I learned to add and subtract in the elementary grades by understanding how to count. I repeated my numbers with due diligence when prompted by my mother. I counted forwards. I counted backwards.
Addition was counting up. Subtraction was counting back down. This was an easily understood concept later demonstrated by macaroni noodles, buttons, and blocks. It was simple counting, which is why I also encourage teaching math facts as soon as counting is accomplished.
Let’s digress. We teach our little ones to hold up their fingers and count to ten. How many times did you hold up a finger and run through the digits until you reached 10?
Many math resources use an abacus, number line, or special blocks. If we use physical objects to demonstrate or enable problem solving, why can we not use our fingers?
Have you used a manipulative of some sort? Regardless of what you use, you are still using a visual representation. I want to note that I will always have my fingers with me, or at least under normal circumstances I will. If not, I can use my toes! (I will only need to commit to wearing flip-flops.)
Is there anything wrong with using your fingers? In ancient history, it is shown that Greece and Persia used a method of finger counting. We subscribe to classical educational techniques, but we recoil when children use their fingers? (The classical finger-counting method used by these ancient civilizations is explained by Estellvenia Sanders.)
If you can complete the same problem like another who does not use fingers, why balk? Are we so intent on focusing on speed that we forget with math that it is the accuracy that matters?
This, of course, means that I must make an off topic statement. I detest and discourage timed tests for math! I see no reason to fail a student for taking too long to get the right answer.
Consider that you may very well have a visual learner. As you have more than likely experienced over time, learning math facts has become or is near impossible. The numbers need to be represented in order for them to understand and to master the arithmetic. Do not be discouraged. Through repetition the finger solutions will inevitably become memorized. How many times do you solve one plus two with your fingers until you have committed the answer of three to your memory? We learn by doing and by repeating.
At this point, we could argue against finger counting. Speed is sacrificed. You could also argue that poor memory is the fault of the child not putting the time into the task. So, memorization is a part of math. I concede, and I agree completely with both arguments.
However, if the concepts of the arithmetic are understood, then you have learned the theory, or number sense. You just have not successfully learned the math facts of the four basic operations. Yes, it would make the arithmetic easier, but does understanding follow memorization too? I would rather have accomplished number sense versus math fact. With the understanding, you can progress to higher arithmetic or math concepts. There is no need to hold a child back because they use their fingers and fail to memorize facts.
So, how do you move on without math fact memorization? Concept and theory do not go hand in hand with fact memorization. You must weight carefully where your own balance and focus will be as well as the time to push forward regardless of memorization.
Memorization is a key component to academic studies. You cannot disregard the need in math either, but it should not be criteria for moving forward with learning. As well, consider not teaching the mental tricks until the child understands the numeric context of why the tricks work. Stick with strict memorization in early math instruction. For those that are visual learners, create pocket charts. While you will need to develop tools, like charts, in order to keep from pulling your hair out while your child adds nine times eight, you do not have to stop the learning. Not memorizing the facts does not stop them from understanding or prohibit them from moving forward, although you will need to make concessions through chart use or extra time for work.
In reality, this will depend greatly on the type of learner that you have. I have a fantastic memory, but I still often use my fingers! At the same time, I am teaching addition math facts 1-10 to the little “terrorist” who is four years old.
Finally, ask yourself if it is so terrible that your child still or has begun using their fingers (which they often start doing out of the blue). Is it that much of a problem? Is the balking by the current math fads truly something to pay attention too? Math U See says go back a book. Should you really? No. Can it really hurt number sense? No. Will it stop at some point? Maybe.