Old and new game ideas for playing with baby; Games Babies Play and More Games Babies Play, by Julie Hagstrom and Joan Morrill. New York: Pocket Books. $2.95.

Play is the centerpiece or work of childhood, and what better ''toy'' is there than a creative companion? This book encourges baby's companions - siblings, baby sitters, relatives, or parents - to love and laugh through music, reading, singing, dancing, and finger plays. These interactions provide a stimulus to the baby's sense of rhythm, the authors maintain. The games also develop word recognition and coordination, along with giving the giggles.

The methods for achieving all this fall into three distinct groups offering a mixture of tested traditional games to new, sometimes questionable, ones.

The authors have provided a thorough reference to the standard baby games that parents probably played as infants, from Peek-a-Boo to Pat-a-Cake. Step-by-step instructions refresh rusty memories, and even offer suggestions about what you say when baby performs.

Out of 84 games, several innovative playtimes merit attention. ''Animal Introductions,'' for instance, familiarizes baby with animal actions and sounds as someone makes stuffed creatures appear from a basket and ''talk.'' Baby then imitates as he returns the animals to the basket.

Finally there's a group of games which, although perhaps fun, may indirectly teach poor habits or promote fears. Sucking toes, tearing up magazines, climbing front stairs at houses where no one appears to be home, pretend stinging bees, and scary games of suspense make one wonder about the authors' wisdom in including these selections.

The cognitive, social development of babies is precious, and wise parents will want to sift through this mixture of games to choose only the best.

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