I stumbled across this when looking for Cold War era historical fiction. We loved the author's sci-fi Daybreak Bond and Firefly Code duology last summer, and I always like to have several novels set in any given time period to recommend to students. So I thought I'd give this a try, although it's a bit older by now. It's a fine addition to an elementary classroom shelf.
Set in 1953 it fits the bill, but tangentially through the main character's attitude, as it's set in the sleepy town of Maple Hill, Vermont. McCarthy's reach was quite long and it stretches right into the imagination of the main character, 12-year-old Hazel Kaplansky, who very quickly (and with no basis at all) pegs her parents' new gravedigger (they run a cemetery) as a spy.
Exactly what he's spying on in Vermont (?!) is never really addressed and perhaps may be the point. McCarthy's hysteria touches even this little girl.
She manages to rope another child, a boy her age, Samuel Butler, into her spy-conspiracy theory. He's much better at reserving judgment, but agrees to help her research at the public library a name on a headstone: Alice. It comes to their attention after the gravedigger leaves a Russian nested doll behind.
Hazel is so young and zealous about catching spies that it never occurs to her to see the man's actions as expressions of obvious pain and grief. As an adult you see it a mile away and it's cringe-worthy. It leads to Hazel causing a lot of pain and grief for others -- the gravedigger, her parents, Sam. Her assumptions and ill-founded judgments harm pretty much everyone she comes into contact with.
Is there any way she can make things right? She tries for her friend, Sam, but for the gravedigger the damage is done.
But for a student who needs a slightly gentler read, this would fit the bill. It's also not quite as focused on the history of the epoch. It's more about Hazel's struggles to see things beyond her own assumptions. Therefore, it's not quite as good for building students' background knowledge of the era, but is still appropriate for lower elementary grades.