State school board candidates in three districts now will settle down to the serious business of campaigning for the general election, each with a goal of improving education statewide.

Incumbents will strive to keep their seats in two districts, while a third contest will pit two challengers entirely new to the system.In District 2, incumbent Keith Checketts, Logan, had slightly fewer votes at 4,434 (38.7 percent) than William L. Garner, Huntsville, who tallied 4,790 (41.8 percent). A third contender, Dale Schimmelpfennig, Pleasant View, was dropped from the race with 2,222 votes (19.4 percent). The district encompasses Rich and Morgan counties, Logan and part of Weber County.

In District 4, Salt Lake City, another incumbent, Ruth Hardy Funk, had a strong showing with 5,178 votes or 57.8 percent. Her competition in the general election will be Randall G. Harmsen, a Salt Lake businessman. The primary election eliminated from the school board race Charles W. Peters, with 1,061 votes, and Otis H. Weeks, with 773.

District 8, which comprises most of Utah County, will have new representation on the state board. The present board member from the district, Margaret Nelson, chose not to seek re-election. Her replacement will be either Lenora Plothow, who gathered 3,127 votes or 43.8 percent in Tuesday's vote, or Jay Liechty, who had 1,688 or 23.6 percent.

Eliminated from the race in District 8 were Charles H. Stewart, 865; Rulon R. Garfield, 754; and N. Lee Crabb, 697.

The general election contest between Garner and Checketts will likely continue to be close. Garner, who retired this year as superintendent of the Ogden School District, has strong support in that part of the district, while Checketts, present chairman of the state board, is likely to make a strong showing in the Logan area, where he is associated with Utah State University.

The battle will be for the votes in the other areas of the district.

If he wins, Garner sees the tax initiatives as the immediate challenge. If the proposals pass, the state board will be faced with designing a school program with less money, in all likelihood. That design must have the least possible impact on children, he said.

"Every decision has to be weighed in that context. There are some things that can be done that would be more cost-effective in education. However, some of the reforms people talk about haven't been proven. I don't like to experiment with lives. We should try new ideas on a limited basis and allow parents who don't want their children to participate to take them elsewhere."

Checketts predicted a close race but hopes to continue in his role on the state board.

"The challenge of the next four years will be to try to get education in Utah structured in such a fashion that we could see that every child has the opportunity to maximize his potential. We're close to being able to do that, with what we know about how to teach and with new technology. But we need systems to evaluate the results. Another problem will be getting the resources to do it. We've lived on borrowed time for the past few years. We have teachers that are becoming increasingly disaffected. Our infrastructure is starting to deteriorate. We have a lot of work to do."

Funk was pleased with the margin of her success in the primary election. "That gives me a fine opportunity for working on the general election."

She has been a member of the Strategic Planning Commission, which is attempting to define a new role for education in Utah.

"I want to do more to influence that direction," she said. "The challenge is lack of funds, coupled with growth. We've got to make dollars go further. The Strategic Planning Commission has uncovered some things that would make that possible."

Her challenger, Harmsen, believes it is time for a change in the district's representation. "If people in Utah believe education needs to change, they had better vote for me," he said. He wants to apply business principles to education.

Harmsen is eager for changes and innovation in Utah education, including the creation of pilot programs that would provide incentive for schools and for teachers. Teachers should be accorded more professional treatment, he said, with significant salary increases. More control at the school level would allow principals latitude to make choices affecting the schools.

Plothow sees no decline in Utah student ranks for the next four years. Until leveling begins in the early 1990s, growth will be the greatest challenge facing the school board, she said.

"I have a deep concern about equity for all our kids. They all need equal opportunity for an excellent education. Those who need remediation should get it. Those who are average should not get lost in the middle. Those who are high achievers should be provided a challenge."

Utah's education system must remain competitive with other states to attract people to improve Utah's economic base, Plothow said.

Liechty said he will be working hard to get all the support he can for the general election.

"I think we just have a great group of children. We need to invest in them to the very best of our ability," Liechty said. "Utah should be right on the leading edge of education nationally."

He also sees teacher morale as a serious problem. "We need to address the circumstances with teachers, to help them stay highly motivated. One thing I feel is very important is to try to get the system switched around so they can enjoy a higher level of professionalism, including better salaries."

The educational system should not be turning out children who lack the basic skills of education, particularly communications and mathematics, Liechty said.