When Mildred Lockridge walks into a classroom, children's eyes light up like the Fourth of July. Some run to her arms for a loving hug. Others pull her to their desks to show off their work, words newly learned and carefully printed on lined paper.

Tobias shows her his new shoes. Consuelas reads her a passage from a first-grade reader, then beams under a shower of praise.

If the children become too excited, Lockridge stabs her strong hand in the air and says, "Freeze." Instantly there is silence.

Mildred Lockridge is principal of Lyles-Crouch and Maury elementary schools in Alexandria, and in the six weeks since this term started she has charmed the socks off "her" students, their parents, the teachers and her boss, Superintendent Robert W. Peebles.

"I am tremendously impressed with Mrs. Lockridge's talents," Peebles said last week. "She has an incredible way with children, with parents, with staff. She is a very charismatic woman."

Lockridge was named principal of the two schools last May, about 18 months after retiring from a 21-year career with D.C. schools. Her educational philosophy is simple:

"We know if we are happy, we want to learn," Lockridge said recently. "The most important job I have is creating a good atmosphere for the children and a constructive atmosphere for the teachers."

That philosophy will be tested in Alexandria, as Lockridge attempts to carry out goals set by Peebles to improve the academic performance of students.

And with that philosophy Lockridge says she is also confident she can live up to Peebles' goals for inproving the academic performance of students. Peebles says he is confident that Lockridge can meet those goals.

In the District, Lockridge is best known for her tenure at Moten Elementary School in Anacostia, where she was principal for 12 years. Moten, with 1,700 students, is in a highly transient neighborhood that is one of the poorest in the District.

Though Moten students' scores on national achievement tests were usually below both national and District averages, Lockridge said the children there learned important lessons when she was principal.

"They had pride and respect for each other," she said. "When a new child would come into school and not behave in the accepted manner, one of the children would pull me aside and say, 'Mrs. Lockridge, you have to have a talk with him. He's not acting like us.' "

"I don't think those achievement test scores reflect on her abilities," said Vincent Reed, former D.C. superintendent who is now The Washington Post's vice president for communications. "She was a fantastic principal. The neighborhood had good students and parents, but many social ills prevented the scores from being where we would have liked."

Last summer, even before school started, Lockridge and assistant principal Marvin Maygarden set out to meet every family that was sending a child to Maury or Lyles-Crouch. Their visits took them into Old Town, the Rosemont area and the two nearby public housing projects.

Parents say they were thrilled with the visits.

"She made the children look her in the eye and say, 'Yes, Mrs. Lockridge.' She expected them to speak properly," said the president of the combined schools' PTA, Sue Lynch. "The children seemed to respond to it, to live up to her expectations. The parents just loved it."

"It is important for parents to know who we are," Lockridge said of the summer visits. "They know to come to me or Mr. Maygarden with any problem or question. Parents become naturally more interested in the school when they know us personally."

Lockridge uses the same approach with her students and teachers. She tells a visitor, with pride, she knows the name of all 625 students at Lyles-Crouch and Maury.

She visits classrooms every day, to hug and praise "her children." She often sits down next to teachers and starts teaching herself, and encourages Maygarden to do the same.

Lockridge, who will be paid $40,100 a year in her new post, was chosen last spring from five candidates--the only one from outside the school system.

"I went outside the system because inbrededness is not always constructive," Peebles said last week. "I was terribly impressed with Mrs. Lockridge. I am confident she will do a terrific job with these students."

Lyles-Crouch and Maury, previously under separate principals, were combined this year as a cost-cutting move. Lyles-Crouch, on S. Asaph Street in Old Town, has 234 students in grades 4 through 6; Maury, on Russell Road in the Rosemont area, is a feeder school for Lyles-Crouch with 291 students in kindergarten through third grade.

Students at both schools reflect Alexandria schools' mix of economic, racial and social backgrounds. The breakdown at Maury last year was 40 percent white, 59 percent black and 1 percent Asian; at Lyles-Crouch it was 47 percent white, 49 percent black and 2 percent Asian.

But that seems to make little difference to Lockridge. When a reporter inquired about racial mix at Lyles-Crouch and Maury, Lockridge replied, "I don't understand. I don't notice color or background. I don't know the difference. Children don't create the problems, adults do."

A few weeks ago, she said, two boys at Lyles-Crouch got into a fight in the school cafeteria. One boy was white, the other boy was black. She took the two into a small conference room outside her office and left them alone.

"I told them we would go along with whatever they decided to do," she said. "It was up to them.

"A little while later they both came out and said the whole argument was 'silly,' " she said, slapping her hand on the table and laughing. "I praised them for being sensible about it. I think children respond to respect and praise. That's what I intend to do here: respect children, praise them and help them to learn."

Last week, Lockridge led a reporter and photograher on a whirlwind tour of her two schools. "You are all my children. I love my children," she told the first graders in Laura Stein's class at Maury. "I told these people how wonderful you are and they've come to visit and take your picture."

"The children like her to come see them," said Stein. "We are all authority figures, teachers as well as the principal. The children see that. They know they have to work hard for us."

When Lockridge talks to children she uses phrases like "excuse me" and "I'm sorry, what were you saying?"

"April, did you go to the nurse?" she asked one small girl. "Don't shake your head, answer me."

Lockridge admonished the children for not all wearing their "Happiness Is Learning at Maury" clip-on buttons. Outside the building, on the way to Lyles-Crouch, she took off her own "Maury" button and rummaged through her purse for a "Happiness is Teaching at Lyles-Crouch" button.

"The children understand I am at one school one week and one the next," said Lockridge, who ordered the Happiness buttons for teachers and students before school started and gently encourages everyone to wear them. "Children understand and accept anything. Sometimes when I'm at Maury the children from Lyles-Crouch will come visit on their way home from school."

At Lyles-Crouch she snagged fifth grader Deniz Artemel, 10, in the hall to ask if she was feeling better after a bout with the flu. Another little girl begged Lockridge to eat lunch with her next week. "I promise you I will," Lockridge told her.

Then it was back to the classrooms, asking students what they were learning and asking teachers how the children were behaving. "I'm just so proud of you," she told one class, as the children squirmed with pleasure over the gold star they had won for good manners at lunch.

Lockridge said her frequent classroom visits are more than just pep talks to students.

"I am observing the teachers, sitting down and teaching with them," she said. "I know their strengths and weaknesses and feel more capable of helping them. Some teachers freeze when the principal walks into the classroom to observe, but I'm there so often they are comfortable. I consider myself a teacher. As principal I am the head teacher."

"I would say teachers here have responded well to Mrs. Lockridge's criticism because of the manner in which she gives it," said assistant principal Maygarden. "She will say, 'Why don't we try this,' and the teachers will almost always come back and say it works."

Before coming to Alexandria, Lockridge had been retired for 18 months. In 1980, while still in the District, Lockridge transferred from Moten to nearby Douglass Junior High School at the request of Reed, but retired four months later at the age of 50.

Although Lockridge said she decided to retire early because she looked forward to a rest after 21 years in the D.C. schools, she concedes that the political controversy surrounding her husband, school board member R. Calvin Lockridge, was a factor in her decision.

Her husband of five years was president of the school board when she left the D.C. schools.

"People who didn't like his ideas would sometimes . . . well, there were rumors," she said, "talk of students fighting in my office -- totally untrue. I don't know who said it, the rumors."

After 1 1/2 years, Lockridge decided it was time to get back to work.

"I missed the hug of a child."