American public schools may be in disfavor with some Americans these days, but Japanese in this area like them just fine. So much, in fact, that they're sending 10 school officials from Fairfax and Montgomery counties and the District on a two-week, all-expenses-paid field trip to Japan as a gesture of appreciation.

"We send our children to American local public schools and Americans are kind enough to treat them exactly like Americans. We don't have to pay . . . and our children learn English and American ways," said Kensaku Hogen, counselor at the Japanese embassy here.

According to Hogen, there are about 500 Japanese children attending public schools in the Washington area, most of them in Fairfax and Montgomery. "Mr. Reagan says education in the U.S. has a lot to do, but we feel that the kind of education our children are getting in these counties is not at all bad and we want to show our appreciation and not in just words. We have been thinking we owe something to these counties," Hogen said.

So for two weeks in November, the 10 officials and teachers will travel to Tokyo, Kyoto and other cities to study Japanese schools and do some sightseeing as well. The money for the trip has been donated by local Japanese residents and their corporate employers, including such firms as Sony, Hitachi and Mitsubishi, according to the embassy.

The itinerary includes eight days in Tokyo and Kanagawa Province inspecting schools and factories and meeting with local school officials, Hogen said. After that, the group will visit the old Japanese capitals of Kyoto and Nara and travel to Osaka and Hiroshima "if they wish," he said, before they head back to Tokyo for two more days.

Hogen said he did not know how much the airfare, hotels and meals for the 10 guests would come to (round-trip airfare costs about $1,400, he said) but added that about 75 percent of the expense is being borne by Japanese corporate sponsors who do business in this area. Japan Air Lines, he said, will offer a discount.

The Fairfax contingent of the group consists of School Superintendent William J. Burkholder, School Board Chairman Mary E. Collier, Teacher of the Year Nancy L. Gibbs and McLean High School Principal Murriel Price, chairman of the High School Principals Association.

The Montgomery travelers will be Dorothy Jackson, head of the social services center, Dr. Neil Shipman, principal at Fox Chapel Elementary school, mathematics teacher Rosalba Rosas, and John Day, principal of Richard Montgomery High School.

The District of Columbia has not yet decided which two officials will take the trip. "The superintendent is putting together a panel to decide who goes on this," said schools spokeswoman Janice Crumm.

In Fairfax, Board Chairman Collier said she and Burkholder selected themselves as well as Gibbs and Price and then presented their choices to the school board.