An extensive study was conducted of students' explanations written in response to 'what if ...?' questions in elementary mechanics.  The study showed that the structure of students' explanations yields roughly the same ranking of students as do problem-solving tests, but in addition provides a wealth of insights into (1) context dependence and categorization in students' use of concepts, (2) the effect of misconception on context dependence, (3)the types of explanations that students tend to produce.  A follow-up study, in which students were presented with pairs of pre-written explanations to 'what if ...?' questions and asked to indicate a preference, showed that students do not necessarily prefer the types of explanations they write, and have a greater difficulty assessing the correctness of explanations that are counter to preference type.  Evidence is presented that, for many students, the links between physics thinking and real-world thinking are all to tenuous.