Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8

Synopsis

Because fluency practice is not a worksheet. 

Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. Real fluency involves reasoning and creativity, and it varies by the situation at hand.

Figuring Out Fluency in Mathematics Teaching and Learning offers educators the inspiration to develop a deeper understanding of procedural fluency, along with a plethora of pragmatic tools for shifting classrooms toward a fluency approach. In a friendly and accessible style, this hands-on guide empowers educators to support students in acquiring the repertoire of reasoning strategies necessary to becoming versatile and nimble mathematical thinkers. It includes:

•  "Seven Significant Strategies" to teach to students as they work toward procedural fluency.
•  Activities, fluency routines, and games that encourage learning the efficiency, flexibility, and accuracy essential to real fluency.
• Reflection questions, connections to mathematical standards, and techniques for assessing all components of fluency.
• Suggestions for engaging families in understanding and supporting fluency.

Fluency is more than a toolbox of strategies to choose from; it's also a matter of equity and access for all learners. Give your students the knowledge and power to become confident mathematical thinkers.

Summary

Chapter 1: Deconstructing Fluency: Dissecting Where and When It Lives

* Fluency encompasses recognizing numbers, patterns, and relationships; performing operations efficiently; and applying math concepts in context.
* Real example: A first-grader who can instantly name the number of dots on a die without counting.

Chapter 2: Fluency at the Core: Multiplicative Relationships

* Multiplicative reasoning is fundamental to fluency in operations.
* Real example: A third-grader who can skip-count by 5s or 10s to solve multiplication and division problems.

Chapter 3: The Heart of Fluency: Foundations of Addition and Subtraction

* Early development of addition and subtraction skills lays the groundwork for future fluency.
* Real example: A kindergarten student who uses finger counting to solve addition and subtraction equations within 5.

Chapter 4: Fluency Under Construction: Extending Addition and Subtraction

* Students transition from concrete representations to mental strategies for addition and subtraction.
* Real example: A second-grader who uses number lines to visualize regrouping in subtraction problems.

Chapter 5: The Art of Multiplication: Fluency in the Times Tables

* Fluency in multiplication is crucial for solving multi-digit problems and other complex math tasks.
* Real example: A fourth-grader who can recall the 7s times table accurately and use it to find products.

Chapter 6: Fluent Division: Breaking Apart and Sharing

* Division involves understanding sharing, grouping, and remainders.
* Real example: A fifth-grader who can use arrays to solve division problems and interpret remainders.

Chapter 7: Fraction Fluency: Developing Meaningful Understanding

* Fluency in fractions requires conceptual understanding and procedural skills.
* Real example: A sixth-grader who can compare and order fractions with different denominators.

Chapter 8: Algebraic Fluency: Focusing on Variables and Patterns

* Algebraic fluency involves recognizing, representing, and manipulating algebraic expressions.
* Real example: A seventh-grader who can simplify algebraic expressions by combining like terms.

Chapter 9: The Affective Side of Fluency: Believe to Achieve

* Students' math anxiety and self-belief impact their fluency development.
* Real example: A teacher who uses games and positive reinforcement to build students' confidence in their math abilities.

Chapter 10: Fluency as a Tool: Supporting Problem Solving

* Fluency frees up cognitive resources, allowing students to focus on higher-level problem-solving tasks.
* Real example: A eighth-grader who uses mental computation to solve multi-step word problems efficiently.