Resources and Tools for Elementary Math Specialists and Teachers
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Developing Fact Fluency

Why is fact fluency so important?

Knowing basic number facts is an important skill for students and this skill is identified as such in NCTM’s Principles and Standards for School Mathematics and Focal Points as well as in the Common Core State Standards for Mathematics. The landmark report from the National Research Council, Adding It Up: Helping Children Learn Mathematics, lists computational fluency as one of its five intertwined strands of mathematical proficiency. Performing mathematical procedures “flexibly, accurately, efficiently, and appropriately” is only possible when students have a command of number facts.

Everyday tasks such as telling time, measuring, shopping and handling money depend on fluency with number combinations. It is the basis for estimation and more complex computation. This “fact fluency” supports problem solving and helps students judge the reasonableness of their results. It frees the mind to engage in higher order thinking.

What should we consider?

Teachers must determine how best to achieve an appropriate level of fact fluency and how to balance it among the other aspects of a successful mathematics program. Number facts learned purely by rote can be forgotten, or not readily applied effectively in problem solving. Timed tests may create anxiety toward math and lead children to think that mathematics is more about memorizing than learning to think and reason. Effective fluency involves not merely quick recall, but also number sense, operation sense, and an understanding of our number system that allows students to work flexibly with numbers. Students with strong conceptual understanding can derive new number combinations from the ones they know; they have strategies for recalling facts they’ve forgotten. 

How will these resources help?

The resources in this collection suggest and demonstrate activities that lead students to develop these skills. They all aim to develop students’ fluency with number facts while strengthening their ability to take advantage of the structure of the number system.  The resources provide a variety of representations and approaches that help lay the foundation for the algorithms and build the essential vocabulary.

None of these ideas diminishes the importance of practice. You’ll find more resources in the Classroom Collection, Achieving Fact Fluency, that provide students with ample practice in a context that promotes reasoning and understanding.

Replies:7
Created:06-25-2012 by Uncle Bob
Last Post:09-30-2012 by Uncle Bob

Resource Title/Description

In this brief article NCTM President Linda Gojak encourages educators to reconsider the notion of fluency with regard to number facts, procedures, and other topics. She elaborates on the NCTM's position of broadening the definition to include conceptual understanding and flexible thinking.
This booklet provides information to guide the improvement of school mathematics from pre-K through grade 8, with a focus on the realm of number. The authors explain five strands of mathematical proficiency and discuss the major changes needed in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system. It answers some of the frequently asked questions regarding mathematics instruction and recommends actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance of working together to create a mathematically literate society. At this website visitors may read the book online, download a free copy (pdf) or purchase a hard copy. This is a 39-page summary of a comprehensive report, Adding It Up: Helping Children Learn Mathematics, which is cataloged separately.
This 14-minute video demonstrates how students learn to persevere through challenging number puzzles and games. Headteacher Kate Frood discusses her philosophy and models teaching children to use core multiplication facts as tools for more complex problems. She differentiates tasks to accommodate advanced and struggling learners.
This 5-lesson unit is intended to help children who already understand the meanings of addition to develop fluency with addition facts. The activities and games take advantage of commutativity, the additive identity, doubles, and number patterns to develop operation sense and foster retention. Lessons include student materials, questions for students and teachers, assessment ideas, and links to interactive applets.
This 5-page article describes a two-person card game that helps develop students' strategic thinking while practicing basic addition skills with whole numbers. The author explains how to adapt the game with more challenging content and demonstrates the game's relationship to magic squares and tic-tac-toe. He provides game instructions, discussion questions and printable cards for the basic version. An online version for one player against a computer, The Game of Fif, is cataloged separately.
In this 14-minute video UK teacher Sally Hill uses patterns to help her students learn the multiples of four and understand how to apply that knowledge to more complex multi-digit problems. Head teacher Kate Frood discusses the school's guiding principles and her own style of leadership. The page includes a link to a pdf document summarizing K-4 Mental Math Strategies [cataloged separately].
This article (pdf) describes a game for 2-5 players that develops fluency with whole number operations. The game is played on a non-standard 8 by 8 number grid with three dice. Players take turns rolling the dice and forming expressions that result in a target number on the grid. The name "Contig" refers to the fact that players score points by claiming a number adjacent to occupied squares. A Contig game board is provided as well as a game board (same numbers rearranged), rule sheet and scoring sheet for Number Neighborhood, an alternative name for the game. The author suggests game variations and discussion questions.
This series of 6 postings on the Let's Play Math blog contains a variety of strategies for helping students learn multiplication facts. After establishing her point of view, the author reviews various meanings and models of multiplication, and then suggests a sequence of methods that take advantage of patterns, number sense, and operation properties. There are numerous links to other websites with helpful ideas.
This article focuses on the role and techniques of effective ("distributed") practice that leads to full and fluent mastery of mental mathematics as well as conceptual growth around properties of arithmetic. It lists the essential mental math skills needed for fluent computation at grades 1, 2, and 3. The article describes a number of strategies for developing mental skills and links to pages with more details on others (some not yet complete). While this article refers to the Think Math! curriculum published by EDC, the methods generalize to any program. The Fact of the Day technique and a related video are cataloged separately.
This article proposes a structured set of lively, brief, daily exercises designed to help children master number facts and mental math skills. Each day's practice focuses on a small, highly focused, manageable, and strategically selected set of facts or skills that builds directly on the previous days' learning. Related resources (Practice and videos) are cataloged separately.
This FAQ from the Teacher2Teacher service at The Math Forum @ Drexel contains many suggestions for learning multiplication facts. It includes ideas contributed by T2T Associates and teacher participants. There are links to Ask Dr. Math resources, children's literature connections, and outside websites with related recources.
This 3-page document (pdf) offers numerous strategies that children can use to perform addition, subtraction, and multiplication mentally. These strategies help develop fact fluency, number sense, operation sense, and use of patterns.