., with the numerals 1–100), patterns in arithmetic (e.g., recognizing that when zero is added to a number, the sum is always that number). |

*Excerpted from Learning Paths and Teaching Strategies Chart in Promoting Good Beginnings: Early Childhood Mathematics. NAEYC/NCTM Joint Position Statement, 2002, updated 2010.*