It’s like the experiment in which you ask a second-grader: “If eighteen people get on a bus, and then seven more people get on the bus, how old is the bus driver?” Many second-graders will respond: “Twenty-five.” They understand when they’re being prompted to carry out a particular mental procedure, but they haven’t quite connected the procedure to reality.
I was awe-struck, so I asked a friend who sometimes teaches second-graders to try this. 11/18 wrote “25″, 5/18 wrote “25 passengers on the bus” and 2/18 returned a blank note.
I think this is a big part of the explanation. If you’re taught addition as a process that happens in a notebook, not in reality, then you have no way to separate answers that make sense from those that don’t. You also have no way to connect math to things you experience in your life, and I think the most common way to develop an interest in something is to find out it’s related to something else that you’re already interested in.
In the last Super Bowl, the Seattle Seahawks scored 8 points in the first quarter, and 14 in the second quarter. Who won the match?