Written Fluency
November 3, 2019
Choral responses and whiteboard exchanges help children practice and master concepts. Once this has been achieved, students are ready to enter them into long-term memory. For some concepts – and age groups – internalizing is best achieved using paper and pencil.
Three of the most common written fluency tools include:
Computer Generated Worksheets
Traditionally, elementary mathematics fluency consisted of flash card drills leading to computer-generated worksheets, in which students were required to recall memorized facts. The latter often had a timed component and student anxiety became an unfortunate consequence of the practice. Over time, tools such as Mad Minute became so alienating to so many students that written fluency has nearly vanished from elementary school classrooms.
For many teachers, thinking of students hunched forward in their chairs, heads bowed, intensely scratching pencil to paper conjures such unpleasant memories that they don’t bother investigating the problems on the page or consider that the exercise could be meaningful. Because of negative associations with timed tests and teachers celebrating speed over thinking and accuracy, written fluency backlash is understandable. Still, it remains largely misunderstood.
Although they may have been misguided in their approach, past educators understood that strong basic skills are essential to succeeding in elementary math, and most students won’t acquire them without practicing. They also knew that concentrating practice into a short time frame intensifies focus, often generating adrenaline, which increases memory.
In the past, this reasoning was pedagogically sensible. Math was taught as a collection of mnemonics and procedures (not as a thinking, reasoning discipline), and massed repetition was a widely accepted approach to practicing. Some students didn’t enjoy it, but school wasn’t always expected to be fun. Struggles were part of life and the classroom was no exception.
Once a child learns a set of facts, randomly practicing them can trigger rapid recall, which helps enter them into long-term memory. Computer generated, massed practice worksheets, therefore, can work well for some students. However, regardless of how well-intentioned their teacher is, this methodology is broadly ineffective for three obvious reasons.
First, because Drill and Kill tasks do not reflect lessons, many students see no connectivity between instruction and their fluency practice. Secondly, problems are presented randomly, which favors students who have a high capacity to memorize. Children who struggle with memorization tasks need sequences and simple to complex progressions to build their confidence and arrive at answers. Lastly, teachers too often adhere to a Practice Makes Perfect philosophy. As a result, they mindlessly distribute randomized problem sets before students have mastered the skills needed to answer correctly. Practice only leads to perfection when students understand content and possess strategies to efficiently solve problems they’re working on.
Each of these factors paired with teachers pressuring their students to work harder and faster, led many children to detest written fluency. As parenting, schools, and society changed, paper and pencil activities fell further and further out of favor. Still, far too many elementary math teachers are eager to distance themselves from their professional predecessors. As a result, they dismiss written fluency rather than trying to shape it into a powerful tool. Blinded by optics, they fail to see the positivity in students silently focused, racing their pencil down a page trying to answer as many questions as they can.
American society is hyper-stimulating and our culture often denigrates success through practice. We praise natural intelligence, mock grit, and regard deep, solitary thinkers as social pariahs. The wise teacher finds this regrettable and thus sees value in providing silent, focused practice time. Succeeding in a high tech world, they understand, requires people to sustain prolonged concentration. They recognize that traditional tools, such as Drill and Kill timed tests were flawed, but not baseless. To improve their students’ fluency skills, they simply need to tweak an antiquated idea, maintaining its best qualities, while improving upon its worst. The end product is written fluency that reflects student lessons, utilizes strategies, and provides confidence-building practice.
Pattern Sheets
When students are asked to internalize facts by rote memorization, a chasm is created in the classroom. Some students succeed while others – with a lower capacity to memorize – struggle. To improve basic skill recall, children need to conceptually understand the topic they’re working on, and possess a strategy or strategies to solve problems. Once this has been accomplished, they need intensive practice to build fluency.
When problems are presented randomly, the struggling student often finds the exercise arduous, because they are overwhelmed by a vast problem set without the competency to efficiently answer. Adding intentionality to practice while narrowing the scope of what children are being asked to memorize, helps children build fluency and confidence.
Pattern sheets bridge conceptualization and automatization. Consisting of small fact sets, they help children focus on a manageable task, while repeatedly exercising the same strategy. The example below is two lines of an eight-row Times Tables of 6 (multiples 1-5) pattern sheet.
6 x 4 = 6 x 1 = 6 x 4 = 6 x 2 = 6 x 4 = 6 x 3 = 6 x 4 = 6 x 5 =
6 x 4 = 6 x 5 = 6 x 1 = 6 x 5 = 6 x 2 = 6 x 5 = 6 x 3 = 6 x 5 =
Before distributing the pattern sheet, the teacher establishes the following expectations:
Beginning at the top left corner of the page, work left to right, top to bottom. Although not numbered, the problems are intentionally sequenced to build fluency.
If students come to a problem that they haven’t memorized, they are expected to employ a skip counting strategy to solve.
Strategy 1: For the problem 6 x 4 =, count forward starting at zero: 6, 12, 18, 24. If they count on their fingers, each digit represents a six. When they’re holding up four fingers or four sixes, they’ve arrived at the answer to 6 x 4.
Strategy 2: For the problem 6 x 4 =, begin at the five-fact and count backwards: 30, 24. Students using their fingers start with an open hand to represent 30 (5 sixes). Then, they fold down one finger and mentally subtract 6 to arrive at 24 (4 sixes).
Throughout the one to two minutes that students will be working, they should either be writing an answer or skip counting on their fingers to solve, but NEVER staring at the paper thinking of an answer.
Pattern Sheet problems are sequenced to wean students off strategies such as counting on fingers. By alternating the same fact every other problem, children gain fluency with the strategy, and eventually answer without it. Because the activity consists of only five problems interwoven in different sequences, students recognize instant measurable improvement, which increases their confidence.
Sprints
Mathematical fluency, of course, consists of much more than basic operation proficiency. Dr. Yoram Sagher, professor of mathematics at Florida Atlantic University, recognized this problem while observing Chicago public elementary schools during the 1990s. He felt that students needed more practice and less teacher explanations. Many classes began with homework reviews. As a result, students were passive learners who frequently became bored and distracted. Over time, he addressed these problems by developing Sprints, a tool that provides more robust practice options than the aforementioned written fluency methods, all the while maintaining their favorable characteristics.
Sprints center students on improving their ability to solve problems during a two part, adrenaline-rich, competitive task. It develops children’s number sense because of its focus on patterns, while building their confidence because of the intricate simple to complex design, paired with immediate documented success and internalization of concepts. More than anything, Sprints help children look forward to math class because they know it will be a time that they’ll feel successful, challenged, and happy.
The advent of Eureka Math, the world’s first Common Core-aligned curriculum, entered Sprints into broader math conscience eight years. In turn, the written fluency tool fell under intense scrutiny by progressive pedagogs, most of whom didn’t take time to closely study Dr. Sagher’s brilliant invention. Sighting student frustration and anxiety, they discounted its beautiful design, never stopping to consider the intentionality behind each stage of the routine.
Unsurprisingly, the swift spread of information created diluted messages, leading teachers to use and deliver Sprints antithetically to their intended purpose. Two of the most common misconceptions that arose from their mishandling were:
Branding Sprints as “Timed Tests”.
Failing to connect Sprints with conceptual math teaching and learning.