Suppose you are interested in how children with severe autism experienced the receipt of special education assistance in public schools. this population is characterized by underdevelopment of social cognition, social skills, and language skills. what is the best method for collecting data to answer your research question? why is this method best? how would you describe the research design?

I would definitely use the qualitative methodology in order to collect the data. 
This method is the best because it is very likely that children with autism would act very irregularly which make any quantitative data become unreliable standard of measurement. I would create a certain situation in order to measure each participants response and use them as an indicator in different types of criteria.