This is all fine and good but when it comes to problem solving in he elementary school the numbers really are just the details. It is what is going on with all the words that surround the numbers that is the most important thing to be thinking about. Does it really matter that much if one train is going 40mph, and not 45mph, and the other 60mph, and not 70mph, when we have to solve the problem involving when they will crash into each other, or how far apart they will be in half an hour. The numbers are, of course, important for calculating the specific answer but they don't tell us what we have to do. It's all the words around the numbers that we have to decipher in order to work out how to solve the problem.
If Mary has 16 Hotwheel cars and Michael has four more Hotwheel cars than Mary has, how many Hotwheel cars does Michael have? To solve this problem the numbers themselves are pretty useless. The most important thing is what the words around the numbers are telling us is happening. The understanding of the situation we can construct from deciphering the words is what tells us what we have to do in order to solve the problem. Recognition of the numbers themselves only provides us with the accuracy for our solution. Our understanding of the linguistic structure will tell us if this is a joining, separating, comparing or part-part-whole problem.