When working with math teachers at any level, one of the complaints I've heard over and over begins with the phrase, "If they only knew their facts..." Fluency with basic facts, however, is only one part of a bigger picture, and I always encouraged teachers to think about the conceptual foundation they were building rather than how quickly students can rattle off some facts. As we consider the increased emphasis on rigor, we need to keep in the back of our minds what rigor is: a balance between conceptual understanding, application, and procedural fluency.
Procedural fluency requires careful attention. We sometimes resort to "basic fact fluency" to address this point of rigor; other times, we brush it aside as carrying little weight in comparison to the other ingredients of rigorous instruction. Either approach misses the intended target because procedural fluency is important and it is more than just memorizing facts. So how do we, as educators, help students develop procedural fluency? One way is through meaningful activities.
Activities that help develop procedural fluency have specific attributes. They are inviting and engaging; they are easy to learn and to prepare; they are repeatable throughout the year; they are adaptable and extendable, and they are open-ended. These activities span all the standards, rather than focusing on the basic operations. Let's look at four different kinds of activities that can help students build procedural fluency, starting tomorrow.
I had a Science teacher in middle school who had a "sponge" on the board every day. I liked these activities because they were more than a couple of warm-up problems; they got me thinking. They were inviting and engaging, and my teacher knew this. Sponge activities should be short, enriching activities that are easily learned and require little or no preparation on the part of the teacher. For example, a teacher may show two rows of ten stars. Students show this amount on a 100 chart with counters, then stating how many rows of ten they have and how many stars they have in all. Students develop fluency as they "see" tens and ones in this kind of activity.
New games are best modeled with the whole class, ensuring that students understand the rules. They then become a fun learning tool for pairs or small groups. Fluency games should be designed to support differentiation, providing easier and more challenging versions of the same game to better meet every student's needs. A fun way for students to practice composing number is to state a target number (e.g, 7) and give students a game board that includes the numbers from 0 to the number one less than the target (0-6, in this case). Students roll one or two dot cubes or numeral cubes, combining their roll with one of the numbers from the game board to make the target number. Students who are still learning the combinations can use just one dot cube; students who are ready for a challenge can use three.
Much has been said about the differences between "drill" and practice. Meaningful independent practice builds conceptual understanding and procedural fluency. This is not an infinite set of problems that students must complete in a finite time period. In reality, a handful of good problems allows students to practice and build their understanding of new concepts. For example, a set of 10 problems where students are asked to fill in each operation symbol to make the problem correct requires critical thinking and an understanding of the concept being practiced.
Assessing students' procedural fluency is necessary, but should not involve a weekly timed test. Short, ten-problem assessments help students and parents to see progress in the basic facts, and provide teachers with formative information that guides future instructional decisions. Consider starting the assessment with a "starter task"- something that gets students thinking about the concepts before taking the test. This can be as simple as asking students to circle the problem on the test that may have an answer greater than 15. At the end of the test, provide an extension question for students who finish quickly.
Procedural fluency is one of the three parts of balanced, rigorous mathematics instruction. When students have the opportunity to work on meaningful problems and activities, they build not only fluency but also a solid foundation for continued growth in math. Encourage students to go out and practice!
Downloadable Activities for Nimble with Numbers
Here are some great activities to get you started with Nimble with Numbers:
- Nimble with Numbers, 2nd Ed. Gr 1 - Sample Pages
- Nimble with Numbers, 2nd Ed. Gr 2 - Sample Pages
- Nimble with Numbers, 2nd Ed. Gr 3 - Sample Pages
- Nimble with Numbers, 2nd Ed. Gr 4 - Sample Pages