Mathematical FLUENCY

Being fluent means being able to do something without much mental energy. In education, this is referred to as a decreased cognitive load. You are better able to apply skills once they are fluent. This is as true in mathematics as it is in many areas of life. While we may not argue about the necessity of needing fluent pilots or doctors, fluency in math education is often debated.

As noted in Effective Math Interventions (Codding, et al., 2017), "Students without basic fact fluency seem to be less able to grasp underlying math concepts, perform procedural computation tasks, solve word problems, or access higher-level math curricula (Fuchs, et al., 2006; Gersten et al., 1999; Jordan et al., 2003)."

Check out the Instructional Hierarchy to learn more about fluency's place within the stages of learning.

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Fluency is bigger than math.

Fluency in small skills leads to performing more complex skills. Being fluent does not mean memorization. It means that you know the concepts and procedures so well, that you are flexible and quick.

Non-Math Examples

Fluency in Painting

Imagine being unable to mix paint, find the right brush, or use the proper brush strokes while learning to use proportions to transferring an image to the canvas. These skills are essential to being an artist. It will be difficult to learn about proportions in painting while you are still trying to figure out what colors to mix to get the right shade of green for the tree being painted. Being fluent in these prerequisite skills allows your mind to focus on the task at hand.

Fluency in Music

Nobody picks up an instrument and becomes a jazz sensation. First, music students need to learn the mechanics of holding the instrument, playing specific notes/chords, and piecing together enough sounds to make a basic version of a song recognizable. After learning the basics, novice musicians practice endlessly to become fluent in playing specific notes, often referred to as muscle memory. Once those skills are fluent attention can be given to learning new, complex sounds or creating original music.

Fluency in Driving

Every parent teaching their child to drive begins the lesson by asking their student to "drive as fast as you can!" Right? NO! New drivers need to learn the location and use of all the internal instruments so that they can operate wipers, signals, etc. without taking their eyes off the road. New drivers often start on back roads and empty parking lots where they can go slow and learn the basics of driving. After the basic as fluent, drivers enter more complex situations like a highway or downtown area.

Calculators

There is no clear answer to the calculator question. Whether or not to provide a calculator to a student is a case by case decision that needs to be made with caution. Educators must consider to instructional goals and the long-term implications of having or not having a calculator in relation to the goals. Mathematics content is extremely sequential, with content building upon itself over time. Educators must be sure they are helping students learn content today in ways that will support tomorrow. A calculator may make today easier, but will it impact tomorrow negatively?

Why might teachers not provide access to a calculator?

If the instructional goal is focused on basic computation, then a calculator will eliminate the need for the student to actually compute which conflicts with the goal. Basic computation has a major impact on future learning. Therefore, it is critical that evidence-based practices be leveraged to build fluency in basic computation so that it can be applied to more advanced math concepts.

Why might teachers provide access to a calculator?

If the instructional goal of a lesson is problem solving and a student is struggling with the prerequisite computation, a calculator may be provided to support the computation and focus attention on the problem solving process. Consider the calculator to be a scaffolded support. As students continue to work on computation during other parts of the lesson, the need for a calculator during problem solving should be reduced/eliminated.

What risk is there in giving access to a calculator at all times?

Math content continues to build upon itself over a students academic career. If the foundational skills are weak, then it becomes more difficult to learn more advanced concepts/procedures. Being fluent means being able to do something with a decreased cognitive load, which frees working memory to focus on the task at hand. If a student never learns to add single-digit numbers, then multi-digit addition algorithms will be difficult to learn because the students working memory will be focused on the adding of digits and not the algorithm. While a calculator may help support the computation, it will still reduce the students capacity to focus on the algorithm.

When does access to a calculator become important?

Mathematics content builds upon itself quickly. By middle school there is a need for students to start using a calculator to deal with functions and data analysis. Eventually, calculators allow students to focus on solving the problems without the need for complex computational demands. However, educators must question access when they observe students using calculators for basic operations. This behavior is eliminating practice so that student can retain basic computation skills. Skills will continue to get worse without practice, this increasing the need for a calculator. Even in middle and high school students should be fluent with the basic computational demands of the curriculum, otherwise more complex tasks become cognitively overwhelming... like the student trying to learn factoring that can no longer multiple or divide.

Classroom Supports for Practicing Fluency