1. Designing English Materials for 10th graders of Social Science Program of Senior High Schools. 2. Designing English Materials for the 10th graders of Social Science Program at Senior High Schools. Is one of them correct? Why? If both are incorrect, please give me suggestion.My lecturer's cnfsng

O.K., the difference between 1. and 2. is that you--correctly--have "the" before "10th graders" in 2., and yes, the definite article ("the") is required in the phrase because you are referring to a *specific* group of 10th graders, i.e., the ones "of Social Science Program."
But by that same rule, I believe you also need "the" before "Social Science Program" because this is a *specific* program "of Senior High Schools," as you have this part of the phrase in 1., or "at Senior High Schools" in 2. (Yes, it might seem annoying and redundant to add also these "the"s, but it's English grammar--which is also annoying and redundant a lot of time, but that's another discussion.)
About "at" vs. "of," I believe that either of these prepositions is acceptable here, but I wonder about what exactly you are referring to by "Senior High Schools." That is, is this a proper name, i.e., is there one school that is actually named "Senior High School," or more than one school *each* with the name "Senior High School"? My guess is that "Senior High School(s)" is *not* a name but rather a common, general noun for a type of high school, so in fact we wouldn't write it with the first letters of each of the three words capitalized. I say this only because "senior high school" is a general noun in my native American English, which we write in all lower case letters like that unless it's part of the name of a specific school, e.g., the name of the school that my own son attends, "Homer Senior High School."
On the other hand, if both 1. and 2. are meant to be titles, for example of a article or a report, then it would be all right--indeed, required--to capitalize the first letters of all the "content words" in the title, as you have done but that would mean the "g" of "graders" would also need to be written as a capital "G."
And in your last line, do you mean that your lecturer is "confusing"? If so, then it sounds familiar; I was a lecturer once and I'd bet most of my students probably texted each other calling me "cnfsng" too; they didn't like me *or* vowels.

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