What is the meaning of 去想？Does it have to do with movement?
It's a colloquial using. 

"去想" is meaning "do thinking" or "think about"

但是学生们看到快餐就会买。他们只知道快餐好吃，不去想这些食品是不健康的。

Students will buy the fast food when they saw it, they only knows the fast food is good to eat, but they never thinking about that fast food is unhealthy.

It's not a really moving but a thinking move in brain. Similar => Do the "think".