Imagine an alien planet where the inhabitants are born with the multiplication table imprinted on their DNA. Let’s call this galactic species Multiplydons. The Multiplydons enter their distant world reciting multiplication facts the way human babies babble and coo for their parents. Like humans, Multiplydons attend school and study math, but their curriculum naturally omits memorization of the multiplication tables and skips ahead to their application. When it comes to multiplication, they possess fact fluency, but not computational fluency.
Computational Fluency vs. Fact Fluency
Computational fluency refers to the ability to calculate accurately, flexibly, and efficiently. For more on computational fluency, visit our blog. Fact fluency makes computational fluency possible. When a student (we’re talking about human students now) demonstrates fact fluency, they can recall the basic rules of the operation at hand. Think about it like this: As students learn a new language they start with basic grammar, syntax, and vocabulary. When they begin piecing these elements together to form sentences, their speech is slow and halting. They must concentrate on recalling the rules. Over time, they incorporate these rules automatically as they become fluent in expressing increasingly complex ideas. It is the same with math.
Relying on Fact-Focused Learning
Over the years, teachers have shifted their instructional focus from rote memorization of facts to a more applied approach. When their focus was on the acquisition of facts, teachers observed that competent students struggled to transfer their knowledge from one context to another. They might be faced with exactly the same math content they aced on a test, but would fail to recognize it in a real-world situation.
Why Fact Fluency Matters
Of course, knowing mathematical facts is necessary for performing any operation. Indeed, STEMscopes Math includes fun and engaging resources for developing fact fluency. Instead of simply memorizing facts, students participate in activities that enliven the sometimes dry business of learning rules. These activities help students move through the three main phases of mastering new math concepts:
- Skill exposure
- Development of fact fluency
- Real-world application and transfer
While students are learning basic rules, they need to be exposed to the math skills that fact fluency will enable them to perform. For example, students need to get hands-on experience adding and subtracting as they steadily memorize basic addition and subtraction equations. STEMscopes Math emphasizes the importance of hands-on learning by offering everything from concrete-representational-abstract (CRA) lessons to our Parent Letter, which includes engaging activities students can do at home with their adult caregivers.
Development of Fact Fluency
As students grow more confident in a new concept or process through hands-on activities, they practice working with the new concept. Practice and repetition are key to developing fact fluency. That’s one of the reasons STEMscopes Math is structured around the 5E + IA model (constructivist teaching)—it leaves room for iterative learning. Note that it is practice, not rote memorization, that leads to fact fluency. Practice draws students into active learning, while memorization presents content in a passive manner.
Real-World Application and Transfer
As we noted earlier, fact fluency is not an end in itself. It enables computational fluency. Fact fluency and computational fluency help students become mathematically dexterous—they can recognize processes across various contexts and apply the appropriate solutions to the problems. Once students can do this, it is safe to say they have mastered a mathematical process.
Both computational fluency and fact fluency serve a greater purpose: the transformation of a math student into a competent real-world problem solver. They are counterparts that cannot be separated. Fact fluency is not the destination of math education, but rather the compass that will guide them through the jungle of real-world mathematics. Indeed, real-world connection is one of the cornerstones of STEMscopes Math—because if we can equip students to solve the complex problems facing us today, we are benefiting ourselves, our students, and future generations.