Math Fluencyby Mary Damer
January 30, 1997
What is the importance of fluency (speed) in math and spelling and reading? A child will be unable to effectively use certain skills unless learned to fluency. For example, unless a child can accurately answer math facts very rapidly, the child will have undo frustration when doing more complicated math tasks involving that skill. (Long division is impossible if the child cannot quickly do the subtraction subtasks.)
Effective teaching research shows that there are four stages to a student's learning. The first stage is the acquisition stage where the goal is helping the child learn the skill accurately. This is the stage of instruction where the child learns how to sound out the word, or to write the correct answer to the math problem is, or to identify the causes of the Civil War.
The second stage of learning is the fluency stage where the learner acquires the information at an automatic level. At this stage, when the child sees the word he/she doesn't have to stop and sound it out; when the child has to write a spelling word he/she doesn't have to think about each letter as it is written; when the child solves the long division problem the subtraction portion is automatic. For some school subjects, fluency isn't that important. One doesn't need to explain the causes of the Civil War with more speed. For other subjects such as math, reading, and spelling, fluency is as important as acquisition and a teacher is remiss if he/she skips this part of instruction. One thing I love about Saxon Math is how many more skills they target for fluency. When I started using the Saxon program with my children this summer and they had to do the timed tests for converting fractions and for figuring percentages, they became more adept at a number of other mathematical operations. I've learned a lot from teaching my children using Saxon because most other math programs don't focus on developing as much fluency in as many areas.
Research shows that to be fluent children should be able to accurately solve math facts at a rate of one per every 2 seconds. Naturally, if the child has poor fine motor skills or is younger, that has to be taken into account on any written timed test. One of the biggest teaching mistakes in math is when teachers don't stick with this part of instruction with children who have more difficulty. I'll give my son as an example. Not only was Justin one of the slowest learners of addition math facts I had ever worked with, but once he finally knew them he had absolutely no fluency. It could take him hours to complete 50 addition math fact problems. (I waited him out once.) Fortunately, his teacher wouldn't let him move on until he was fluent with them and I started to work with him on fluency every evening for ten minutes. Now many an educator would have said, "He has an attention deficit disorder and just doesn't have the attention span to do a timed math test." I was not willing to put this limitation on my son in second/third grade. To work on fluency, every night I set aside a time and gave him a sheet with all his addition math facts. I then set the timer and his goal was to complete one more problem than he had answered the night before. I think when he started he could answer 4 or 5 problems in the ten minutes. He literally progressed problem by problem. If he didn't beat his goal, we would practice saying the answers and then set the timer again. Fortunately once he could do the addition, the other facts came much easier. By fifth grade Justin was the fastest student to complete the once-a-year check-up math timed tests, and not only will he be studying algebra in eighth grade, but he can take any timed math achievement test and score around the 90th percentile. If we hadn't focused on the fluency, none of this would have been possible.
After fluency comes the maintenance stage of learning, which my dad always called "overlearning". At this stage of learning, the goal of instruction is to maintain a high level of performance over time. This is a critical stage for individuals with any type of memory problems. Any of us can recognize how important this stage is for our toughest subjects. Science was always my "killer" subject and I had to spend a lot of extra time rereading and working on the material or it was quickly forgotten as if I had never learned it.
The fourth stage of learning is the generalization stage during which the learner needs to perform the skill at different times and in new situations. This is the part of the learning process when those group activities and hands on projects can actually be helpful if they involve skills that the students have already learned to fluency. Unfortunately, today's educators expect studentsto acquire the skills and learn them to fluency when doing the hands-on-projects and groups. They have it all backwards! If the teacher has taught the student to solve subtraction problems with borrowing ( the student has acquired the skill); if the student can now do the subtraction problems with appropriate speed (fluency); and if the student has had practice doing those type of problems over a period of time (maintenance), then a project such as one requiring the student to compute the length of wood needed for bookcase shelves which required the student to subtract with borrowing would promote generalization. Likewise, the student learning about the Civil War is much more likely to have truly learned the material and to remember it years later if the teacher not only requires the student to answer the question, "What were the causes of the Civil War", but also requires the student to give a presentation or write a paper referring to the causes of the Civil War.