There are two kinds of mathematics: memorizing rules and understanding them. Memorizing rules is referred to as procedural fluency, the “how” in performing procedures accurately, efficiently, and with flexibility. On the other hand, conceptual understanding is the “why” behind knowing what makes the operations work. It enables students to understand the concepts they study and find connections among them. Students need both procedural and conceptual understanding.
In kindergarten through sixth grade, fluency is vital and expected to be mastered by the end of the year. The learning of “basic facts”—single-digit combinations for addition, subtraction, multiplication, and division—has long been a focus of elementary mathematics. Many of us remember completing endless worksheets, timed tests, and flash card drills as we attempted to “master” our basic facts as children. However, research over the past thirty years, recommendations from Principals to Actions (NCTM, 2014) on effective mathematics teaching practices, and goals for students outlined in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010), suggest a very different approach that has the promise of greater student engagement and success. The chart below lists the fluency expectations as described in the Common Core State Standards for Mathematics for grades K-6.
In elementary classrooms across the district, teachers are guiding students towards fluency in a number of ways. Fact based games, workstation activities, and interactive websites/games are some of the more nontraditional ways students are engaged in fact experiences.
Teachers are explicitly teaching strategies that support student thinking and understanding of basic facts. Students have the opportunity to apply these strategies in practice in the form of story problems, ten frames, and games. In the table below, are some of the strategies students are learning to develop fact fluency.
|Addition Strategies||Subtraction Strategies||Multiplication Strategies||Division Strategies|
|Counting on||Counting back||Array||Repeated subtraction|
|Making ten||Removal||Area model||Equal groups|
|Friendly or Landmark Numbers||Compensation||Equal groups||Array|
|Doubles/Near Doubles||Fact families||Repeated addition||Fact families|
|Break each number into place value||Distributive property|
|Compensation||Doubling and Halving|
|Fact families||Skip counting|