Am I correct in restating your questions: What do you think about cognitive skills? Are cognitive skills really contextually bound? Is there any possibility that the cognitive skills are linear? Because if so... I'd like to take a shot at answering...
It all depends on what you mean by linear. Piaget, writes about the epigenetic development of cognition. I wish I could give you the reference off the top of my head, but unfortunately I read this several months ago. I believe it is in The Epigenetics of Epistemology. In this book I seem to remember him talking about cognitive development and skills are both a form of linearity and non-linearity. I believe his argument would sound like this:
A newborn takes in the world and the stimulation of the surrounding environment accrues and accrues in, what I believe would be something akin to your meaning of linear fashion. But at a critical point in this linear development (of distinguishing boundaries from one thing or another) the mind reaches a critical level of skills such that it is able to function in an entirely qualitatively different manner. It now is able to assess and identify certain objects and people. Eventually this identifying ability grows in linear fashion until again it reaches a critical level of competence and then again takes on new qualitative form (which again would be somewhat non-linear). Each new qualitative jump forward provides the mind with apparently new mathematico-logico skills that progress to a level of sufficiency and then a new leap forward ensues.
The contextualization that you bring to the discussion and the non-linear tone that the questions assumes, would, in my opinion, ultimately hold true, only because (a) a new environment stimulates our mind in a way unlike before, (b) we come to this context with a new set of skills upon which to tackle the issue, (c) even if the context is the same as before, our internal development acts upon it in a new way.
So, this is just my opinion, but it might be helpful to see cognitive skills as those that grow in "linear" fashion, but then take "non-linear" leaps. Hope that helps.
I just wanted to clarify my position, that's all. I'm always impressed by people who are able to engage in high level conversations in a foreign language. Who cares about grammar, I wish I could do what you do. :-)
I have read the answers to this question and I wanted to throw an ingredient, i.e, geographical contexts. People who live in a two-way street tend to think in a go and return way only. People who live in spacious places, cities, etc, tend to have different perspectives. Yet, I believe that we sometimes shape our environment and decisively alter our minds. Bearing this in mind, I wonder how administrators and politicians think. I believe their thoughts go through a one-street mind. They have no flexibility, no alternative routes, and worst of all, I wonder if they can think!!!!