ON A HOUSEBOUND Saturday, board games may be a parent's best defense against mayhem. Just about any board that will keep them from getting bored will do, including such kid favorites as Clue, Monopoly, Life and either child or adult versions of Trivial Pursuit. But if you want to be sneaky, you can get your children to play games that will help them with math and logical thinking skills.

According to Ann Kuppinger, who teaches an after-school games course at Capitol Hill Day School, the best games are those that "require kids to plan ahead and think logically to a solution that's not contained in the next move." In this category Kuppinger puts such games as chess, Othello, Pente, Chinese Checkers and Mastermind. To illustrate, she whips out a game mat for Pente, a game developed from the Japanese game of Go.

"Okay, you're a green, and I'm a yellow," she says, dumping some flattened marbles out of their pouches. "The idea is to surround a pair . . . What kids learn from this game is that they have to plan ahead or lose. At first, they lose right away. Then they develop a strategy to keep from losing. Eventually, they discover patterns. In this game, if you get your markers into a V-shape it gives you more options, more ways to win. This is a game that develops strategic thinking."

Another game Kuppinger favors is Mastermind, in which players have to guess the pattern of hidden colored pegs or tiles by a process of elimination.

"They have to estimate what the colors are and what position they're in," explains Kuppinger. "It gets them to file things in their minds."

Kuppinger is most pleased when her students throw out the rules and invent their own games.

"You start with an existing game, then change the rules," she says. "Changing the rules involves negotiation, getting the oher person to agree. What do you want the goal to be? Are they going to be able to jump? You have to consider the possibilities. Maybe you have to move a certain distance from the other person's last move."

To encourage kids to invent their own games, Kuppinger suggests supplying them with an all-purpose board game, such as Othello. If they prefer to start from scratch, all they'll need is graph paper, poker chips or other markers, dice -- and logical thinking.

GAMES KIDS PLAY

For information on Capitol Hill Day School's after-school games course, call 547-2244. Here are some other game-ing places for children:

DOLL'S HOUSE & TOY MUSEUM -- is featuring an exhibit of antique cat games. Included are board games called Cats and Mice, Cat Tiddly Winks, Cat Ten Pins and Cat Skittles. In addition to this special exhibit, the museum has a collection of more than 500 Victorian board and card games. According to director Flora Gill Jacobs, the favorite game of Victorian children was Old Maid. The museum is at 5236 44th St. NW, near the Friendship Heights Metro stop. Admission is $2 for adults, $1 for children under 14. Hours are Tuesday through Saturday, 10 to 5; Sunday, noon to 5. 244-0024.

DAR MUSEUM -- has on permanent display one of the first board games patented in the United States, Mansions of Happiness. It's something like Parcheesi, in that players move around a board toward home, but it was developed by a clergyman's daughter in order to teach children right from wrong. If you land on a virtue -- such as charity -- you move forward; if you land on a vice -- such as cheating or stealing -- you go back to square one. Children can't play this rare antique game, but in the museum's "touch area" are puzzles and ball-and-stick games as well as toys. The DAR Museum, at 1776 D St. NW, is open Monday through Friday, 8:30 to 4 and Sunday 1 to 5. Admission is free.

CLOISTERS CHILDREN'S MUSEUM -- just outside Baltimore, features one of the earliest European board games, The Game of Goose. Players propel goose markers around a board, avoiding such hazards as motor cars. The museum, at 10440 Falls Rd., Brooklandville, is open Wednesday through Friday, 10 to 4:30; Saturday, noon to 4. A $2 donation is requested from adults.

MUSEUM OF AMERICAN HISTORY -- In the Hands-On History section of the museum, pre-schoolers can play a game called From Sheep to Scarf and, in the process, learn all about wool. This section, which includes other 18th-century activities, is located in the "After the Revolution" exhibit. It's open Tuesday through Sunday, noon to 3. Free tickets may be obtained at the door to Hands- On History.

MUSEUM OF AFRICAN ART -- The most popular game in Africa is played on a mankala, a rectangular board about the size of an egg carton with indentations for putting in -- and taking out -- beans or pebbles. The gift shop at the museum, 318 A St. NE, sells these games with instructions for $20 and up. Hours are weekdays, 10 to 5; weekends, noon to 5.

NATIONAL ZOO -- Herplab, at the zoo, features a board game designed to teach kids about lizard behavior. In the game of Territory, two players take on the roles of lizards confronting each other in an aggressive encounter. The draw of the cards determines which lizard prevails and which backs off.