The Mystery at Fire Island by Hope Campbell, 1978.

Darcy Littlewood, called “Dash,” is appalled when her art teacher tells her not to draw anything over the summer.  Drawing comes almost as naturally as breathing to Dash, who wants to be a cartoonist when she grows up.  She’s always doing sketches and caricatures of people she sees, especially her younger brother, JC (James Colson Littlewood, also known as “Coleslaw”).  But, her art teacher thinks that her style has grown too strong and inflexible too early in her life.  He thinks that if she takes a break from drawing for the summer, she’ll be able to come back to it with a fresh approach that will allow her to try different styles as she grows older.

To Dash, the idea of not drawing at all is intolerable, especially since she broke her leg shortly before the start of summer vacation.  She can’t go much of anywhere or do much of anything while her family is staying at their beach house on Fire Island.  Without much to do, she doesn’t know how she’d entertain herself if she couldn’t draw.

Her older sister, Candace, isn’t happy about spending the summer on Fire Island, either.  She says that there’s never anything to do there, although their mother attributes part of her boredom to the fact that she’s the only one in the family who doesn’t have an outstanding talent or a particular goal in her life.  Everyone else in the family is artistically-inclined in some way.  Mrs. Littlewood is a writer, Mr. Littlewood teaches drama, JC has acting skills and a special talent for imitating people, and Dash has her art.  Mrs. Littlewood thinks that Candy’s attitude would improve if she found something that she was especially good at and truly cared about.

While Dash is brooding about her inability to stop drawing in spite of her art teacher’s request, she makes the acquaintance of Mrs. Guizot, an eccentric older woman who spots her drawing caricatures.  It turns out that Mrs. Guizot is an art lover, and she quickly becomes a fan of Dash’s work.  But, there is something mysterious about Mrs. Guizot, or at least the man they see her talking to.

Both Dash and JC notice that the man has a peculiar way of standing and walking.  Dash draws it, and JC imitates it.  So, when they see the same man on the beach later that night, looking different without his beard and wig, but still walking and standing the same way, they wonder why the man was in disguise.  Also, he seems to be going out surfing when there aren’t any waves for surfing.  Then, they discover that he’s bringing scuba tanks with him, and they aren’t real scuba tanks.  What is the man doing?

The kids try to investigate the mysterious man with JC doing much of the leg work at first because Dash can’t get around very well.  JC is worried about what they might learn because the man might turn out to be truly sinister and violent.  He even has suspicions about Mrs. Guizot.  Later, Dash’s leg improves and she’s able to take a more active role in the investigation, but the kids pretend like she’s still laid up as a cover for their activities.  The kids’ investigation doesn’t go as planned, but they do uncover a crime and also inadvertently help their sister to find her life’s vocation.

Part of the story has to do with seeing with depth.  Part of the reason why Dash’s art teacher wants her to observe more and draw less is so that her art will contain more depth.  Dash also learns to see the depths of people, the things they keep hidden behind their facades.  Her sister, Candy, also has hidden depths which even she doesn’t appreciate yet.

The story was later made into a tv movie by the same name, and the picture on the front cover of this edition of the book is from the movie.