Novel of courage, determination; The Girl on the Outside, by Mildred Pitts Walter. New York: Lothrop, Lee & Shepard Books. 149 pp. $9.50. (Ages 11-16.)

Until the final moment, the leering mob was uncertain. Stolid and unspeaking, with gleaming bayonets at their sides, the guardsmen waited outside the high school. They gave no sign of whether they were for or against the antagonistic, all-white crowd.

''The Girl on the Outside,'' a teen novel based largely on the true story of a 1957 desegregation case, takes the reader back to events that came in the wake of a US Supreme Court decision overturning 65 years of ''separate but equal'' education for black and white students. A 15-year-old black girl, Elizabeth Eckford, was about to take her first brave steps toward fulfillment of a National Association for the Advancement of Colored People (NAACP) plan for the integration of Central High School in Little Rock, Ark.

The event is history: the state's National Guard turned its bayonets on the advancing girl, denied her entrance, and forced her back into the hostile crowd. Aided by only one defiant woman, Grace Lorch, a non-Southern white, Elizabeth was drenched in spit by the time she staggered back to a city bus, which carried her to safety. But her story reached beyond Little Rock to a shocked and outraged nation. Twenty-one days later, nine black students succeeded in penetrating the white bastion and initiated an era of school desegregation in the South.

Using ''Mossville'' as the setting of her new novel, Mildred Pitts Walter traces two communities as they wait for a judge's decision in a case similar to Little Rock's. Will the court allow black teen-agers to climb the steps to the city's exclusively white high school?

Walter tells her story from two points of view - that of the confused, rich Sophia, who dreads the ''invasion'' of her sweet white world, and of the trusting Eva, a black teen-ager who consents to go first so that others will have a choice to go.

Well crafted and focused, sizzling with details appropriate to her teen audience, Walter's book is more than a reminder of the courage of Elizabeth and her guardian. It tells just how far the nation has come, and - because of its sensitivity to the feelings of both races - just how much further we may hope to go together.

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