(A preteen novel, obscurely set in the 50s, only skimmed by me. I was attracted by the Moebius strip on the cover of the Scholastic edition. It was a National Book Award finalist, I presume in some children's category.)

The main character, 11-year old Amanda, is finding growing up challenging. She finds the still childish side of herself, which she calls "Amanda Woods", and the new maturing side of herself, which she calls "Amanda K. Woods", difficult to reconcile.

When it comes to her math homework, the AKW side finally triumphs, and she gets an A+. There is a scene involving long division.

But the real mathematical surprise comes later, when Antoine, her pen pal from France, visits with his parents during summer vacation. *Both* the parents are mathematicians! On being told that Amanda is smart at math, they give her a Moebius strip, and she immediately figures out that it is one-sided:

"It is called a Moebius strip," Mrs. Bonnier said. "It is important to geometry. And in life, too, sometimes the outside turns into the inside and the inside into the outside."

And after the Bonniers went back to France,

... her mother wanted to know if she realized that the Bonniers were very special people and that being a mathematician was a very special thing, and that Amanda could be a mathematician one day, too, if she wanted.

At the end of the book, Amanda adopts the Moebius strip as a metaphor for her growing maturity and ability to reconcile opposing demands.

(I must say, this blatant propaganda surprises me.)