The Importance of Math Fluency

WHAT WE DO

Fluency Games’ apps and products are designed to develop math fluency in students of all ages. We believe that a factor of the struggles a student experiences with math in middle and high school is because of a lack of computational fluency in the early grades. Even students moving to more procedural math topics (long multiplication, long division, or finding averages) can be traced back to a student’s inability to quickly and accurately recall basic math facts.

Developing computational fluency is not something that can be done quickly. It is a process of re-writing or re-creating pathways in the brain, and then strengthening these connections through repetition and feedback. Developing fluency requires repetition, time constraints, immediate feedback, allowing for failure and gradual increases in difficulty.

WHY FLUENCY?

“Educators and cognitive scientists agree that the ability to recall basic math facts fluently is necessary for students to attain higher-order math skills… If a student constantly has to compute the answers to basic facts, less of that student’s thinking capacity can be devoted to higher level concepts than a student who can effortlessly recall the answers to basic facts.”1 Computational Fluency is part of an essential foundation for more advanced performance.2

The key is here– “If a student constantly has to compute the answers to basic facts, less of that student’s thinking capacity can be devoted to higher level concepts…”

“Compute” is the key word; compare that to “Recall”. If a student spends so much mental energy on computing 6×8, 9×7, or 3+9+7+1, then there will be less mental energy to work through word problems or process-oriented calculations such as:

  • Operations with Fractions
  • Long Division
  • Finding Means/Averages
  • Word Problems
  • Solving Equations

However, if the basic operations and skills are automatic (fluency), then there literally is no mental energy spent on that part of the problem because the values are memorized, and students can devote all of their thought processes to solving longer and more complicated problems. This also leads them to know when a solution is incorrect or (probably) correct, the ability to check their work, and the ability to communicate their thought processes to others.

BUILDING FLUENCY

Fluency is created by the brain by building new synaptic pathways when making a new association (ie, 6 x 8 = 48, or 1 + 2 + 3 + 4 = 10). These pathways are strengthened through repetition. The idea of computational fluency, then, is having the brain create new pathways and moving students away from inefficient methods (counting on fingers to add, skip-counting for multiplication, etc). That is why you can have middle schoolers, high schoolers, or even adults who have trouble with their times tables– the synaptic pathways were never corrected as a child.

There are five keys to developing fluency:

+ Repetition

Repetition of common facts or procedures (i.e. solving equations, long division). This critical for strengthening those neural pathways. The saying, “Use it or lose it” is correct!

+ Time Constraints

Time constraints force the student way from slow, inefficient methods. Counting on fingers or skip-counting for multiplication just takes too long. Students who spend too much mental energy on simple addition or multiplication will not have the energy to spend on multi-step or more process-oriented problems.

+ Immediate (or near-immediate) feedback

To build correct pathways in their brain, students need to know they have a correct answer! If half the time the student answers 7×8=56 and the other half of the time 7×8 = 54, and never find out if they are correct until the next day, how will they every strengthen those pathways?

+ Allow for failure

Just as it is important to know you get a correct answer, it is just as important to know when you get an incorrect answer! How may times has a coach said (and as a former coach myself, agree with the statement) “We learned more from this loss…”. Knowing (immediately) that an answer is incorrect will weaken and effectively ‘kill’ incorrect associations in the brain.

+ Gradual Increases in Difficulty

Moving too fast in difficulty will discourage children from moving forward. A person does not learn to ski and then try a double-black diamond slope! However, never moving off basic facts will never get that child to move forward in their learning.

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USING SPEED TESTS

Speed Tests (or drills) can be used to build fluency, if done correctly. Math fluency is developed over time, through repetition, with immediate feedback; not created in a day with a single speed drill. Doing a speed ‘test’ once a grading period or once a semester– is just that, a test.

Speed Tests should be done at regular intervals throughout a grading period and throughout the year. This not only allows your student to be prepared for them, it will remove the apprehension commonly associated with these activities. The key, however, is to have the speed tests assessed immediately. Grading them yourself and returning the next day will not allow the student’s brains to weaken/strengthen the neural connections with incorrect/correct answers.

Students should self-grade the test with an answer sheet, and then record their answers in a graphical format. This allows gives the student a picture of the increase of their speed and accuracy (which also builds confidence!).

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