When you think of fluency what comes to mind? What about computational and procedural fluency?
This introductory post is the first in a series on fluency. We will share common fluency fallacies and their truth, significant strategies to develop fluency, automaticities beyond the basic facts and ways to best assess all components of fluency. The posts we will share are from a recent webinar and recently published book by Jennifer Bay-Williams and John SanGiovanni.
Fluency refers to being able to work through a process in a reasonable amount of time with accuracy. When a math content standard states the phrase, “fluently add” it goes beyond implementing a procedure efficiently. It is also knowing when that procedure is a good choice.
Further, computational fluency refers to the four operations while procedural fluency includes more than just the four operations – for example comparing fractions.
Procedural fluency is a term that is well-defined by NCTM (National Council of Teachers of Mathematics) and the NRC (National Research Council). Both groups describe fluency as being able to apply procedures efficiently, flexibly and accurately.
Let’s further define these terms:
Efficiency: Solving a procedure in a reasonable amount of time by selecting an appropriate strategy and then implementing that strategy.
Flexibility: Knowing multiple procedures and applying or adapting strategies to solve procedural problems (Baroody & Dowker, 2203; Star, 2005).
Accuracy: Correctly solve a procedure.
These 3 Big Ideas are captured well in this diagram which has been adapted from Jennifer Bay-Williams.
We must acknowledge that fluency is more complex as it goes beyond basic facts and extends into upper grades in areas such as fraction concepts, solving proportions, and simplifying expressions. We need to delve deeper into strategies that go beyond flashcards and memorization of basic facts. It is also important to note, “A reasonable amount of time means moving through a process without getting stuck, lost, or bogged down. Time is not constant or definitive”(Bay-Williams & SanGiovanni, 2021). Collectively, these six fluency actions will provide observable student work for the three components of fluency. The more we can help everyone see what fluency looks like in action, the better we can ensure our students develop fluency.
Reflecting on these six fluency actions, which tend to be the focus of fluency assessments? Which actions tend to be overlooked?
If you answered Accuracy you are correct. Typical assessments rarely focus on flexibility or strategy selection. Unfortunately, I’m sure you would also agree that if something is not assessed, it is not valued. The MCAP assessments will address the other fluency components and actions, so we need to shift our thinking to include these components. We will dive deeper into assessing fluency in a later blog post. For now, consider your own practices in terms of fluency. Are you maximizing the value of Number Talks while focusing on efficiency and flexibility? When your students share their solutions, are they selecting appropriate strategies and applying it to new problems?
You may also want to take a few moments and read the Foreword of this book as I think many of you can relate to the early math experiences of Christina Tondevold. She shares how her experiences as a student influenced her pedagogy as a beginning math teacher. As she worked toward her earning her master's degree her understanding of fluency in math led her to make a shift.
In our next blog post we will explore the 12 fluency fallacies that are shared in the book, suggestions to address these, and examine the truths that will help deeper define the true meaning of fluency in mathematics. The coaches will also share the downloadable resources that you can implement in your classrooms.
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