In response to our column “There’s One Key Difference Between Kids Who Excel at Math and Those Who Don’t,” Noah Smith and I received many comments. Some of them gave good advice about teaching math to kids. Among those was this email from Kevin Remisoski, who graciously gave me permission to share this with you:

I liked most of the points you addressed in this article, however, I feel you missed one very important and crucial point.  There are a good number of people who also have dyscalculia.  This disorder is often times undiagnosed, and while some estimate that 5% of our population has this disorder, I would venture a guess that this in some form could likely affect as many as 20% of our population.  Many of the symptoms seem fairly common to people I have helped with math over the years and my wife didn’t even know she had it until I gave her an assessment after she was complaining about how she always switched numbers around.  This assessment went over 30 questions that are common symptoms of dyscalculia, and she answered 27 of them with yes.

I myself always excelled in math.  This wasn’t due to parental drilling, flash cards, or anything of the sort.  This was purely genetic, and this also seems to be the case with my stepson, though I’ve been teaching him more advanced techniques for his age as well as basic physics (he is 8). 

I think somewhere along the way, teachers forgot how to teach math and left it to the text books and the curriculum to teach for them while they assist the book in the learning process.  I’m sure this is most certainly due to laziness, but most human beings are lazy and just want to get home at the end of their work day.  I know I struggled with some of my teachers in my youth, because countless times I’d approached them with easier ways of solving problems from basic math in elementary school all the way through college.  I just don’t understand why some teachers are so focused on only teaching one solution to a problem.

You see the problem with dyscalculia, is that it is not impossible to teach math to people who suffer from this disorder.  You just have to be creative, even if that means providing creative and abstract solutions at times.  I have taught my wife quite a bit simply by using unorthodox approaches to math. 

With all of that being said, in a base 10 number system, I feel that it is important that children understand a few basic concepts:

If A + B = C, then C – A = B, and C – B = A.  I am not suggesting teaching 5 year olds the concept of substituting numbers with variables, but rather that they understand this concept as much as they will later be expected to memorize their multiplication tables.  One exercise, I’ve worked on with my stepson is repetition.  We don’t play with flash cards or have any visual representation, because I feel that defeats the purpose of memorization. 

So, instead I would go with the range of numbers 0-9, and have him add and subtract different numbers within that range to see the relationships between those addends, sums, subtrahends, and difference.  One way I went about this is as follows:

1+1, 1+2, 1+3……2+1, 2+2, 2+3…..3+1,3+2,3+3, and so on until each starting addend was added to zero through nine (despite starting with one in this example).

After I was sure he was comfortable with this, I would then have him add 1+2 for example and then 3-2, and 3-1.   I would continue to have him solve addends, and then solve the difference from the sum when one of those addends was converted to a subtrahend, and then solve for the second one.

You see, I don’t believe in waiting for children to memorize addition and subtraction on their own.  They should be able to look at any two numbers and solve either the sum or difference just as easily as they breathe.

The same can be said for multiplication when they are ready.  They should not only write their multiplication tables out ten to twenty times a day until they have them committed to memory, but much like in my above example, they should understand the following: 

If A * B = C, then C / A = B, and C / B = A.

This is the way to teach children math.  I also firmly believe that until a child has memorized their multiplication tables at least through ten as well as committed addition and subtraction to memory, that they should not be allowed to even learn how to use a calculator.  Genetic dispositions, as well as disorders, can be toppled by the human brain’s efficiency at memorization through repetition.  If we are to believe that the day may come when no one will utter the words “I’m just not good at math.”, we also need to believe that there is a better way of instilling confidence in those young minds.  Without the fundamentals of understanding the basic building blocks as I’ve described here, it’s really no wonder why so many children bomb in basic math much less algebra, geometry, trigonometry, and calculus.  If Einstein could find a way to overcome dyscalculia, anyone can.