We all know the importance of math fact memorization as a part of the framework that underlies success in all math concepts. One of the most common “go to” math manipulatives students use to learn their math facts are their fingers.
Some students are able to transition from finger counting to rote memorization. However, many become more reliant on finger counting and do not transition. I have no doubt there are mathematicians out there who, as adults, have figured out how to be successful without mastering facts.
Most of the parents I speak to regarding their struggling math student report that the student is still counting to solve single-digit math facts. Many parents who themselves struggled in math know the limitations of finger counting.
Long-Term Effects of Counting on Fingers
Often the finger counter can “get by” for a few years. However, the wheels often fall off when they encounter long division. With all the steps involved in long division, even when the student understands the concept, the process becomes cumbersome due to working memory over load. The bottom line is that there is only so much room in the brain’s working memory to process the growing complexity of more advanced math concepts. Finger counting requires the use of working memory. There just is not enough room, or as my colleague told me recently, “Finger counting drains the battery.” That “shut down” you may have observed in your student is not intentional or a lack of intellect; it is how the brain is designed.
The Role of Subitizing
For the student who has learned to add, subtract, multiply. or divide by counting fingers, there is no other place for them to look for the answer. The answer is not in their mind (unless they envision the counting there.) It is important to replace the physical action of counting with a better, more effective tool. The most effective tool will be some form of subitizing.
My favorite way to describe subitizing is, “To suddenly see without counting.”
Think about what you experience when you roll dice and you see a four and a five. Through repetitive exposure of the same pattern combination, you eventually do not need to count the individual dots and know immediately the combination is nine. Another example is building with LEGO® blocks. As a child repeatedly plays with these blocks, they no longer need to count the nubs on the top to distinguish between the pieces. If they run out of a specific size block they quickly learn that they can substitute smaller blocks to replace the larger missing block. This is what subitizing or using visual memory “looks like.” Research shows that rectangular and dot arrangements are the easiest to retain in long-term visual memory.
Students of all ages are unfairly judging themselves as “just not good in math” because of the missing tool of fact automaticity. It is important to think of fact memorization recall as a vital tool for math success. For many students, their reliance on finger counting is preventing this tool from developing.
Story of Success
In closing, I tried to think of a specific story to share with you to personalize this topic and provide an example of hope.
The “story” has been shared with me hundreds of times over the past 25+ years collaborating with Math-U-See parents. It is more important to me to speak to the heart of you, the parent who has tried everything to encourage your student to no longer count on their fingers to solve math facts. I hear your concern every day in my phone conversations that you have tried everything. You may be just discovering the effect it is having on your student’s ability to find success as math concepts become more complex. Your student could be anywhere from 6-16 years old. Some of you are homeschooling for the first time; others have always homeschooled. You have not failed your child.
Many curricula teach counting as a pathway to learn math facts, and for some it does work. Most students, whether they have it modeled to them or not, will discover the option of finger counting if counting is presented as a process. You did not know it would become an ingrained habit instead of a temporary method. If you personally still use counting to solve math facts yourself and consequently do not feel confident in math, think of it is a bonus, not a limitation. To model to them your willingness to seek solutions to set them up for academic success and learn alongside them will one of the most important lesson you ever teach them.
Linda Gerhard says
Suzie Homemaker says
Inused figure counting and had them memorized by 5th grade. Ad sub. Mutli and devide by tenth. Never needing to count it till after school. Now 48 I have long gone back to counting. I see no reason for this to be an issue. It’s important they can figure it out. After all it’s about being able to count money and figure size of room to paint. Or lay flooring later in life. It’s just like spelling. Go to all about spelling and read about how many words we can memorize how to spell. Very little. We end up sounding them out. Same with math. Very little stays unless you use it all the time. Those of us who memorized them as kids forget if we only need to do a few problems a month. Then where would you be. Standing saying I can’t count my figures it’s wrong too and not knowing how to get the answer. Go ahead and use your finugres. Pray dots on the paper for mutliply.
Aimee Crawford says
Thanks, Suzie, we’re glad it is working out so well for you, but we believe that most students – and adults – find everyday math much more simple and less stressful if they master their facts and don’t have to count on their fingers.
Ruth Font, OHIO says
Homeschool mother of four adults, former Jr. High and Sr. High math teacher – my thoughts – I believe that finger counting is often a reflection of the student who may not be ready to move from the concrete (counting on fingers) to the symbolic (math problems on paper). It is a very developmental stage and probably cannot be rushed. When it is ‘easier’ to count on your fingers than to ‘memorize’ your facts, you brain may not be able to yet “figure out” the answer.
Practicing and drilling facts will be helpful but don’t try to rush the “math understanding” until you see a change or improved growth in math comprehension. I do homeschool assessments for many families and see this so often, especially in younger grades.
Aimee Crawford says
Thank you, Ruth, we couldn’t agree more! It’s important to move at your student’s pace. Memorization of facts can’t be rushed, but it is important for student success when they get to higher levels of math. If you get to a point where your student is struggling and you’re not sure why, it is quite possible that they don’t have an automatic recall of their multiplication or addition facts. It’s never too late to stop where you are and establish that mastery. It will help your student immensely!
Dr. Linda Neuzil says
Check out this TedTalk:
I use this when I teach my math methods class for future teachers.
I still count on my fingers for some things, yet I have a master’s of science and taken several years of calculus and fluid dynamics.