The following are the key shifts called for by the Common Core:
1. Focus strongly where the Standards focus
2. Coherence: Think across grades and link to major topics within grades
3. Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application with equal intensity
Fluency does not require using one particular method over another. Rather, students should be able to work confidently and efficiently.
However, speed and memorizing should not be the emphasis when we develop fluency.
Below are resources for further reading about these topics:
In this article, "Fluency Without Fear", Jo Boaler discusses both the damage that is caused by the practices that often accompany the teaching of math facts – speed pressure, timed testing and blind memorization – and summarizes the research evidence of something very different – number sense. High achieving students use number sense and it is critical that lower achieving students, instead of working on drill and memorization, also learn to use numbers flexibly and conceptually. Memorization and timed testing stand in the way of number sense, giving students the impression that sense making is not important. One way to do this is via games and tasks in which students learn math facts at the same time as working on something they enjoy, rather than something they fear.
One of the 8 Teaching Practices named in the NCTM Principles to Action is: Build Procedural Fluency from Conceptual Understanding: Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.
For example, this Kindergarten standard, K.OA.4, says:
For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
While this 1st grade standard, 1.OA.6, says:
... demonstrate fluency for addition and subtraction within 10
If a first grader is struggling with fluency for addition and subtraction within 10, the focus on supporting is finding those combinations as described in the K standard.
This table summarizes the required fluency in grades K-6:
Fluency is developed via routines such as math talks and counting routines.