Point of teaching generalization of skill to a child with asd

Among the myriad of challenges, presented in unique packages by each child on the autism spectrum disorder, is one experts often observe as a commonly seen trait - the inability to generalize a learned skill across different situations or environment on their own. Once they have been taught a skill and have been observed to have mastered it in one environment, for example, at home with the therapist, the question that needs to be asked is can the child perform the same skill with another person or another room or outside or when there are more than one person in the room even before venturing out to social/community situations like school or homes of extended family members? If the child is being taught a skill e.g not running out on to the street in front of his home, they say he/she will need to be taught the same skill across various situations likely to emerge when the family goes and mingle with the community outside of their home. Specific time will have to be set aside to focus on the skill wherever the child goes until the skill is mastered in being applied to at least situations such children are likely to encounter as part of family life - going for shopping, community gatherings, schools, visits to extended families - virtually any situation that might involve parking lots, crowded places and visits to places located near busy streets.
What I observe in my son with respect to his inability to generalize skills is much more abstract. His, I notice, has mainly to do with academic skills.(Our number one overall concern is his receptive language, more specifically, comprehension of directions or instructions, both verbal and written, given to him). One example, I hear great reviews of the tasks he can do in the classroom from the teacher and the EA, observations I cannot share when I do his homework with him. At home I see that he is unable to do his homework on his own because he is unable to understand what is being asked of him in the task presented to him. I let him do his homework as best as he could on his own and when he is done I review the work with him and find that his answers are miles off. I concluded that this must be a case of his not being able to generalize or transfer his skill from school with his teacher to home with me. Anyways, this is where we are at at this time. Like everything else, it's a work in progress with him and I guess, one that will take its own sweet time.