In Surely You're Joking Mr. Feynman he tells of harrassing mathematicians by bringing them back to the real world. "Imagine a sphere," the mathematician says. "OK, like an orange?" Feynman replies. The mathematician agrees. "Now, take an infinitesimal slice..." But Feynman stops him: You cannot do that with an orange because at some small slice, it ceases to be a piece of an orange and is something else. If you know the book, then you know that that is just one story out of very many. Feynman admits to being bested by a school of rabbis. He is staying there to save money while attending a conference in NYC. They find out that he is a physics professor. They want him to tell them whether or not electricity is fire. You see, the Sabbath has rules about fire. The problem is the elevator. Can they use it? He and the rabbis go back and forth and they decide to hire a Christian to run the elevator for them. "Wait!" objects Feynman. It is not moral to hire someone to do something that is wrong for you, but not wrong for him. "Why?" they ask. Feynman admits that he should have known better than to continue the argument, but... One possible way to group the aliens would be two and two and two and two in which case the answer is 8. Or two and two and two and one because one alien gets motion sick and doesn't want to ride in which case the answer is 7. Or two and two and two because one spaceship is in the shop getting a new warp drive in which case the answer is 6. Or one and one and one and one but there will be two trips because all the aliens want to ride alone in which case the answer is 4 for the first ride and 4 for the second ride. Or what if all the aliens want to stay home today? That's the way my kid thinks, and why this word problem is not ideal for teaching 4x2 if the answer the teacher expects is 8.
So, Deanna's son is just creative and insightful. The broader problem is that we have three different modes of learning, teaching, and enjoying mathematics. 1. Memorize the tables. Again, at the start of the capitalist age, no one did that. They had the multiplication tables in front of them 10x10. But we memorize today and it is handy. 2. Story problems. Again, they go back 500 years... 2500 years... 3000.... because those were the motivations to create, invent, and learn arithmetic and geometry. 3. Math for math's sake. Once you learn how it goes, you can go wherever you want with it. I have several of the Martin Gardner books here. Most of it is uninteresting to me, personaly, but I am impressed (even awed) by the range what mathematicians find interesting: folding paper, stacking coins, coloring, cutting, stealing cigarettes, ... And then, once you learn the language, you think in it  which I do not. Get a textbook on geometry from a university math library and you will not find a single picture, shape, or figure. They do it all with symbols as in algebra. Contra Deanna, it is not the purpose of a story problem to teach that 4x2=8. If you do not know that, you cannot do the problem. The purpose of a story problem is discover which of the infinite mathematical facts are relevant. A train leaves Chicago... A pail with a hole is filled from the top... There once was an episode of Death Valley Days where a farmer lost a henhouse that was insured for fire. The argument was over the distributive law of arithmetic. The school marm taught him how to understand the problem and prove his case to a judge. Story problem...
