I have observed teachers who really challenge their students to achieve higher order thinking These teachers take their students as early as the Second Grade and teach them how to add, subtract, multiply and divide using only their bran. We call this Mental Math. When I observed a Second Grade Class that had their students mentally answering math computation questions, I put my own son in that class. Shortly after being enrolled, He, too, learned how to do Mental Math. From that point on, math was my son's best subject. Teachers can really make a difference and parents can help affect change.
Also, when the child is in the second or third grade and their child can't add simple two digit numbers, it is up to the parent to make sure that their child gets the extra help needed to become successful. Parents cannot wait on the school every time their child has an academic deficiency. Part of being a good parent is making sure that your child functions at the correct grade level throughout their academic career.
For example, all children should learn their multiplication tables by the third grade. They should be able to repeat them, verbally, without using a calculator. Children in elementary school who rely on the calculator for the answers are creating math deficiencies, which could have a negative impact on their math development.
While the newer method does require computer access for every child, most schools now have that capability. As children do more hands-on learning on computers and less in books, these programs are capable of reaching them on a level they can understand.