Search
When math feels slow, frustrating, and full of one step forward, two steps back, the issue may not be ability so much as fluency. Math is like learning to read. A traditional math curriculum relies on rote memorization, similar to some older reading programs, which teach students to memorize sight words rather than decode letter sounds. Memorization can provide a quick win because the student learns to match memorized answers to math facts or to read by recognizing sight words.
In the long run, this hinders their ability to read at a higher level because it conditions their brains to rely primarily on the region responsible for memorization. They haven’t had much practice using all their reasoning capabilities to decode words, so the mental muscles are flabby.
Math works the same way. A child may memorize a multiplication fact like 5×6=30, but have no real understanding that 30 represents 5 groups of 6 objects or 3 groups of 10. Without math fluency, they don’t understand a word problem, for example, that asks them to find the total number of marbles when 5 children each have 6 marbles.
Developing math fluency takes time, consistency, and mastery of concepts. All About Math incorporates a research-based, three-step method to teach each math concept:
The National Research Council defines fluency with math as the ability to carry out mathematical procedures accurately, efficiently, and flexibly, emphasizing that true fluency involves more than speed or memorization.1 As the NRC says, fluency also includes flexibility with numbers, the ability to understand a concept so well that you can apply it to new situations.
Math drills and worksheets build speed and memorization. This gives the student a shallow grasp of math operations with no real understanding of how numbers work.
Memorizing math facts is knowing that 5×6 = 30.
Math fluency is the understanding that 30 is 5 sets of 6, or 6 sets of 5, and is part of a larger number pattern. A child is fluent when they intuitively grasp that 5X7 is one more group of 5 than 5×6.
When a child is fluent in math, often called procedural fluency, they can explain why adding, subtracting, multiplying, or dividing numbers works to find the correct answer and when to use each operation. They demonstrate an understanding of the concepts behind the math, rather than relying on rote memorization.
The importance of mathematics fluency lies in its role as a bridge between basic skills and higher-level thinking.
Fluency:
Going back to our reading comparison, when a student is fluent at decoding words, they can read much more smoothly and with less effort. This allows them to focus on comprehension. Fluency leads to confidence and a willingness to tackle harder material.
A math fluency example in real life: When you are baking cookies, and the recipe calls for ¾ C of flour, what do you do if you don’t have a 3/4C measuring cup? Because you are fluent in math, you aren’t stymied by the problem; you know that you have other options. A 1/4C measure could be used 3 times. Or you could use 1/2C and 1/4 C to equal 3/4 C (or you could use my method and just wing it!).
Finding a solution doesn’t take much mental effort. You understand the concept of fractions and can easily devise a different way of achieving the outcome.
A child with strong math fluency can play with the concept, develop a higher-level model of it, and apply the concepts to new situations, even creating unique solutions to problems.
Truly effective math learning equips students with a deeper understanding of math concepts, helping build fluency rather than settling for surface-level learning like memorizing facts.
Memorizing math facts relies on only one area of the brain: memory recall. Facts are often quickly forgotten after the lesson ends, and the test is over. Here’s a quick way to prove this: what is 11×12? If you don’t use multiplication daily, you likely had to pause and figure out the answer; it didn’t jump to mind instantly.
You forgot the memorized answer, but you had the tools to figure it out another way. You understand the concept.
All About Math helps students master math at a conceptual level by:
Explore a sample of the All About Math Level 1 student activity book
These lessons engage multiple regions of the brain to construct mental models, allowing mathematical understanding to become a set of flexible tools that transfer naturally into other areas of learning, such as:
All About Math builds conceptual understanding, and students see why math works. Review the pages of the level 3 teacher’s manual sample to learn more.
Think of building fluency through mastery, not memorization. This requires developing the conceptual framework for why math works the way it does.
In early grades, it starts with building a concrete understanding of number sense through hands-on manipulatives. There’s more about number sense in this article.
Use visual representations, such as creating equal groups, to support multiplication. The child might have a problem, such as: If we have 30 guests and 5 tables, draw a picture showing how many people we need to seat at each table to model N x 5 = 30.
Make meaningful connections through story problems by encouraging the student to analyze, evaluate, and determine what data is needed to solve them.
Include verbal reflection questions that encourage your student to think through how they arrived at an answer.
Practical strategies for parents:
Pre-school math fluency begins with number sense. At this stage, fluency is defined by familiarity with numbers rather than math operations.
Effective early activities include:
A key to building math fluency is more than just traditional math practice; it includes exposure to numbers in a variety of settings and applications. Well-designed math fluency activities increase hands-on involvement with numbers, helping children to see different relationships and patterns.
A game like Make Ten, using a 10 frame for example, provides a number of benefits. You’ll need:
Give the student a cup with 10 counters in it. They can shake the cup and pour out the counters. Some will land with the yellow side up, others will be red. Have the child put the yellow counters on the 10-frame, followed by red ones.
If they are still in the concrete stage of learning, they can verbalize the resulting math fact (ie 6 yellow plus 4 red equal 10)
Once they are confidently verbalizing the math facts you can start having the child write the math problem created by the counters.
Using activities like this:
More math fluency ideas:
To help build math fluency, All About Math combines:
Students manipulate numbers physically before solving them mentally .Each step of the Concrete-Representation-Abstract approach mentioned above is assessed for mastery before moving on to the next step. For example, your student should be comfortable with addition using manipulatives before he is asked to add using pictures of objects. Once he is doing well performing the operations using pictures, then you move on to solving written problems. This process ensures your child understands the concepts at a mastery level before they move on to the next topic.
| All About Math | Drill-Based Math Programs |
|---|---|
| Building conceptual understanding | Rote memorization |
| Develops confidence | Pressure to be faster |
| Long-term retention | Facts are quickly forgotten |
| Uses 10- frames and other tools / manipulatives to visualize | Flashcards |
| Pattern recognition and reasoning | Learns facts in isolation from patterns |
Explore All About Math sample lessons and discover how the program incorporates a variety of hands-on, visual, verbal, and written work to build math fluency
The ability to solve math problems accurately, effectively, and flexibly, demonstrating the ability to apply math concepts to unfamiliar problems.
It helps children solve complex problems with ease and confidence as they master concepts and build automaticity.
You can build math fluency with regular, consistent practice and using manipulatives, games, and reasoning strategies instead of memorization. Talking about math when it shows up in daily life, and giving your child exposure to numbers in many different ways, develops fluency in ways you can’t do with only math drills.
Fluency develops gradually with time. Each child will master math facts at their own pace. All About Math offers low-stress, multisensory lessons that incorporate visual representations, hands-on manipulatives, and discussion questions to foster reasoning skills. Building math fluency with a focus on understanding over memorization will thoroughly prepare your child for higher-level math and critical thinking.
References
