>If I ask one of these adult students a question involving negative numbers, and I phrase it in terms of money and debt, they answer it immediately. If I ask th

>If I ask one of these adult students a question involving negative numbers, and I phrase it in terms of money and debt, they answer it immediately. If I ask them using just numbers, they have no clue. This doesn't just happen with students who are bad at math. If you sit in on most introductory advanced math classes (eg. introduction to abstract algebra), you will see the same thing: students imminently understand what is being asked when it is phrased in terms of something concrete, but have more difficulty answering even basic questions when they are asked in the abstract. The main difference, in my experience, is that in advanced classes, a "concrete" example would be something like the set of 2x2 real valued matrixes; so non mathamaticians do not recognize it as being simple. There is also the difference that experienced mathematicians have learned that "simple" things will become simple with enough exposure; and have honed the ability brute force their way through while they get that exposure.