Suppose I'm a youth (say about 13) in the USSR in 1977 and I ask my history teacher why so many people were purged in the 1930s. Would I be given a an answer or just told to drop the issue? If the former what would that answer be?

You can get some sense of what was the orthodox view at the time by looking at the entry on Stalin from the 1979 edition of the Great Soviet Encyclopedia. (The GSE was the official state encyclopedia and what was included and removed over time makes for a great study of changing official stance on historical facts.) It makes for an interesting read. Most of it is positive, but there are some "mistakes and errors" acknowledged:

The key task in building socialism was socialist industrialization to ensure the country’s economic independence, the technical modernization of all national economic sectors, and the defense capability of the Soviet state. The most complex and difficult of the revolutionary transformations was the reorganization of agriculture along socialist lines. Mistakes and excesses were allowed in the collectivization of agriculture, and Stalin bears some of the responsibility for the errors. The mistakes were corrected, however, through decisive steps taken by the party, with Stalin’s participation. The cultural revolution was important for the victory of socialism in the USSR. [...]

Apart from the positive aspects of Stalin’s leadership, theoretical and political mistakes were committed, and certain of his character traits had negative repercussions. During the first years after Lenin’s death he took account of the critical remarks addressed to him, but later he departed from the Leninist principles of collective leadership and the norms of party life and overestimated his own merit in the successes of the party and people. The cult of Stalin’s personality gradually evolved, leading to flagrant violations of socialist legality and doing great damage to party work and the cause of building communism.

The Twentieth Congress of the CPSU, held in 1956, condemned the cult of personality as a phenomenon alien to the spirit of Marxism-Leninism and to the nature of the socialist social order. On June 30, 1956, in a decree of the CPSU Central Committee entitled On Overcoming the Personality Cult and Its Consequences, the party gave an objective, comprehensive analysis of Stalin’s work and a thorough critique of the cult of personality. The cult of personality did not and could not change the socialist essence of the Soviet system and the Marxist-Leninist character of the CPSU and its Leninist policy. Neither did it arrest the natural course of development of Soviet society. The party worked out and implemented a system of measures to ensure the restoration and further development of the Leninist norms of party life and the principles of party leadership.

So there is acknowledgment of "mistakes and errors" there, and a general understanding that Stalin did some bad stuff. The depth of that bad stuff is understated (though by that point the fact that it was Quite Bad Indeed would have been rather commonly understood, if not talked about), and it is portrayed in a light which implies that it was really just a slight blemish on his overall record, one that does not in any way reflect negatively on the founding decades of the USSR or its present-day (late 1970s) existence, and one that was recognized and "corrected" after Stalin's death.