In Austin, Texas, visiting the art museum is far more than a walking tour

His classmates call him Hawkeye, but not because he is particularly observant. Quite the contrary. Hawkeye is in the sixth grade and is reading at lower than fourth-grade level. He had never been known to go to the public library to check out a book on his own.

Hawkeye, however, is changing. He was chosen this school year to participate in an art enrichment program, a joint project of the University of Texas Huntington Art Gallery and the Austin (Texas) Independent School District. After the latest excursion to the Huntington Gallery, where Hawkeye and his classmates were introduced to the Chinese artist, Ling-Ling Tong, who showed them how to do calligraphy and Chinese painting, Hawkeye became enthusiastic about learning.

''He made a trip by bus to the Austin Public Library to check out some books on China,'' reports Susan M. Mayer, education coordinator for the Huntington Gallery. ''He told his teacher he was going to learn to read and speak Chinese.''

Hawkeye's dramatic conversion to an interest in learning is a byproduct of the art enrichment program, now in its fifth year. It began with a small group of museum visitors from one Austin elementary school.

Now 350 students from 16 Austin schools participate in the exhibition-based curriculum, which includes a series of museum visits, with pre-visit preparation and follow-up art lessons taught by museum professionals who go to the classrooms in the 16 individual schools.

The school district has a waiting list of schools wanting to participate in the program, which is partially funded by the Institute of Museum Services of the US Department of Education. The museum received so many inquiries about its program that it has published an implementation manual to help other schools start a similar program.

The manual has now been mailed to schools in 28 states. (The manuals are available by writing to the Archer M. Huntington Art Gallery, College of Fine Arts, University of Texas at Austin, Austin, Texas 78712.)

While the program is an art program, it is not designed to educate artists, explains Ms. Mayer. ''It is to increase a student's visual awareness - not only of paintings and drawings, but of the larger world as well.

''It makes the students see and experience and appreciate beauty in everyday life and, we hope, strive to create it with whatever talents and resources are available.''

The 350 fourth- through sixth-grade students now in the Austin program participate in five separate curriculum units each year. Three activities are included in each unit:

* Preparation. Students are introduced in their home classroom to the exhibition they will see, learning something about its historical or cultural context; its theme; biographical information about the artist(s); and the media and techniques used by the artist(s).

* The museum visit. During the visit to the museum, the students are divided into small groups and guided by docents through the exhibition. The docents chosen for these are well-versed in the particular exhibition as well as knowledgeable about working with elementary school children and answering their questions.

* Follow-up. Within a week (timing is important) after the visit to the museum, the program's art teacher visits the school and leads the children in a studio lesson. The children work in the same media or with the same aesthetic or conceptual themes as those seen in the exhibition. For example, the children who attended the Chinese art exhibition were introduced to calligraphy.

''A museum is an ideal environment for an educational program,'' believes Ms. Mayer, ''but only if it is used in a planned way. Before we developed this program, many of Austin's 57,000 schoolchildren visited the museum - and still do. As 'walking students,' they just looked, unprepared.''

While Ms. Mayer recognizes that this kind of random looking may accidentally kindle a spark in a child, she points out that it does not provide the kind of continuity of learning and appreciation of art that will bring a person back to a museum week after week throughout his life, or will make him, as an adult, a patron of the arts.