Set primarily in the 1950s, Tell Me a Riddle is set against a background of conformity and conflict. It is extremely useful to understand this era when studying the work.
The Cold War and the struggle between capitalism and communism was at its ideological height in the 1950s. Wisconsin Senator Joseph McCarthy led witch hunts for supposed communists, while the House Un-American Activities Committee began to blacklist people (especially in Hollywood) for "subversive activities."
Further, there was great paranoia over the Cold War with the USSR, and the fear of nuclear destruction. The threat of nuclear war (touched on in "I Stand Here Ironing") drove people to build bomb shelters, and schools to practice nuclear attack drills. The United States and the USSR fought both literally and metaphorically over the political ideologies of many restless countries. In 1959, Fidel Castro rose to power as the communist leader of Cuba, a close neighbor to the United States. Personal freedoms were squashed under the need to protect the ideological and political future of the world, and many artists found themselves in jail for practicing self-expression.
At the same time as this international political conflict, American experienced a huge economic post-war boom, and consumerism sprang to the forefront of the nation's consciousness. The middle class grew markedly during this time period (which is reflected in David and Eva's children's families). Advertising became increasingly ubiquitous, and lives were perceived as being much better than in the past. In a world where everything seemed clean and wonderful to many, conformity to a certain family ideal was widespread. On the other hand, those who refused to conform found it more difficult to find a place in society.
A third important change in the 1950s was the beginning of the Civil Rights movement. The Supreme Court's 1954 Brown v. Board of Education decision ended de jure segregation, and the Little Rock Nine paved the way for the difficult path to racial integration. Carol and Parry's tension-fraught friendship engages with these changes, and foreshadows the future development of the Civil Rights movement, including those of Dr. Martin Luther King Jr, Malcolm X, and Rosa Parks.