Bear with me as I force an analogy between watching basketball and grading physics quizzes.
When I watch basketball on TV, especially during March Madness, I’m often annoyed by the way they handle the replays. After an exciting play, I’ll yell at the TV, begging for a replay so that I can see again exactly how the play developed. When they do show the replay, I’ll often end up yelling at the TV again, because they left out all the important part of the play.
They show the shot being released, traveling through the air and splashing through the net, ignoring the pick and roll and the deft pass that set up the shot. The time that the ball is in the air is really the least interesting part of that play. The ball flies the same way every time, and we already know the result of the play. Show us how they got there.
Or they show the dunk at the end of a fast break, hiding the defense that set up the break and the smart decicion making of the point guard that got the ball to the right player to finish the play. The dunk gets the fans excited and shows up on Sports Center, but it doesn’t happen without the key plays that set it up.
Now the switch to physics…
Students in introductory physics classes ineveitably place too much focus on the final numerical answer of the problem, which in reality is the least important part. I graded a quiz last week where I spent way too much time trying to decipher the numbers the students wrote down, because they placed the numbers in their equations rather than writing them clearly with the symbols representing the quantities in question. Grading problems written in this way is like trying to analyze a basketball play from the replay that only shows the shot. It can be done, but it requires more effort on the part of the grader. It’s also a bigger risk for the student, because if they don’t get everything right, it’s harder for the grader to assign partial credit when there’s no symbols to show exactly what they’re doing.
This is something that I think most physics teachers try to drive home: the setup and the problem-solving process is more important than the final answer. Basketball coaches drive home the idea that focus on execution of the play is paramount and that the scoring will take care of itself. But the fans always focus on the shot, and the students always want you to tell them if they got the right answer.
How can we change their focus? Any ideas?
The First Excited State 
By doing the same thing as you are doing here, drawing analogs to “daily-life encounters”, and by doing this give an semantic lesson on the importance of the method contra the result. You don’t get into a physical good shape by studying an athleet through a mirror…
Another obstacle is the way students are motivated. By managing to come up with the correct answer, (regardless of the method) the student (read, I’m one of them) feels an amount of achievement and thereby joy, leading to added motivation. One approach to the problem are therefore: how can the process of problem solving, with focus on the actual method, give some euphoric asset?
In other words, how to make understanding the syntax, fun.
The human mind has an interesting feature too. People distinctively remember negative encounters clearer and better then those of a positive nature. Learn by your mistakes, or as more fitted for my next approach:
Remembering by selecting whats important.
Nearly all students have to some degree a fear of tests or even unannounced tasks. By having some tests, where the actual rating is entirely based on the procedure to the problem, totally ignoring if the answer is correct or not. In this way, maybe the student will re canalize his or hers focus points, finally leading to new study-methods. Perhaps giving the importance of the method, no result produced without, its necessary high priority.
Just some thoughts from an young man in Norway…