Article: Effects of a Story-Mapping procedure Using the iPad on the Comprehension of Narrative Texts by Students with Autism Spectrum Disorder. In Focus on Autism and Other Developmental Disabilities, 2017, 32(4). By Browder and others.
Learning to read is a complex task. I have never taught a child how to read, but there are people who do it every day, and I think we as a society under-appreciate the skill and the method of these teachers. Teaching ASD children to read is a whole different thing though. In fact, I know many inquisitive, highly intelligent children on the Spectrum who reach high school age and have not mastered some of the basics of reading. Reading is, after all, more than just sounding out and knowing the definition of words. One must be able to know what the words mean in relation to each other, and the overall point the author is trying to make. A primary reading task that many ASD students struggle with, and ultimately find limits their academic progress, is reading comprehension. ASD children are often wonderful at decoding (sounding out words and knowing their definitions), but deplorable at reading comprehension.
I lack the knowledge and will-power to tell you about Story-Mapping and some of the other methods the authors talk about in this study. What I can tell you is that the researchers thoughtfully pulled together several effective methods for teaching reading comprehension to children with disabilities and were able to improve the reading comprehension for elementary-age ASD kids with low IQs. I think this is truly astounding. These are kids that, if lucky, would have devoted teachers devote hours and hours to their education in reading comprehension and ultimately achieved at a very low level. And that is problematic because reading comprehension is the key to just about all other formal education. If you cannot read and understand the directions, it does not matter how good you are at math, or how much you like history or science. Reading comprehension is key.
Some terms for you to research on your own and ultimately discuss with your ASD child's reading teacher:
Constant Time Delay
Modified System of Least Prompts
These last two terms are ways of presenting information to and practicing new information with students that commits the information to memory and makes it readily available for recall (e.g., using the info to answer questions about what you just read). Both terms are based on behavioral principles, of course. Based on the descriptions in the article, you do not have to be a Behaviorist to effectively use them in the classroom.