I am tutoring a 16-year-old student from my home country (in Asia) in, roughly speaking, precalculus. I would like to give him a feeling of procedural justice, so to speak, in modern mathematics, which I wish at some point in my youth a math teacher would somewhat stress. Since my home country's culture possibly overly stresses that sort of engineering mathematics all through the math classes prior to college education, I especially would like to show him a sense of pure mathematics. 

However, it seems that perhaps *I need to find a way to make this process more smoother*; I found that I am losing this student little by little gradually. 

I can understand that many people naturally won't appreciate or even care about how one arrives at a result, let alone the discernment of logical rigor. I have no intention to convert any student to become an automatic reasoner; but some experience suggests that many, without a proper sense of procedural justice, would hold instead a business mindset that only learning or seeing important results matters and how a result, important or not, is obtained does not matter. This concerns me in the sense that such a thinking always looks anti-scientific to me; I mean I cannot think of any esteemed field of study that does not stress a sense of procedural justice. Besides, a sense of procedural justice is natural in a sense, since I can hardly find someone who is not curious about what really happened after a magic trick was done for them. On the contrary, many seem surprisingly impatient when being asked to prove $1+1 = 4/2$, whose proof (with properly delimited deepness) involves nothing beyond and possibly well below most people's working knowledge.