Issues with text problems When I tutor, I often see people who kind of know the stuff they cover in school at the moment and succeed at straight problems like:

Find the derivative of $f(x) = \frac 12 x^2$

But when it comes to text problems, they struggle to get started with the problem at all.

A hill that can be modeled with a parabola like $f(x) = \frac 12 x^2$. Somebody wants to walk up that hill but cannot cope with slopes more than 10%. To which point can that person walk?

My problem is that I am not really sure what their issue is. When I ask them what the derivative is, they can tell me. If I ask what the tangent is, they also know that. But they somehow cannot solve this problem.
When I solve such problems I start with "What do I know?", then "What does that mean in mathematical definitions?" and then try to think what the result has to look like. The steps in between are easily filled then.
How can I teach people this general, diffuse "art of problem solving"?

One idea is cognitive load. The student knows enough to establish any particular piece of the problem, but has trouble juggling everything when there are too many components. I think word problems have a higher cognitive load than drill problems because the reader has to read through the whole thing and keep several ideas in their head at once before beginning to synthesize a response. This is related to math anxiety where in a sense a student's own negative perceptions about math and their ability to do it start to drain cognitive energy. I agree with Krishnakanth that this problem has been exacerbated by the educational system in some places, which teaches math as a list of recipes to follow and doesn't emphasize the analytical, critical thinking aspects.
